連續模糊控制系統之非二次穩定性分析

Stabilization Analysis for Non-quadratic Continuous-time Fuzzy Control Systems

李家洪(Jia-hong Li)

指導教授 ： 羅吉昌

國立中央大學/工學院/機械工程學系/碩士(2012年)

摘要

本篇論文主要研究連續時間強健 (Robust) 控制系統及連續時間 Takagi-Sugeno(T-S)模糊控制系統的非二次(non-quadratic)穩定寬鬆條件; 我們利用波雅定理(Polya Theorem)的代數性質加上寬鬆矩陣變數(slack matrix variables)來建立一組寬鬆的線性矩陣不等式(LMI)，因為非二次(non-quadratic)穩定的分析加上寬鬆矩陣變數 (slack matrix variables) 的使用，使得此組線性矩陣不等式(LMI)的求解保守性更進一步的降低，亦即當使用波雅定理(Polya Theorem)時，齊次多項式的階數不用太高，就可以找到解，這是本論文最大的優點；最後會提出幾個例子來證明我們理論的優越性。
關鍵字：強健(Robust)控制系統 Takagi-Sugeno(T-S)模糊控制系統、 非二次 (non-quadratic)穩定、 波雅定理 (Polya Theorem)、寬鬆矩陣變數(slack matrix variables)、 線性矩陣不等式 (LMI)

關鍵字

強健控制系統 ； 線性矩陣不等式 ； 模糊控制 ； 非二次穩定性分析 ； 寬鬆矩陣變數

並列摘要

In this thesis, we investigate non-quadratic ralaxation for continuous-time robust control systems
and continuous-time fuzzy control systems, which are characterized by parameter-dependent LMIs (PD-LMIs), exploiting
the algebraic property of Polya Theorem to construct a family of finite-dimensional LMI relaxations with righ-hand-side
slack matrices that release conservatism. Lastly, numerical
experiments to illustrate the advantage of relaxations, being less conservative and effective, are provided.
it keyword: Robust control systems; Takagi-Sugeno fuzzy control systems; Non-quadratic relaxations;
Parameter-dependent LMIs (PD-LMIs); Polya Theorem; Slack matrices; Linear matrix inequality (LMI).

並列關鍵字

non-quadratic ； Takagi-Sugeno(T-S) ； LMI ； slack matrix variables

參考文獻

[1] T. Taniguchi, K. Tanaka, H. Ohatake, and H. Wang, “Model construction, rule reduction and robust compensation for generalized form of Takagi-Sugeno fuzzy systems,” IEEE Trans. Fuzzy Systems, vol. 9, no. 4, pp. 525–538, Aug. 2001.

[2] H. Wang, J. Li, D. Niemann, and K. Tanaka, “T-S fuzzy model with linear rule consequence and PDC controller: a universal framework for nonlinear control systems,” in Proc. of 18th Int’l Conf. of the North American Fuzzy Information Processing Society, 2000.

[3] K. Tanaka, T. Taniguchi, and H. Wang, “Generalized Takagi-Sugeno fuzzy systems: rule reduction and robust control,” in Proc. of 7th IEEE Conf. on Fuzzy Systems, 2000.

[4] H. Wang, K. Tanaka, and M. Griffin, “An approach to fuzzy control of nonlinear systems:

[5] K. Tanaka and H. Wang, Fuzzy Control Systems Design: A Linear Matrix Inequality