• Title/Summary/Keyword: linear matrix inequalities (LMls).

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Design of robust LQR/LQG controllers by LMIs (Linear Matrix Inequalities(LMIs)를 이용한 강인한 LQR/LQG 제어기의 설계)

  • 유지환;박영진
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.988-991
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    • 1996
  • The purpose of this thesis is to develop methods of designing robust LQR/LQG controllers for time-varying systems with real parametric uncertainties. Controller design that meet desired performance and robust specifications is one of the most important unsolved problems in control engineering. We propose a new framework to solve these problems using Linear Matrix Inequalities (LMls) which have gained much attention in recent years, for their computational tractability and usefulness in control engineering. In Robust LQR case, the formulation of LMI based problem is straightforward and we can say that the obtained solution is the global optimum because the transformed problem is convex. In Robust LQG case, the formulation is difficult because the objective function and constraint are all nonlinear, therefore these are not treatable directly by LMI. We propose a sequential solving method which consist of a block-diagonal approach and a full-block approach. Block-diagonal approach gives a conservative solution and it is used as a initial guess for a full-block approach. In full-block approach two LMIs are solved sequentially in iterative manner. Because this algorithm must be solved iteratively, the obtained solution may not be globally optimal.

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$H_2$ Control of Continuous and Discrete Time Descriptor Systems (연속/이산 특이치 시스템의 $H_2$ 제어)

  • 이종하;김종해;박홍배
    • Proceedings of the IEEK Conference
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    • 2001.06e
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    • pp.29-32
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    • 2001
  • This paper presents matrix inequality conditions for H$_2$optimal control of linear time-invariant descriptor systems in continuous and discrete time cases, respectively. First, the necessary and sufficient condition for H$_2$control and H$_2$controller design method are expressed in terms of LMls(linear matrix inequalities) with no equality constraints in continuous time case. Next, the sufficient condition for H$_2$control and H$_2$controller design method are proposed by matrix inequality approach in discrete time case. A numerical example is given in each case.

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Intelligent Digital Redesign of Uncertain Nonlinear Systems : Global approach (불확실성이 포함된 비선형 시스템에 대한 전역적 접근의 지능형 디지털 재설계)

  • Sung Hwachang;Joo Younghoon;Park Jinbae;kim Dowan
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.11a
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    • pp.95-98
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    • 2005
  • This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete -time system have proper reason. Sufficiently conditions for the global state -matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMls). Finally, we prove the effectiveness and stabilization of the proposed intelligent digital redesign method by applying the chaotic Lorentz system.

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An Improved LMI-Based Intelligent Digital Redesign Using Compensated Bilinear Transform (보상된 bilinear 변환을 이용한 향상된 LMI 기반 지능형 디지털 재설계)

  • Kim, Do-Wan;Joo, Young-Hoon;Park, Jin-Bae
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.11a
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    • pp.91-94
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    • 2005
  • This paper presents a new linear- matrix- inequality- basedintelligent digital redesign (LMI-based IDR) technique to match he states of the analog and the digital control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the multirate control is employed, and the control input is changed N times during one sampling period; 2) The proposed IDR technique is based on the compensated bilinear transformation.

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Stochastic Stabilization of TS Fuzzy System with Markovian Input Delay (마코프 입력 지연 시스템의 확률적 안정화)

  • Lee, Ho-Jae;Park, Jin-Bae;Lee, Sang-Youn;Joo, Young-Hoon
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2001.12a
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    • pp.153-156
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    • 2001
  • This paper discusses a stochastic stabilization of Takagi-Sugeno (75) fuzzy system with Markovian input delay. The finite Markovian process is adopted to model the input delay of the overall control system. It is assumed that the zero and hold devices are used for control input. The continuous-time 75 fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretized 75 fuzzy system is represented by a discrete-time 75 fuzzy system with jumping parameters. The stochastic stabilizibility of the jump 75 fuzzy system is derived and formulated in terms of linear matrix inequalities (LMls).

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Output feedback $H^{\infty}$ contol for linear systems with delayed state and control input (상태와 제어입력에 시간지연을 가지는 선형 시스템의 출력궤환 H^\infty 제어)

  • 정은태;권성하;박홍배
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.688-691
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    • 1997
  • This paper presents an $H^{\infty}$ controller design method for linear time-invariant systems with delayed state and control. Using the second method of Lyapunov, the stability for delayed systems is discussed. For delayed systems, we derive a sufficient condition of the bounded real lemma(BRL) which is similar to BRL for nondelayed systems. And the sufficient conditions for the existence of an output feedback $H^{\infty}$ controller of any order are given in terms of three linear matrix inequalities(LMls). Futhermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give a simple example to illustrate the validity of the proposed design procedure.e.

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Fuzzy H2H Controller Design for Delayed Nonlinear Systems (시간지연을 갖는 비선형 시스템의 퍼지 H2H 제어기 설계)

  • Jo, Hui-Su;Lee, Gap-Rae;Park, Hong-Bae
    • Journal of Institute of Control, Robotics and Systems
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    • v.8 no.7
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    • pp.578-583
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    • 2002
  • This paper presents a method for designing fuzzy $H_2/H_{\infty}$ controllers of nonlinear systems with time varying delay. Takagi-Sugeno fuzzy model is employed to represent nonlinear systems with time varying delay. Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. A sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMls). The proposed fuzzy $H_2/H_{\infty}$ controllers minimizes the upper bound on the linear quadratic performance measure.