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Transactions of the Institute of Systems, Control and Information Engineers Vol. 15 (2002), No. 5

ISIJ International
belloff
ONLINE ISSN: 2185-811X
PRINT ISSN: 1342-5668
Publisher: THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)

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Transactions of the Institute of Systems, Control and Information Engineers Vol. 15 (2002), No. 5

Well-posedness Analysis for a Class of Hybrid Dynamical Systems with Autonomous Switches and/or Jumps

Supachai VORAPOJPISUT, Shinji HARA

pp. 223-231

DOI:

10.5687/iscie.15.223

Abstract

A general framework for hybrid dynamical systems is proposed for the modeling of certain classes of dynamical systems consisting of mixed continuous-time/logical dynamics and autonomous discontinuities. Separating different dynamics into two subsystems connected through interfaces, our proposed hybrid model offers generality and also high level of compatibility with existing approaches. The main theoretical result in the paper concerns the well-posedness property (existence and uniqueness of solutions) of the system. We derive a sufficient condition of the well-posedness property which proves that nondeterminism and livelock phenomenon do not exist in the system dynamics.

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Well-posedness Analysis for a Class of Hybrid Dynamical Systems with Autonomous Switches and/or Jumps

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Ris

Stability of a Switched System

Daisuke FUJISAWA, Eiichi MURAMATSU

pp. 232-237

DOI:

10.5687/iscie.15.232

Abstract

We consider stability of a switched system which consists of multiple linear time-invariant subsystems. It is assumed that the state coefficient matrices of the subsystems belong to a certain class and the subsystems are switched according to their dwell times. We present a necessary and sufficient condition for stability of the switched system in terms of eigenvalues of the coefficient matrices and the dwell times of the subsystems.

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Stability of a Switched System

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Feedback Connection of Complementarity Systems

Yasushi IWATANI, Masato ISHIKAWA, Shinji HARA

pp. 238-245

DOI:

10.5687/iscie.15.238

Abstract

This paper is concerned with well-posedness (existence and uniqueness of solutions) problem of hybrid feedback systems and its application. We first consider feedback interconnections of complementarity systems and derive a sufficient condition for the closed loop systems to be well-posed. We then apply the result to design of a switching controller which belongs to complementarity systems for a driftless nonholonomic system, where the well-posedness of the feedback system is guaranteed and the norm of steady-state error is less than each given value.

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Feedback Connection of Complementarity Systems

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Optimal Control of Nonholonomic Chained Systems Using Hybrid Time-State Form

Keigo KOBAYASHI, Yugo SHIBATA, Toshimitsu USHIO

pp. 246-252

DOI:

10.5687/iscie.15.246

Abstract

In this paper, we propose a control method for nonholonomic chained systems. We transform the systems into time-invariant linear systems using a hybrid time-state control form and solve an optimal control problem to get an optimal trajectory with a switching point. The optimal input is derived as a feedback controller for the system. We apply the proposed method to a 4-wheeled vehicle and give numerical simulation results to show its effectiveness.

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Optimal Control of Nonholonomic Chained Systems Using Hybrid Time-State Form

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Line Following Control of Two Wheeled Vehicle Based on Symbolic Input and Output Controller

Eiji KONAKA, Tatsuya SUZUKI, Shigeru OKUMA

pp. 253-261

DOI:

10.5687/iscie.15.253

Abstract

Hybrid Dynamical Systems (HDS), which contain both discrete symbol and continuous signal, are attracting great attention in the field of system control. In this paper, a new symbol based control strategy for a line following control of a two wheeled vehicle is proposed. The vehicle is supposed to have a low-resolution sensor and actuator. The control requirement, however, is specified so as to keep the vehicle as close as possible to the center of the line. The controllability and observability issues are investigated, and a concrete control policy based on the continuous state estimation is proposed. Some experimental results are shown to demonstrate the usefulness of our idea.

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Line Following Control of Two Wheeled Vehicle Based on Symbolic Input and Output Controller

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On Stability Analysis of Switched Systems and Its Applications

Izumi MASUBUCHI

pp. 262-269

DOI:

10.5687/iscie.15.262

Abstract

This paper is concerned with stability analysis of switched systems and its application for synthesis problems. For a class of switched systems, we propose a discontinuous Lyapunov-like function to derive a condition that guarantees exponential stability of switched systems. This condition is stated with LMIs for switched systems that have linear continuous dynamics and an output feedback switch-scheduled control design method is presented in terms of LMIs. These results are applied to control design of a class of nonholonomic systems in the time-state control form.

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On Stability Analysis of Switched Systems and Its Applications

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Control Strategy for Optimal High Jump Based on Complementarity Modeling

Yutaka SAITOU, Masato ISHIKAWA, Shinji HARA, Takashi SEKI

pp. 270-277

DOI:

10.5687/iscie.15.270

Abstract

In this paper, we propose an optimal high jump control strategy for a jumping robot system, based on complementarity modeling approach. The jumping robot system is composed of a simple jumper part, an environment (trampoline) part and some hooks to limit the robot length. It is essentially a hybrid system, due to variable mechanical constraints, such as collision with trampoline, and length limitations. At first, we provide an efficient model of the system as a complementarity-slackness, which enables us to handle discontinuous phenomena of hybrid systems, i.e., discontinuous change of dynamics and leap of solution, in a unified and mathematically sound framework. Then we formulate the high jump problem as a maximizing problem of the peak height of the robot's center of gravity in a given time interval. The optimal control is derived numerically by performing a dynamic programming algorithm, and its validity is verified with computer simulations. The advantage of this modeling approach is that we need not to deal with the awkward variable constraints when we formulate control problem, since they are all considered in the model itself.

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Control Strategy for Optimal High Jump Based on Complementarity Modeling

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