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Adaptive backstepping synchronization of uncertain chaotic system. (English) Zbl 1062.34053

The paper is devoted to the synchronization of systems, which can be represented in so-called strict-feedback form, i.e., x ˙ 1 =f 1 (x 1 ,x 2 ), x ˙ 2 =f 2 (x 1 ,x 2 ,x 3 ), , x ˙ n-1 =f n-1 (x 1 ,,x n ), x ˙ n =f n (x 1 ,,x n )+g 1 (t), where f 1 is a linear function. The response system is coupled via the last nth component x ¯ ˙ n =f n (x ¯ 1 ,,x ¯ n )+g 2 (t)+u.

The authors suggest an adaptive design of the coupling term u, including a law for the parameter adaptation such that the systems are synchronized, that is, |x(t)-x ¯(t)| as t for all initial conditions x(0) and x ¯(0).

MSC:
34D05Asymptotic stability of ODE
34D23Global stability of ODE
34C28Complex behavior, chaotic systems (ODE)