Synchronizing chaotic systems using backstepping design. (English) Zbl 1035.34025

Tan, Xiaohui; Zhang, Jiye; Yang, Yiren

Chaos Solitons Fractals 16, No. 1, 37-45 (2003).

The paper deals with the problem of synchronization of coupled systems. Given two systems (possibly exhibiting chaotic dynamics) \(x'=f(x,t)\) and \(y'=f(y,t)+u\), \(x,y\in \mathbb{R}^{n}\). The authors propose a recursive procedure for designing an appropriate control \(u\), which makes the systems synchronized, i.e., \(\| x(t)-y(t)\| \to 0\) as \(t\to\infty\), for some set of initial conditions. The algorithm combines the choice of the Lyapunov function with the design of a controller.

Reviewer: Sergiy Yanchuk (Berlin)

MSC:

34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
37N35	Dynamical systems in control
34D23	Global stability of solutions to ordinary differential equations
37B25	Stability of topological dynamical systems
93C10	Nonlinear systems in control theory

Keywords:

backstepping control; Lyapunov function; control; synchronization; coupled systems

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