Adaptive backstepping synchronization of uncertain chaotic system (Q1878234)

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, \(| x(t)-\bar x(t)| \to \infty\) as \(t\to \infty\) for all initial conditions \(x(0)\) and \(\bar x(0)\).