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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., $\dot x_1=f_1(x_1,x_2)$, $\dot x_2 = f_2 (x_1,x_2,x_3)$, $\dots$, $\dot x_{n-1}=f_{n-1}(x_1,\dots,x_n)$, $\dot x_{n}=f_{n}(x_1,\dots,x_n)+g_1(t)$, where $f_1$ is a linear function. The response system is coupled via the last $n$th component $ \dot {\bar x}_{n}=f_{n}(\bar x_1,\dots,\bar 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, $\vert x(t)-\bar x(t)\vert \to \infty$ as $t\to \infty$ for all initial conditions $x(0)$ and $\bar x(0)$.

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