Extended-Space Control Design with Parameter-Dependent Lyapunov Functions
| Project/Area Number |
14550445
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Control engineering
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
SHIMOMURA Takashi Osaka Prefecture University, Graduate School of Engineering, Assistant Professor, 工学研究科, 講師 (40243191)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | robust control / gain-scheduled control / multiobjective control / matrix polytope / linear parameter-varying / linear matrix inequality / extended space / elimination lemma / パラメータ依存Lyapunov関数 / 拡張空間 / 消去補題 / 行列ポリトープ / LPVシステム / 多目的制御 / ロバスト制御 / ゲインスケジューリング制御 |
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| Research Abstract |
This research attempts to establish a new framework of control design that allows for parameter-dependent Lyapunov functions. In this research, we particularly consider multiobjective control, robust control for polytopic uncertainties, and gain-scheduled control for LPV (Linear Parameter-Varying) systems. Through inverse use of the elimination lemma, we translate a given BMI(Bilinear Matrix Inequality) problem into an extended LMI(Linear Matrix Inequality) problem while introducing a virtual parameter. In this translation, the original BMI variables are split into two different LMI terms at the expense of generating some new BMI terms with the virtual parameter, and we can solve the problem with distinct Lyapunov solutions. In other words, we can solve mixed problems or matrix polytope problems with parameter-dependent Lyapunov functions. Based on this idea, we develop a theory described in detail and verify the applicability of the proposed method through some numerical design exampl
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es. In 2002, we have formulated extended LMI representations of Lyapunov stability, H2 control, and H∞ control. Combining them, we have successfully solved multiobjective control design problems with distinct Lyapunov solutions. In 2003, we have formulated extended LMI formulations of both robust control for polytopic uncertainties and gain-scheduled control for LPV systems. In every case, the past conservatism of common Lyapunov solutions has been considerably improved. In robust H2 control in matrix polytope problems, we cannot know which vertex achieves the worst H2 cost in advance. In 2004, we have derived an excellent formulation in which the worst H2 cost is minimized even though we cannot which one achieves it in advance. Moreover, a condition regarding dP/dt should be included in the formulation for gain-scheduled control, where the Lyapunov function is given by Ψ=x'Px. In 2004, we have successfully included a condition of dP/dt and reduced it to a set of conditions at vertices. Less
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Report
(4 results)
Research Products
(14 results)
