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Adaptive robust synchronization of Rössler systems in the presence of unknown matched time-varying parameters. (English) Zbl 1222.93114

Summary: We deal with the problem of adaptive robust synchronization of chaotic systems based on the Lyapunov theory. A controller is designed for a feedback linearizable error system with matched uncertainties. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system as time tends to infinity. Since this approach does not require any information about the bound of uncertainties, this information is not needed in advance. In order to prevent the frequent switching phenomenon in the control signal, the method is modified such that the norm of tracking error is bounded. Numerical simulations on two uncertain Rossler systems with matched uncertainties show fast responses of tracking error, while the errors are uniformly ultimately bounded, and the control signal is reasonably smooth.

MSC:

93C40 Adaptive control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D09 Robust stability
34H10 Chaos control for problems involving ordinary differential equations
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