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Stable Fuzzy Logic Control Solution for Lorenz Chaotic System Stabilization

Radu-Emil Precup, Marius L. Tomescu, Stefan Preitl, Igor Skrjanc

Abstract


Nonlinear systems that exhibit sensitivity to initial conditions are called chaotic systems. Linear control solutions may fail in providing their stability. This paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The design of the FLCs is based on heuristic fuzzy rules. The stability analysis (in the sense of Lyapunov) of these fuzzy control systems is performed using the global invariant set theorem due to La Salle. The stability theorem presented in this paper offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs.

Keywords


chaotic systems, fuzzy control, Lyapunov functions, nonlinear equations and systems

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