Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems. (English) Zbl 1181.93032

Ma, Jun; Zhang, Ai-Hua; Xia, Ya-Feng; Zhang, Li-Ping

Appl. Math. Comput. 215, No. 9, 3318-3326 (2010).

Summary: Based on the Lyapunov stability and adaptive synchronization theory, optimization design of adaptive controllers and parameter observers with controllable gain coefficient are investigated in detail. The linear errors of corresponding variables and parameters are used to construct different appropriate positive Lyapunov functions \(V\) and the parameter observers and adaptive controllers are approached analytically by simplifying the differential inequality \(dV/dt \leqslant 0\). Particularly, an optional gain coefficient is selected in the parameter observers and positive Lyapunov function, which decides the transient period to identify the unknown parameters and reach synchronization. The scheme is used to study the synchronization of two non-identical hyperchaotic Rössler systems. The theoretical and numerical results confirm that the four unknown parameters in the drive system are estimated exactly and the two hyperchaotic systems reach complete synchronization when the controllers and parameter observers work on the driven system. To confirm the model independence of this scheme, an alternative hyperchaotic system is investigated, whereby the results confirm that the five unknown parameters are identified rapidly and exactly, and that the two hyperchaotic systems reach complete synchronization as well.

MSC:

93B40	Computational methods in systems theory (MSC2010)
93A05	Axiomatic systems theory
34H10	Chaos control for problems involving ordinary differential equations
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

parameter estimation; adaptive synchronization; hyperchaotic Rössler; controller; gain coefficient

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