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DOI： 10.1587/nolta.10.431

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier Ltd  

Stochastic calculus indicates that allowing a Lyapunov candidate function to be non-differentiable at the origin helps its expected value to decrease. To utilize this observation, this paper investigates stability of stochastic systems, supposing that the origin of the state space is an equilibrium before influenced by Gaussian white noises. For identifying such stability properties, notions of instantaneous points and almost sure equilibria, which are mutually exclusive, are introduced. This paper clarifies the relationship between the stability properties, and develops their Lyapunov-type characterizations without differentiability at the origin. Discussions are given in relation to the notion of noise-to-state stability, and this paper proposes a method to address both transient and global-in-time properties simultaneously with a single positive definite function even when stochastic noises prevent the origin from being an equilibrium.

DOI： 10.1016/j.automatica.2018.03.013

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

This paper discusses the finite-time stability of state-dependent homogeneous systems. The state-dependent homogeneous systems have been employed in recent studies, and the systems can be regarded as a generalization of homogeneous systems. This study shows that the finite-time stability of the state-dependent homogeneous systems can be concluded from the combination of the asymptotic stability and a certain condition of the homogeneity. In the proof of the finite-time stability, we provide an approach to prove the finite-time stability without using Lyapunov functions. We also provide a numerical example of finite-time stable systems.

DOI： 10.1109/ASCC.2017.8287280

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DOI： 10.1016/j.ifacol.2018.07.289

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DOI： 10.1016/j.ifacol.2018.07.298

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

This paper provides a stabilization strategy for input-affine systems by adding state-dependent rough signals, a particular kind of continuous processes having unbounded variations. The effective use of rough path analysis enables state-feedbacks to gain entrance to the mechanism of rough signals. The results demonstrate that the addition of rough signals also invocates 'hidden control inputs' that make the systems controllable using Lie derivatives. This implies that control Lie algebra can be constructed by Lie derivatives instead of Lie brackets.

DOI： 10.1109/CCTA.2017.8062478

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：電子情報通信学会  

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Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical and Electronics Engineers ({IEEE})  

DOI： 10.1109/tac.2016.2522087

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

In this paper, we investigate local asymptotic stability ensured by the addition of Gaussian white noise into dynamical systems. There are different stability notions for stochastic systems, such as asymptotic stability in probability (ASiP) and uniform almost sure asymptotic stability (UASAS). The local ASiP property is incapable of ensuring that sample paths converge to the origin with probability one, whereas the local UASAS property is capable of it. However, in general, the local UASAS property requires tight conditions. Here, we provide our notion of local almost sure asymptotic stability (local ASAS) to relax the conditions with both almost sure convergence of sample paths to the origin and the existence of bounded (weak) invariant sets. We find that the addition of Gaussian white noise always prevents the origin from being locally UASAS as long as we consider smooth Lyapunov functions; however, it is possible to make the origin locally ASAS. The result is confirmed by a simple example of elimination of unstable equilibria by deliberately adding Gaussian white noise. (C) 2016 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.sysconle.2016.05.001

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical and Electronics Engineers ({IEEE})  

The objective of this study is to present a noise-assisted stabilization method and a constructive method for designing a stabilizing controller. We investigate the stabilization of a deterministic nonlinear affine system by using a controller with a Wiener process. Our approach focuses on the global asymptotic stabilization of nonholonomic systems. The proposed method for designing a stabilizing controller is based on the notion of a stochastic control Lyapunov function. We show that if there exists a stochastic control Lyapunov function with small control property, the designed controller globally asymptotically stabilizes a given system with probability one.

DOI： 10.1109/tac.2015.2495622

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical and Electronics Engineers ({IEEE})  

This paper addresses integral input-to-state stability (iISS) for stochastic nonlinear dynamical systems and develops Lyapunov-type criteria. The developments offer an iISS small-gain framework for verifying robustness of interconnected systems with respect to disturbances. The framework not only includes input-to-state stability (ISS) as a special case, but also highlights fundamental differences between the stochastic and deterministic systems. In particular, dealing with nonlinearities in interconnection gives rise to a unique issue of degradation in the presence of stochastic noises. This paper addresses this issue by coping judiciously with the effect of the gradient of Lyapunov functions of subsystems through diffusion fields in composing a Lyapunov function of the entire system. This paper employs two types of robustness notions, and demonstrates that the influence of the stochastic degradation on one notion is considerably different from the influence on the other notion in dealing with interconnected systems.

DOI： 10.1109/tac.2015.2471777

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：ELSEVIER SCIENCE BV  

The purpose of this study is to establish a method of estimating, in real time, the machining error caused by vibrations of the cutting point of an end mill. The vibration displacement at the shank of the end mill and the dynamic cutting force were measured during cutting tests while spindle speed was increased from medium to high. It was found that the vibration displacement at the cutting point at the moment when the radial direction of the cutting edge is normal to the feed direction showed a good agreement with the height of the machined surface at a spindle speed of 4500 rpm or less. (C) 2016 The Authors. Published by Elsevier B.V

DOI： 10.1016/j.procir.2016.03.121

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

In this paper, we derive a finite-time positioning controller for an ultrasonic motor based on homogeneous control Lyapunov functions and stochastic stability analysis. In theory, finite-time stabilizers are useful for accelerating a settling time neighborhood of a target position. However, in practical experiments, the stabilizers cause chattering-like phenomena around the target position. In this paper, we treat the chattering-like phenomena as Gaussian white noises appearing around the target position in order to construct a new compensator for them by using stochastic stability analysis. In the procedure for achieving practical experiments, we construct a state-space model for an ultrasonic motor control system by analyzing step responses, design a homogeneous finite-time controller, and propose a compensator of the chattering-like phenomena caused by the controller. Then, we confirm the availability of the compensator via the investigation of the simulation and experimental results.

DOI： 10.1109/IECON.2016.7793124

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

In this paper, we derive a finite-time positioning controller for an ultrasonic motor based on homogeneous control Lyapunov functions and stochastic stability analysis. In theory, finite-time stabilizers are useful for accelerating a settling time neighborhood of a target position. However, in practical experiments, the stabilizers cause chattering-like phenomena around the target position. In this paper, we treat the chattering-like phenomena as Gaussian white noises appearing around the target position in order to construct a new compensator for them by using stochastic stability analysis. In the procedure for achieving practical experiments, we construct a state-space model for an ultrasonic motor control system by analyzing step responses, design a homogeneous finite-time controller, and propose a compensator of the chattering-like phenomena caused by the controller. Then, we confirm the availability of the compensator via the investigation of the simulation and experimental results.

DOI： 10.1109/iecon.2016.7793124

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

In this technical note, we restage the positive effects of Gaussian white noises for continuous-time driftless input-affine nonholonomic systems. Compared with previous studies, we found that the positive effects are hidden in the shadows of nonuniqueness of stochastic integrals over multi-dimensional Wiener processes. Furthermore, we found that the positive effects are artificially restaged by numerical calculations with use of Euler scheme for ordinary differential equations. Our results demonstrate that the positive effects act as "hidden independent control inputs" for nonholonomic systems. This implies that our results provide a constructive procedure for designing control inputs such that the origins become p-th moment exponentially or finite-time stable.

DOI： 10.1109/TAC.2016.2522087

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

The objective of this study is to present a noise-assisted stabilization method and a constructive method for designing a stabilizing controller. We investigate the stabilization of a deterministic nonlinear affine system by using a controller with a Wiener process. Our approach focuses on the global asymptotic stabilization of nonholonomic systems. The proposed method for designing a stabilizing controller is based on the notion of a stochastic control Lyapunov function. We show that if there exists a stochastic control Lyapunov function with small control property, the designed controller globally asymptotically stabilizes a given system with probability one.

DOI： 10.1109/TAC.2015.2495622

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

This paper addresses integral input-to-state stability (iISS) for stochastic nonlinear dynamical systems and develops Lyapunov-type criteria. The developments offer an iISS small-gain framework for verifying robustness of interconnected systems with respect to disturbances. The framework not only includes input-to-state stability (ISS) as a special case, but also highlights fundamental differences between the stochastic and deterministic systems. In particular, dealing with nonlinearities in interconnection gives rise to a unique issue of degradation in the presence of stochastic noises. This paper addresses this issue by coping judiciously with the effect of the gradient of Lyapunov functions of subsystems through diffusion fields in composing a Lyapunov function of the entire system. This paper employs two types of robustness notions, and demonstrates that the influence of the stochastic degradation on one notion is considerably different from the influence on the other notion in dealing with interconnected systems.

DOI： 10.1109/TAC.2015.2471777

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

The objective of this paper is to tackle point stability of stochastic systems without requiring noise diffusion coefficients to vanish at the point of interest. Behavioral differences between vanishing coefficients and non-vanishing coefficients arising in adding stochastic noises are illustrated by examples. To identify the differences appropriately, this paper examines the concept of equilibria and proposes several stability properties by introducing the notions of instantaneous points and almost sure equilibria. In addition to clarifying the relationship between those stability properties, Lyapunov-type characterizations are presented as sufficient conditions for those stability properties by making use of functions which are not necessarily twice differentiable at the point of interest. Discussion is also given to relate the stability property of an instantaneous point with noise-to-state stability. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.ifacol.2016.10.185

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WILEY  

In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations of rough systems based on rough path analysis; then, we provide the notion of asymptotic stability for rough systems to analyze the stability for the systems. In the procedure, we also confirm that the system representations include stochastic differential equations; we also found that asymptotic stability for rough systems is the same property as uniform almost sure asymptotic stability provided by Bardi and Cesaroni. After the discussion, we confirm that there is a case that deterministic noises are capable of making the origin become asymptotically stable for rough systems while stochastic noises do not achieve the same stabilization results. Copyright (c) 2016 John Wiley & Sons, Ltd.

DOI： 10.1002/rnc.3553

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：ELSEVIER SCIENCE BV  

Titanium alloys have been widely used in the aerospace, biomedical and automotive industries because of their good strength-toweight ratio and superior corrosion resistance. However, it is very difficult to machine Titanium alloy materials due to their poor machinability, resulting in short tool life. The effects of oil mist and air jet flushing on tool wear in the milling of Ti6Al4V were investigated at a cutting speed of 300 m/min in this study. Tests with various flushing directions of oil mist and air jet during up, and down-cut were carried out. Tool wear and chip shape were measured and analyzed. As a result of these cutting tests and considerations, it was revealed that up-cut with oil mist flushed from any direction and air jet flushed from the side were desirable, and dry down-cut was also desirable. (C) 2016 The Authors. Published by Elservier B.V.

DOI： 10.1016/j.procir.2016.03.125

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Materials Science Forum  

As titanium alloys have a high strength-to-weight ratio and superior corrosion resistance, they are widely used in the aerospace, biomedical, and automotive industries. However, these alloys exhibit very poor machinability, which results in problems such as short tool life. This study investigates the effect of the cutting atmosphere on tool wear during high-speed end milling of the titanium alloy Ti6Al4V. Dry cutting, cold air jet cutting, cutting fluid mist jet cutting, and cutting fluid flush cutting were considered in order to determine the optimum cutting atmosphere and conditions. For down-cutting speeds of 200−300 m/min, the cutting atmosphere and cutting speed were adopted as experimental parameters. Down-cutting was performed in order to measure the width of the tool flank wear land as the cutting length was increased. The results indicated that the optimum cutting method was cold air jet cutting. For a cutting length of 500 mm, this method produced a narrower flank wear land than dry cutting. In addition, for longer cutting lengths of up to 4000 mm, the wear rate for cold air jet cutting was less than or equal to that for dry cutting, and no chipping or excessive wear was observed.

DOI： 10.4028/www.scientific.net/MSF.874.46

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

This paper presents the asymptotic stabilization of the Artstein's circle using stochastic processes in a control law. To construct a C2 control Lyapunov function (CLF) for a stabilization method using stochastic processes, we synthesize a nonsmooth CLF for a nonsmooth stabilization method and a smooth function. By synthesizing these functions, we obtain a C2 CLF. By this C2 CLF, we can obtain a continuous stabilizing feedback using stochastic processes for the Artstein's circle.

DOI： 10.1109/CCA.2015.7320638

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

This paper studies integral input-to-state stability of stochastic nonlinear systems in the Stratonovich sense and develops Lyapunov-type criteria. Instead of merely extending previous results on deterministic systems and stochastic systems of Itoˆ type, this paper focuses on the unique feature that allows one to stabilize a system globally by stochastic noise when the system is not stable globally in the absence of the noise. Making use of the Lyapunov-type characterization of integral input-to-state stability developed in this paper, the capability of admitting unstable subsystems in establishing stability of interconnected systems is also pursued. Numerical examples are presented to illustrate these curious points.

DOI： 10.1109/CDC.2015.7402477

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：Japanese   Publisher：The Japan Society of Mechanical Engineers  

Active dynamic vibration absorbers are widely known as vibration control device exhibiting good performance for disturbance signal with various frequencies. Linear quadratic (LQ) control is often used in active dynamic vibration absorbers. We show that nonlinear control laws provide vibration control performance higher than the LQ controller by designing homogeneous control Lyapunov function (CLF) controllers guaranteed convergence rates and high robustness. In this paper, we design homogeneous exponential stabilization controllers based on Riccati solutions of LQ controllers and finite-time stabilization controllers for vibration control device using fixed surface and confirm that designing convergence rates are quite effective for vibration control performance. Moreover, the effectiveness of our controllers is verified by the analysis of transient and steady-state frequency responses for hybrid dynamic vibration absorbers with numerical simulation.

DOI： 10.1299/transjsme.15-00373

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Nonholonomic systems such as port-Hamiltonian systems are well known to be difficult to control. To reduce the difficulty, in this paper, we derive quasi-optimal regulators for nonholonomic systems such as a typical chained system with some restriction to the form of control inputs. To achieve the solution, we employ a notion of stability in roughness, which is Lyapunov stability theory for dynamical systems driven by rough paths. The rough paths are capable of transforming some nonholonomic systems into holonomic systems with "hidden control inputs". Thus, the control problems are simplified in exchange for the degradation of some control performances.

DOI： 10.1016/j.ifacol.2015.10.213

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

In this paper, we derive Lyapnov stability theory for rough systems, which are dynamical systems driven by rough paths. To simplify the discussion, we only consider the class of geometric p-rough paths with p? [2,3) that contains some limit processes of periodic inputs and Wiener processes created by some approximation theorems such as McShane and WongZakai's results. The main advantage of the rough path analysis is making Itô maps continuous
hence, the related stability analysis enable us to consider deterministic and stochastic asymptotic stability notions in uniform way. This paper is the first step to show the effectiveness of the rough path anlaysis on stability analysis and stabiliation designs for nonlinear dynamical systems having various unbounded variation signals.

DOI： 10.1016/j.ifacol.2015.09.322

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

For stochastic nonlinear dynamical systems, this paper addresses several stability notions in the path-wise sense. Lyapunov characterizations are developed to verify those properties. The notions investigated here are stricter than boundedness properties ensured by popular input-to-state stability and noise-to-state stability whose probability is taken at each instant. It is demonstrated that Lyapunov functions constructed frequently in the literature not only establish the instantaneous probabilistic properties, but also path-wise probabilistic ones. Differences appear when one wants to estimate the convergence of initial effect. The differences disappear if diffusion fields are remotely orthogonal to the gradient of Lyapunov functions.

DOI： 10.1109/ACC.2015.7172279

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper presents the asymptotic stabilization of the Artstein's circle using stochastic processes in a control law. To construct a C-2 control Lyapunov function (CLF) for a stabilization method using stochastic processes, we synthesize a nonsmooth CLF for a nonsmooth stabilization method and a smooth function. By synthesizing these functions, we obtain a C-2 CLF. By this C-2 CLF, we can obtain a continuous stabilizing feedback using stochastic processes for the Artstein's circle.

DOI： 10.1109/cca.2015.7320638

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper studies integral input-to-state stability of stochastic nonlinear systems in the Stratonovich sense and develops Lyapunov-type criteria. Instead of merely extending previous results on deterministic systems and stochastic systems of Ito type, this paper focuses on the unique feature that allows one to stabilize a system globally by stochastic noise when the system is not stable globally in the absence of the noise. Making use of the Lyapunov-type characterization of integral input-to-state stability developed in this paper, the capability of admitting unstable subsystems in establishing stability of interconnected systems is also pursued. Numerical examples are presented to illustrate these curious points.

DOI： 10.1109/cdc.2015.7402477

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

This paper develops tools to verify stability and robustness of cascaded nonlinear stochastic systems based on Lyapunov functions. Constituent systems are formulated in terms of integral input-to-state stability (iISS) and input-to-state stability (ISS) which are popular notions for both stochastic and deterministic systems. This paper highlights differences between the stochastic and the deterministic cases. In contrast to deterministic systems, it is demonstrated that assuming ISS systems having unbounded decay rates in dissipation inequalities is restrictive. Taking this fact into account, stability criteria are formulated without assuming unboundedness of decay rates, so that ISS systems with bounded decay rates and iISS systems which are not ISS are covered in a unified manner. Stability criteria for stochastic cascades involve the growth rate conditions at connecting channels. This paper clarifies how noise diffusion fields affect the growth rate conditions and the influence depends on definition of stochastic robustness. (C) 2015 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.automatica.2015.09.011

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Publisher：IEEE  

DOI： 10.1109/cca.2014.6981469

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Language：Japanese   Publisher：IEEE  

Active dynamic vibration absorbers are widely known as vibration controllers exhibiting good performance for disturbance signal with various frequencies. Generally, LQ control is used in active dynamic vibration absorber. In this paper, we show that nonlinear control laws supply vibration control performance higher than the LQ control laws by designing homogeneous CLF control laws. The effectiveness of our controllers is confirmed by the analysis of transient and steady-state frequency responses with numerical simulation.

DOI： 10.1109/CCA.2014.6981503

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

In this paper, the problem of verifying integral input-to-state stability (iISS) and input-to-state stability (ISS) of interconnected stochastic systems is addressed. The aim is at extending the deterministic iISS small-gain framework to stochastic systems by including ISS as a special case. This paper highlights fundamental differences between the stochastic and deterministic cases. Dealing with nonlinearities in interconnection gives rise to a unique issue in the presence of stochastic noises. The key is to cope effectively with the gradient of Lyapunov functions of subsystems in composing a Lyapunov function of the entire system. It is demonstrated that the influence of the gradient appears considerably different in two types of robustness notions. This paper also clarifies the influence of the gradient on the establishment of a trajectory estimate of iISS which is weaker than ISS.

DOI： 10.1109/ACC.2014.6858778

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

In this paper, the problem of verifying integral input-to-state stability (iISS) and input-to-state stability (ISS) of interconnected stochastic systems is addressed. The aim is at extending the deterministic iISS small-gain framework to stochastic systems by including ISS as a special case. This paper highlights fundamental differences between the stochastic and deterministic cases. Dealing with nonlinearities in interconnection gives rise to a unique issue in the presence of stochastic noises. The key is to cope effectively with the gradient of Lyapunov functions of subsystems in composing a Lyapunov function of the entire system. It is demonstrated that the influence of the gradient appears considerably different in two types of robustness notions. This paper also clarifies the influence of the gradient on the establishment of a trajectory estimate of iISS which is weaker than ISS.

DOI： 10.1109/acc.2014.6858778

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Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

DOI： 10.3182/20140824-6-za-1003.00725

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper presents a method for the homogeneous stabilization of homogeneous driftless input-affine systems using feedback controllers with Wiener processes. Although previous studies have shown methods for the stabilization of nonholonomic systems by using Wiener processes, the closed-loop systems sometimes show slow convergence. To improve the convergence rate, we show a method that gives a homogeneous controller by redesigning the controllers designed by the previous methods. By the virtue of the homogeneity, the closed-loop systems exhibit almost sure exponential stability with respect to homogeneous norms. A numerical example shows the effectiveness of the proposed method.

DOI： 10.1109/CDC.2014.7039878

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Other Link： http://orcid.org/0000-0003-3665-8827

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper presents a method for the homogeneous stabilization of homogeneous driftless input-affine systems using feedback controllers with Wiener processes. Although previous studies have shown methods for the stabilization of nonholonomic systems by using Wiener processes, the closed-loop systems sometimes show slow convergence. To improve the convergence rate, we show a method that gives a homogeneous controller by redesigning the controllers designed by the previous methods. By the virtue of the homogeneity, the closed-loop systems exhibit almost sure exponential stability with respect to homogeneous norms. A numerical example shows the effectiveness of the proposed method.

DOI： 10.1109/cdc.2014.7039878

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Language：Japanese   Publisher：The Society of Instrument and Control Engineers  

This paper deals with a kind of feedback linearization method for the nonlinear affine systems. In case of the standard feedback linearization method, the coordinate transformation is used and the nonlinear terms are canceled by using the nonlinear state feedback. Then, the input-output relation of the systems are linearized in the wide range of the state space. It is well known that the control system does not work well enough if there exists the modeling error and the disturbance. We propose a novel feedback linearization method to achieve good robust performance for the modeling error and disturbance. In our previous researches, a control structure to minimize the model error is proposed for the linear control systems. This structure of the control system is extended to the nonlinear control systems with some improvement. Since the extended control structure includes a feedback path of the error between the plant output and the desired model output, it is expected that the robustness is increasing in the meaning of input-output relation rather than the previous feedback linearization methods. The effectiveness of proposed structure is shown by numerical examples.

DOI： 10.9746/sicetr.50.869

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper proposes a disturbance attenuation strategy for nonlinear controlled systems against the addition of additive Gaussian white noises. To achieve the purpose, we firstly revisit the following stochastic stability notions for stochastic systems: uniform almost sure asymptotic stability (UASAS), exponential p-stability, and finite-time stability in probability. Combining the previous notions, we propose new asymptotic stability properties and new stochastic Lyapunov functions, p-stability with respect to (w.r.t.) EV, and quasi almost Lyapunov functions (quasi-ALFs) for nonlinear systems with stochastic disturbance terms, the values of which are nonzero at the origins. Subsequently, we propose a strategy of noisy surface control to obtain sufficient conditions so that stochastic systems almost restore their smooth trajectories of the time when they were not vibrated by additive noises. The effectiveness of the control strategy is confirmed by the consideration of disturbance attenuation problems for stochastic linear systems with linear quadratic (LQ) controls.

DOI： 10.1109/CCA.2014.6981469

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：ELSEVIER SCIENCE BV  

This paper considers global asymptotic stability and robustness of cascaded nonlinear stochastic systems, and presents Lyapunov-based criteria. Constituent systems are characterized in terms of dissipation inequalities almost in the form of input-to-state stability (ISS) which is popular for both stochastic and deterministic systems. As an important unique feature of stochastic systems, this paper first demonstrates that assuming ISS systems having unbounded decay rate is restrictive, which contrasts sharply with the deterministic case. This motivates the second part of the main results focusing on ISS systems with bounded decay rate as well as systems which are not ISS. With these developments, this paper proposes a framework based on integral input-to-state stability (iISS) and demonstrates its usefulness.

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Language：Japanese   Publisher：The Society of Instrument and Control Engineers  

This paper shows that there is no one-dimensional Wiener process making the origins of deterministic affine systems become locally asymptotically stable with probability one. We clarify that Khasminskii's stochastic Lyapunov functions (SLFs) are not equivalent to deterministic Lyapunov functions (DLFs), and claim that Bardi and Cesaroni's almost Lyapunov functions (ALFs) are the same as DLFs with probability one. We also summarize randomization problems briefly, and explain why deterministic systems become Stratonovich-type stochastic systems by randomization with one-dimensional Wiener processes. Then, we prove that the origins of the randomized systems are not locally almost surely asymptotically stable if the original systems are not locally asymptotically stable. Further, we compare asymptotic stability with probability one ensured by global SLFs with almost sure asymptotic stability ensured by local/global ALFs via linear stochastic systems and its computer simulations.

DOI： 10.9746/sicetr.49.432

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

The purpose of this paper is to present a constructive design method of a stochastic feedback law for a deterministic nonlinear affine system. This design method gives a feedback law in the case that a randomized system is given as a Stratonovich-type stochastic differential equation, based on a result of Wong and Zakai. It is proved that a designed feedback law can globally asymptotically stabilize a randomized system with probability one. The design method employs a notion of a stochastic control Lyapunov function and the so-called Sontag's formula. The method in this paper aims the stabilization of nonholomic systems and non-Euclidean systems, which cannot be stabilized by any continuously differentiable time-invariant feedback laws. We can obtain a continuous feedback law for a state variable in the stabilization of such systems.

DOI： 10.1109/acc.2013.6580846

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffusion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.

DOI： 10.1587/transfun.E96.A.1695

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

In this paper, we derive stochastic asymptotic state-feedback stabilizers for Brockett integrators by using simple stochastic control Lyapunov functions and Sussmanntype artificial Wiener processes. First, we consider the problem of controlling nonholonomic systems via Brockett integrators. Second, we show properties of stochastic asymptotic stability in probability (GASIP) and exponential almost sure asymptotic stability (EASAS). Third, we summarize Sussmann's approximation theorem to randomize Brockett integrators. Then, we design two stochastic state-feedback laws such that the origins become GASIP and EASAS, respectively. We also confirm the validity of our method via numerical simulations. © 2013 IEEE.

DOI： 10.1109/CDC.2013.6761136

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Publisher：IEEE  

DOI： 10.1109/cdc.2013.6761136

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

In this paper, we show that stochastic asymptotic stability supplied by "stabilization by noise" is an extended version of deterministic asymptotic stability. To solve the problem, we first revisit the randomization problem of nonlinear dynamical systems by adding multi-dimensional Wiener processes. We also summarize uniform almost sure asymptotic stability (UASAS) is almost the same as asymptotic stability for deterministic systems. Then, we clarify necessary and sufficient conditions for the origins of randomized systems to be UASAS. Furthermore, we also discuss the possibility of the stabilization by noise with considering the randomization problem and UASAS property.

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：The Japan Society of Mechanical Engineers  

Measurement of pressure distribution in gaseous pipeline is important from a view point of control or safe management. In the present paper, a linear Kalman filter is developed to estimate the pressure estimation of small amplitude pressure wave in a single straight gaseous pipeline with constant circular cross section. The Kalman filter uses the linear dynamic system of the pipeline derived by using the approximation method of the unsteady friction, high speed and accurate computing method. The inputs to the Kalman filter are inlet and outlet pressures, and the pressure at the point one third of the pipe entrance is used as the observation point for feedback compensation. The performance of the developed method is tested using two experimental results by comparing with calculation results without feedback compensation. The comparison demonstrated that the developed method has better performance in the presences of measurement noise and erroneous boundary condition than does the ordinary calculation. It also showed much higher ability in error reduction than the ordinary calculation in computation with an erroneous initial condition.

DOI： 10.1299/kikaic.79.2830

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The purpose of this paper is to present a constructive design method of a stochastic feedback law for a deterministic nonlinear affine system. This design method gives a feedback law in the case that a randomized system is given as a Stratonovich-type stochastic differential equation, based on a result of Wong and Zakai. It is proved that a designed feedback law can globally asymptotically stabilize a randomized system with probability one. The design method employs a notion of a stochastic control Lyapunov function and the so-called Sontag's formula. The method in this paper aims the stabilization of nonholomic systems and non-Euclidean systems, which cannot be stabilized by any continuously differentiable time-invariant feedback laws. We can obtain a continuous feedback law for a state variable in the stabilization of such systems.

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

This study considers homogeneous stochastic systems and shows their stability and stabilization. We define a homogeneous stochastic system as an extension of a homogeneous deterministic system. We show that homogeneous systems can exhibit exponential stability or finite-time stability according to the degree of homogeneity. Further, we show a control law for the stabilization of homogeneous stochastic control systems. Numerical examples of stable homogeneous systems and the stabilization of a homogeneous control system are also presented. © 2013 IEEE.

DOI： 10.1109/CDC.2013.6760050

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This study considers homogeneous stochastic systems and shows their stability and stabilization. We define a homogeneous stochastic system as an extension of a homogeneous deterministic system. We show that homogeneous systems can exhibit exponential stability or finite-time stability according to the degree of homogeneity. Further, we show a control law for the stabilization of homogeneous stochastic control systems. Numerical examples of stable homogeneous systems and the stabilization of a homogeneous control system are also presented.

DOI： 10.1109/CDC.2013.6760050

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This study considers homogeneous stochastic systems and shows their stability and stabilization. We define a homogeneous stochastic system as an extension of a homogeneous deterministic system. We show that homogeneous systems can exhibit exponential stability or finite-time stability according to the degree of homogeneity. Further, we show a control law for the stabilization of homogeneous stochastic control systems. Numerical examples of stable homogeneous systems and the stabilization of a homogeneous control system are also presented.

DOI： 10.1109/cdc.2013.6760050

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Language：Japanese   Publisher：日本AEM学会  

Control of a travelling-wave ultrasonic motor is difficult due to its nonlinearities appearing everywhere in its dynamics. In this paper, we aim to develop a model-based angular position control method for a travelling-wave ultrasonic motor by the driving frequency operation. To obtain a precise mathematical model, we compensate the nonlinearity in the input-output relation by a nonlinear transformation, analyze the nonlinearity appeared in the relation between input amplitudes and time responses, and find that the sufficiently small input does not cause heavily nonlinear phenomenon. We therefore restrict the input amplitudes in sufficiently small values. According to the above discussion, we obtain a linear state equation as a local approximate model of the ultrasonic motor. Furthermore, we apply the LQI (Linear Quadratic Integral) control to the model to compensate nonlinearities owing to the modeling errors. And then, the effectiveness of the proposed method is confirmed by experiments; moreover, we show advantages of the model-based control by comparison with computer simulations.

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Language：English   Publishing type：Research paper (international conference proceedings)  

In this paper, we discuss almost sure asymptotic stability for deterministic systems, which are randomized by adding one-dimensional standard Wiener processes. First, we clarify the difference between the deterministic Lyapunov stability theory and the stochastic stability theory proposed by Hasminskii, and show that local asymptotic stability in probability causes trouble in randomization problems. Second, we describe the Lyapunov stability theory based on almost sure stability, as proposed by Bardi and Cesaroni, and show that the stability is almost the same as the deterministic Lyapunov stability. Third, we survey randomization problems briefly, and show that Stratonovich integrals are valid for such problems based on one-dimensional Wiener processes. Finally, we derive the necessary conditions for stochastic Lyapunov functions to ensure almost sure stabilities and discuss the difference between Hasminskii's stabilities and those of Bardi and Cesaroni via linear stochastic systems with numerical simulations. © 2012 IEEE.

DOI： 10.1109/MED.2012.6265672

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ICIC International  

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DOI： 10.9746/jcmsi.5.162

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Language：English   Publisher：The Society of Instrument and Control Engineers  

This paper deals with an output consensus problem of multiple agents and first presents a centralized algorithm for solving it by a model predictive control method based on linear matrix inequalities. It is shown that the outputs of all the agents controlled by the presented method asymptotically converge to a common point, i.e., a consensus point. Then two kinds of algorithms for solving the consensus problem in a decentralized way are presented by using primal and dual decomposition methods. In general, these algorithms require a large number of iterations, i.e., a large number of communications between agents. To cope with this communication burden, a method that can reduce the number of iterations and guarantee the convergence to a consensus point is proposed by exploiting the property that the primal and dual decomposition methods can give upper and lower bounds of the optimal value of the optimization problem to be solved. A numerical example is given to illustrate the effectiveness of the proposed method.

DOI： 10.9746/jcmsi.4.230

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DOI： 10.3182/20110828-6-it-1002.01782

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper describes a robust controller for a constant angle regulation problem of a travelling wave ultrasonic motor. Generally, control problems of ultrasonic motors are difficult because the motors have various nonlinearities. Further, construction problems of physical models of ultrasonic motros are also difficult. In this paper, we propose an approximate model of the travelling wave ultrasonic motor taking the nonlinearities into consideration. Then, we design a CLF (control Lyapunov function) based controller, which has robustnesses for modeling errors and friction forces. Finally, by experiments, we show that our control model is useful for constant angle regulation problems of the ultrasonic motor.

DOI： 10.1109/IECON.2011.6119398

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ICIC INT  

This paper proposes a distributed model predictive control method for solving an optimal consensus problem, where a system consists of networked multiple agents and the outputs of all agents converge to a common point. The problem is formulated as a convex optimization problem involving linear matrix inequalities, and then solved by using dual decomposition. In the proposed scheme, the state feedback matrix for each agent is computed at each time in a decentralized manner. It is proven that the outputs of all agents asymptotically converge using the proposed method if the optimization problem is feasible at the initial time. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

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Language：Japanese   Publisher：The Japan Society for Industrial and Applied Mathematics  

Pontryagin formalized optimal control problems as canonical systems, which are concepts from analytic mechanics. Recently, a canonical quantization method for optimal control problems was proposed. In this paper, we derive a sufficient condition that particular solutions to the canonical quantized optimal regulator problems converge to strict solutions to the original optimal control problems with infinite-time horizons. Further, we discuss possibility that the canonical quantization method yields useful approximate methods for nonlinear optimal regulator problems.

DOI： 10.11540/jsiamt.21.3_197

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper describes a robust controller for a constant angle regulation problem of a travelling wave ultrasonic motor. Generally, control problems of ultrasonic motors are difficult because the motors have various nonlinearities. Further, construction problems of physical models of ultrasonic motros are also difficult. In this paper, we propose an approximate model of the travelling wave ultrasonic motor taking the nonlinearities into consideration. Then, we design a CLF (control Lyapunov function) based controller, which has robustnesses for modeling errors and friction forces. Finally, by experiments, we show that our control model is useful for constant angle regulation problems of the ultrasonic motor.

DOI： 10.1109/iecon.2011.6119398

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOS PRESS  

In this paper, we develop a meal assistance robot for people with disabilities of upper limbs and pacemakers in the body. In the robot, ultrasonic motors are used because the motors do not generate an electromagnetic field. The robot is handled using acts of user's eyes so that the people can use it. Moreover, the vibration is small because the arms of our robot move independently of each other. In this paper, we introduce structure of our robot and show the advantage with experiment results.

DOI： 10.3233/JAE-2011-1356

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical Engineers of Japan ({IEE} Japan)  

Ultrasonic motors (USMs) intrinsically have a dead-zone property which is sensitive to load changes. This paper proposes a fictitious reference iterative tuning (FRIT) method for systems with a dead-zone property such as USMs. The standard FRIT method is basically developed for linear systems and may not give a satisfactory control performance for noninvertible nonlinear systems including USMs. In contrast, the proposed FRIT method can achieve such a performance by introducing a right inverse of a dead-zone function as a dead-zone compensator. In the optimization process of FRIT, the so-called covariance matrix adaptation evolution strategy (CMA-ES) is used for simultaneously searching a dead-zone parameter as well as controller parameters. CMA-ES is a kind of stochastic multi-point search techniques and is effective for nondifferentiable and nonconvex optimization problems. Experimental results for a USM are given to show the effectiveness of the proposed method. © 2011 The Institute of Electrical Engineers of Japan.

DOI： 10.1541/ieejeiss.131.1209

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In this paper, we propose a new method for constructing approximate value functions for nonlinear optimal regulator problems with infinite time horizons. We consider a canonical quantization, which is an operation to change classical mass systems to quantum mass systems. First, we apply the canonical quantization to mass systems equivalent to the optimal regulator systems. Second, we construct approximate optimal regulators by using the canonical quantized mass systems. Third, we clarify the conditions under which approximate solutions converge to the strict solutions. In addition, we demonstrate some examples with one-dimensional systems. © 2011 IFAC.

DOI： 10.3182/20110828-6-IT-1002.01782

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：The Institute of Electrical Engineers of Japan  

In Japan, the number of elderly people living alone has increased in recent years. Therefore, we propose a safety confirmation system that includes an ultrasonic radar for confirming the safety of elderly people living alone. This system consists of an ultrasonic radar, a power line communication unit, and an information processing communication unit. The safety confirmation method performs the human body detection in the restroom using ultrasonic radar. In addition, the proposed system contains a self-checking function. The effectiveness of the proposed system has been confirmed by the results of a field experiment.

DOI： 10.1541/ieejias.131.202

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Language：Japanese   Publisher：日本AEM学会  

Although the ultrasonic motors are useful in various cases, they are very hard to control because of the following reasons: the motors have nonlinear relations between the input (phase difference) and the output (revolving speed), the property fluctuation is caused by change of load, and the structure is quite complicated. Therefore we propose the variable gain type PID controller, in which parameters are adjusted using the particle swam optimization (PSO). Then, the effectiveness of the proposed method is confirmed by the experiments.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Wiley-Blackwell  

The behavior of the particle swarm optimization (PSO) algorithm is analyzed by regarding its dynamics as a system with multiplicative noise and applying control-theoretic analysis methods. In order to evaluate the convergence and diversity of the PSO algorithm, two new measures related to the decay rate and l2 gain of the PSO dynamics are introduced. These measures are characterized by linear matrix inequalities and are therefore efficiently computed by convex optimization tools. Numerical experiments suggest that the measures are effective enough to evaluate the convergence and diversity of the PSO algorithm, which can lead to better understanding of the PSO algorithm from the viewpoints of exploitation and exploration abilities.

DOI： 10.1002/asjc.263

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper deals with an output consensus problem of multiple agents and first presents a centralized algorithm for solving it by a model predictive control method based on linear matrix inequalities. It can be shown that the outputs of all the agents controlled by the presented method asymptotically converge to a common point, i.e., consensus point. Then two kinds of algorithms for solving the consensus problem in a decentralized way are presented by using primal and dual decomposition methods. In general, these algorithms require a large number of iterations, i.e., a large number of communications between agents. To cope with this communication burden, a method that can reduce the number of iterations and guarantee the convergence to a consensus point is proposed by exploiting the property that the primal and dual decomposition methods can give upper and lower bounds of the optimal value of the optimization problem to be solved. The numerical example is given to illustrate the effectiveness of the proposed method.

DOI： 10.1109/cca.2010.5611194

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ICIC INTERNATIONAL  

This paper proposes a simultaneous tuning method for PID controllers and dead-zone compensatom based On particle swarm. optimization By the proposed algorithm, PID gains and dead-zone parameters are tuned online to minimize the error between the control output. and the reference input However, since ultrasonic motors intrinsically have a varying dead-zone in the control input associated with applied load torque, dead-zone compensation is required for precise control of these motors The proposed method is applied to an ultrasonic motor, and its effectiveness is verified by experimental results

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical Engineers of Japan ({IEE} Japan)  

The covariance matrix adaptation evolution strategy (CMA-ES) is a kind of stochastic optimization such as particle swarm optimization (PSO), and has been shown to have a good performance. However, there are few control applications of the CMA-ES except for only one paper. This paper deals with a PID control problem with constraints on sensitivity and complementary sensitivity functions, and proposes a PID controller tuning method based on the CMA-ES. Numerical examples are given to show the effectiveness of the proposed method in comparison with the recently proposed PSO-based method. © 2010 The Institute of Electrical Engineers of Japan.

DOI： 10.1541/ieejeiss.130.737

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Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

DOI： 10.3182/20100826-3-tr-4015.00031

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Language：Japanese   Publisher：The Society of Life Support Technology  

Meal-assistance robots are required for people with disabilities of upper limbs because they need help with eating. However, they can not use some famous robots because they can not handle the robots using joysticks or touch sensors. Some people, who have pacemakers in the body, can also not use the robots because electromagnetic motors are included. We therefore develop a meal-assistance robot using ultrasonic motors and eye-interfaces. The features of our robot are as follows: our robot has electromagnetic compatibility because we use the ultrasonic motors, which are driven by frictional forces. Our robot is handled by using acts of user's eyes. Moreover, our robot does not vibrate so much because the arms of our robot move independently of each other. In this paper, we show the detail of our robot.

DOI： 10.5136/lifesupport.22.63

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Language：English   Publishing type：Research paper (international conference proceedings)  

The behavior of the particle swarm optimization (PSO) algorithm is analyzed by regarding its dynamics as a system with multiplicative noise and applying control-theoretic analysis methods. In order to evaluate the convergence and diversity of the PSO algorithm, two measures related to the decay rate and l2 gain of the PSO dynamics are used. These measures are characterized by linear matrix inequalities (LMIs) and are therefore efficiently computed by convex optimization tools. As for the measure related to the decay rate, moreover, an alternative condition in terms of nonlinear scalar inequalities is presented which can be checked more shortly and accurately than the LMI. Numerical experiments suggest that the measures are effective enough to evaluate the convergence and diversity of the PSO algorithm, which results in better understanding of the PSO algorithm from the viewpoints of exploitation and exploration abilities. © 2010 IEEE.

DOI： 10.1109/CACSD.2010.5612763

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

The behavior of the particle swarm optimization (PSO) algorithm is analyzed by regarding its dynamics as a system with multiplicative noise and applying control-theoretic analysis methods. In order to evaluate the convergence and diversity of the PSO algorithm, two measures related to the decay rate and l2 gain of the PSO dynamics are used. These measures are characterized by linear matrix inequalities (LMIs) and are therefore efficiently computed by convex optimization tools. As for the measure related to the decay rate, moreover, an alternative condition in terms of nonlinear scalar inequalities is presented which can be checked more shortly and accurately than the LMI. Numerical experiments suggest that the measures are effective enough to evaluate the convergence and diversity of the PSO algorithm, which results in better understanding of the PSO algorithm from the viewpoints of exploitation and exploration abilities. © 2010 IEEE.

DOI： 10.1109/CACSD.2010.5612763

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper deals with an output consensus problem of multiple agents and first presents a centralized algorithm for solving it by a model predictive control method based on linear matrix inequalities. It can be shown that the outputs of all the agents controlled by the presented method asymptotically converge to a common point, i.e., consensus point. Then two kinds of algorithms for solving the consensus problem in a decentralized way are presented by using primal and dual decomposition methods. In general, these algorithms require a large number of iterations, i.e., a large number of communications between agents. To cope with this communication burden, a method that can reduce the number of iterations and guarantee the convergence to a consensus point is proposed by exploiting the property that the primal and dual decomposition methods can give upper and lower bounds of the optimal value of the optimization problem to be solved. The numerical example is given to illustrate the effectiveness of the proposed method.

DOI： 10.1109/CCA.2010.5611194

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)  

The existence of stochastic Lyapunov functions assures that the systems are stable in probability. However, general scheme of obtaining stochastic Lyapunov functions has not been introduced yet. This paper extends the authors&rsquo; previous method[21] obtaining Lyapunov functions for deterministic cases to stochastic cases. In the method, difference-approximation scheme[6,10] and quantization of Markov processes[1,14] are used to approximate Lyapunov equations by linear quantum-like equations. We propose a method of obtaining approximate stochastic Lyapunov functions for nonlinear stochastic systems by superimposing the eigenfunctions of the quantum-like equations. <br>

DOI： 10.5687/iscie.22.295

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This paper proposes a method to stabilize the origins of deterministic dynamical systems by state feedback control laws with Wiener processes. First, we obtain Ito-type stochastic dynamical systems by randomizing ordinary differential equation systems. Second, we design the diffusion coefficients. Then, we obtain Sontag-type global asymptotically stabilizers based on the stochastic control Lyapunov functions. Moreover, we show the usefulness of our results by some examples, i.e., systems with noncontractible state spaces and nonholonomic systems. ©2009 IEEE.

DOI： 10.1109/CDC.2009.5400439

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

This paper proposes a method to stabilize the origins of deterministic dynamical systems by state feedback control laws with Wiener processes. First, we obtain Ito-type stochastic dynamical systems by randomizing ordinary differential equation systems. Second, we design the diffusion coefficients. Then, we obtain Sontag-type global asymptotically stabilizers based on the stochastic control Lyapunov functions. Moreover, we show the usefulness of our results by some examples, i.e., systems with noncontractible state spaces and nonholonomic systems.

DOI： 10.1109/CDC.2009.5400439

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Publisher：The Society of Instrument and Control Engineers  

This paper proposes a new method of getting Lyapunov functions using randomization, state discretization, and quantization of the Markov process. We deal with continuous deterministic systems as discrete stochastic systems and quantize the systems. The randomization of deterministic systems is introduced because we are aiming at the extension of the method to the stable stochastic case in future works. This procedure introduces Schr&ouml;dinger-like equations. The problem of obtaining Lyapunov functions is replaced by the problem of solving eigen equations of the Schr&ouml;dinger-like equations. In previous works of obtaining Lyapunov functions, for example, Fleming and Soner's method, there is the case that numerical approximated values diverge because of iteration of calculation. However, our method does not cause the problem because it is based on eigen analysis.

DOI： 10.9746/ve.sicetr1965.44.26

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

We propose a new procedure for designing approximate stochastic Lyapunov functions (SLFs) for nonlinear Ito stochastic systems. We approximate nonlinear stochastic Lyapunov equations (SLEs) by linear Schrodinger-like equations with Kushner's scheme of difference approximation and Alcaraz et al.'s "quantization of Markov processes." We construct time-invariant functions concerned with the solutions of Schrodinger-like equations and then obtain sufficient conditions for converting the time-invariant functions into approximate SLFs.

DOI： 10.1109/CDC.2008.4738923

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

We propose a new procedure for designing approximate stochastic Lyapunov functions (SLFs) for nonlinear Ito stochastic systems. We approximate nonlinear stochastic Lyapunov equations (SLEs) by linear Schrodinger-like equations with Kushner's scheme of difference approximation and Alcaraz et al.'s "quantization of Markov processes." We construct time-invariant functions concerned with the solutions of Schrodinger-like equations and then obtain sufficient conditions for converting the time-invariant functions into approximate SLFs.

DOI： 10.1109/cdc.2008.4738923

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DOI： 10.3182/20080706-5-KR-1001.2894

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Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

DOI： 10.3182/20080706-5-kr-1001.00473

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Language：Japanese   Publisher：The Society of Instrument and Control Engineers  

DOI： 10.11499/sicejl.61.171

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DOI： 10.11499/sicejl.61.146

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Language：Japanese   Publisher：The Society of Instrument and Control Engineers  

DOI： 10.9746/sicetr.58.1

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

DOI： 10.11511/jacc.65.0_738

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DOI： 10.11511/jacc.65.0_497

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DOI： 10.11499/sicejl.60.327

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DOI： 10.11499/sicejl.60.385

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DOI： 10.11499/sicejl.60.381

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DOI： 10.11511/jacc.63.0_1232

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Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS  

DOI： 10.11509/isciesci.64.7_264

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DOI： 10.11511/jacc.63.0_876

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This paper proposes a notion of viscosity weak supersolutions to build a<br />
bridge between stochastic Lyapunov stability theory and viscosity solution<br />
theory. Different from ordinary differential equations, stochastic differential<br />
equations can have the origins being stable despite having no smooth stochastic<br />
Lyapunov functions (SLFs). The feature naturally requires that the related<br />
Lyapunov equations are illustrated via viscosity solution theory, which deals<br />
with non-smooth solutions to partial differential equations. This paper claims<br />
that stochastic Lyapunov stability theory needs a weak extension of viscosity<br />
supersolutions, and the proposed viscosity weak supersolutions describe<br />
non-smooth SLFs ensuring a large class of the origins being noisily<br />
(asymptotically) stable and (asymptotically) stable in probability. The<br />
contribution of the non-smooth SLFs are confirmed by a few examples;<br />
especially, they ensure that all the linear-quadratic-Gaussian (LQG) controlled<br />
systems have the origins being noisily asymptotically stable for any additive<br />
noises.

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DOI： 10.11511/jacc.61.0_750

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DOI： 10.11511/jacc.60.0_658

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DOI： 10.11511/jacc.60.0_771

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DOI： 10.11511/jacc.60.0_799

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Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS  

DOI： 10.11509/isciesci.61.9_375

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DOI： 10.11499/sicejl.55.381

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Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)  

<p>Ultrasonic motors are available for the construction of precise positioning servo systems because of having high holding torque. However, deriving their dynamical models are generally difficult due to the complicated physical structures and a specific driving principle. Especially, their transient states in driving at high velocities need higher-order system models that are generally make the problems more difficult. In this paper, we provide a second-order linear system model for a ultrasonic motor by taking nonlinearity of steady-states into account. The modeling errors of transient states are compensated by a finite-time stabilizer based on homogeneous control Lyapunov functions. Then,after tuning the control parameters via computer simulation, we show the effectiveness of our servo system by comparing simulation and experimental results.</p>

DOI： 10.5687/iscie.29.235

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

<p>In this paper, we discuss the stability of stochastic homogeneous systems. Regarding the stability, we show that the homogeneity is strongly related to their convergence rates with respect to homogeneous norms. Based on the stability result, we deal with the stabilization of homogeneous control systems with guaranteed convergence rates. For the purpose of the guaranteed convergence rates, we show a design method of homogeneous stabilizing control laws. We also show numerical examples of the homogeneous stabilization.</p>

DOI： 10.11511/jacc.59.0_69

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

<p>In this paper, we present a new stability notion for the origins of stochastic systems by identifying the origins into two categories and allowing stochastic Lyapunov functions without smoothness at the origins. The necessity of the definition is discussed by two simple examples; the one has no stochastic Lyapunov function smooth at the origin while the origin is stable in probability, and the other has a stochastic Lyapunov function without smoothness at the origin while the origin is not an equilibrium. Lyapunov-type characterizations and brief discussions are given to the new notion. Proofs, more rigorous materials and advanced/detailed discussions are presented in separate papers ^{15, 16)}.</p>

DOI： 10.11511/jacc.59.0_227

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

<p>This paper provides sufficient conditions for asymptotic stability in probability independend of defining stochastic integrals. We confirm that a stochatic integral over a Wiener process has an unknown parameter by revisiting Stratonovich's definition of stochastic integrals, derive an infinitesimal operator including the parameter, and then define a stability such that an equilibrium of a stochastic system keeps stability under any value of the parameter. A useful condition for a linear stochatic system is also derived.</p>

DOI： 10.11511/jacc.59.0_231

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Language：Japanese   Publisher：システム制御情報学会  

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Language：Japanese   Publisher：システム制御情報学会  

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Language：Japanese   Publisher：日本フルードパワーシステム学会  

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

For stochastic nonlinear dynamical systems, path-wise probability is employed to define integral input-to-state stability and input-to-state stability in this paper. These notions are stricter than popular counterparts which take probability at each instant. Some of Lyapunov characterizations for the path-wise notions developed by the authors are outlined and compared with the ones for instantaneous probability. This note briefly sketches several preliminary results. More advanced results, details and other insightful discussions are reported elsewhere.

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

In this paper, we consider sufficient conditions that the addition of white noises helps the origins of Stratonovich-type stochastic systems become asymptotically stable in probability. We firstly extend the basic notion of stochastic asymptotic stability. Furthermore, we also define "artificial Wiener processes" to justify the choise of Stratonovich-type. Then, we clarify the design of nonlinear diffusion coefficients is effective for the strategy of stabilization by noise.

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Language：Japanese   Publisher：システム制御情報学会  

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Language：Japanese   Publisher：公益社団法人 計測自動制御学会  

DOI： 10.11499/sicejl.53.1153

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Language：Japanese   Publisher：システム制御情報学会  

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Language：Japanese   Publisher：The Japan Society of Mechanical Engineers  

DOI： 10.1299/jsmekyushu.2013.205

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Language：Japanese   Publisher：The Japan Society of Mechanical Engineers  

DOI： 10.1299/jsmekyushu.2013.66.375

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Language：Japanese   Publisher：一般社団法人 電気学会  

本記事に「抄録」はありません。

DOI： 10.1541/ieejias.132.132

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Language：Japanese   Publisher：公益社団法人 精密工学会  

エンドミル加工の高精度化に伴って，切削中に生じる振動による加工精度の低下が問題となっている．振動抑制方法の一つに動吸振器を利用するという方法がある．セミアクティブ型動吸振器である可変剛性型動吸振器は，動吸振器の固有振動数を任意に変えることができるため，断続切削で生じる強制振動の大幅な低減が期待できる．そこで，本研究では，可変剛性型動吸振器による主軸ヘッドの振動低減効果を調べた．

DOI： 10.11522/pscjspe.2012A.0.159.0

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Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS  

DOI： 10.11509/isciesci.55.12_513

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

The number of the elderly person who lives alone is increasing recently in Japan. With this, lonely death of the elderly person becomes the big problem. To solve this problem, the study of the safety confirmation system for elderly people becomes active. In this study, we measure a pulse wave and build a safety confirmation system calculating the pulse based on this. We have inspected the usefulness of this system in a field examination.

DOI： 10.11511/jacc.54.0.380.0

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Language：Japanese   Publisher：The Institute of Systems, Control and Information Engineers  

非線形システムの最適レギュレータはHamilton-Jacobi-Bellman方程式から得られる．しかし，同方程式は非線形偏微分方程式であるため解を得るのが困難である．この問題に対し，近年，最適制御系を拘束力学系とみなして正準量子化し，HJB方程式と等価なSchroedinger方程式を導く手法が示されている．本稿では，Schroedinger方程式と局所的に一致するマスター方程式を持つMarkov過程を考えることで，非線形最適レギュレータの近似解法を構築する．

DOI： 10.11509/sci.SCI10.0.126.0

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Language：Japanese   Publisher：The Institute of Systems, Control and Information Engineers  

本研究では、1回の実験データから直接PIDゲインを調整するFictitious Reference Iterative Tuning (FRIT)を不感帯をもつシステムに適用する方法を提案する。制御対象は入力部に不感帯をもつと仮定し、この不感帯の逆関数をPID制御器に後段に挿入した制御系を考える。不感帯幅をパラメータとしてFRITに組み込むことにより、従来よりも良い制御性能が得られるようになる。提案法を使用環境によって不感帯の変化しやすい超音波モータに適用し、その有効性を検証する。

DOI： 10.11509/sci.SCI10.0.349.0

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

In this paper, we propose a stochastic Lyapunov function design method using a difference approximation scheme and quantization of the Markov process. We approximate a stochastic Lyapunov equation by a Schrodinger-like equation. We obtain sufficient conditions for the stochastic Lyapunov function. The discretized stochastic Lyapunov function is obtained from the eigenvalue problem of a sparse matrix, which is generated by a Hamiltonian operator of the Schrodinger-like equation.

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