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Generalized synchronization of nonlinear chaotic systems through natural bioinspired controlling strategy. (English) Zbl 1350.93082

Summary: A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1) apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by S.-Y. Li and Z.-M. Ge [Phys. Lett., A 373, No. 44, 4053–4059 (2009; Zbl 1234.34038)], (2) a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3) three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen system, and Roessler system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

MSC:

93D99 Stability of control systems
34H10 Chaos control for problems involving ordinary differential equations
93B51 Design techniques (robust design, computer-aided design, etc.)
93C10 Nonlinear systems in control theory
93C42 Fuzzy control/observation systems

Citations:

Zbl 1234.34038
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Full Text: DOI

References:

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