Lorenz system stabilization using fuzzy controllers

被引:70
作者
Precup, Radu-Emil [1 ]
Tomescu, Marius L. [2 ]
Preitl, Stefan [1 ]
机构
[1] Politehn Univ Timisoara, Dept Automat & Appl Informat, RO-300223 Timisoara, Romania
[2] Aurel Vlaicu Univ Arad, Fac Comp Sci, RO-310330 Arad, Romania
关键词
chaotic systems; fuzzy control; Lyapunov functions; nonlinear equations and systems;
D O I
10.15837/ijccc.2007.3.2360
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The stability analysis of the fuzzy control system is performed using Barbashin-Krasovskii theorem. This paper proves that if the derivative of Lyapunov function is negative semi-definite for each fuzzy rule then the controlled Lorentz system is asymptotically stable in the sense of Lyapunov. The stability theorem suggested here offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs. An illustrative example describes the application of the new stability analysis method.
引用
收藏
页码:279 / 287
页数:9
相关论文
共 11 条
[1]  
[Anonymous], 1993, The essence of chaos
[2]   Fuzzy control of chaos [J].
Calvo, O ;
Cartwright, JHE .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1998, 8 (08) :1743-1747
[3]  
KHAHIL HK, 2002, NONLINEAR SYSTEMS
[4]   SUPPRESSION OF CHAOS BY RESONANT PARAMETRIC PERTURBATIONS [J].
LIMA, R ;
PETTINI, M .
PHYSICAL REVIEW A, 1990, 41 (02) :726-733
[5]   CONTROLLING CHAOS [J].
OTT, E ;
GREBOGI, C ;
YORKE, JA .
PHYSICAL REVIEW LETTERS, 1990, 64 (11) :1196-1199
[6]   Optimisation criteria in development of fuzzy controllers with dynamics [J].
Precup, RE ;
Preitl, S .
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE, 2004, 17 (06) :661-674
[7]   CONTINUOUS CONTROL OF CHAOS BY SELF-CONTROLLING FEEDBACK [J].
PYRAGAS, K .
PHYSICS LETTERS A, 1992, 170 (06) :421-428
[8]   EXPERIMENTAL CONTROL OF CHAOS BY DELAYED SELF-CONTROLLING FEEDBACK [J].
PYRAGAS, K ;
TAMASEVICIUS, A .
PHYSICS LETTERS A, 1993, 180 (1-2) :99-102
[9]  
WANG HO, 2006, FUZZY MODELING CONTR
[10]  
Zhong L., 2006, INTEGRATION FUZZY LO