Adaptive synchronization of Lü system with uncertain parameters
The paper addresses the problem of complete synchronization of two systems \(dx/dt=f(x)\), \(dy/dt=f(y)+g(x-y)\), where \(x,y\in \mathbb{R}^3\), \(f,g: \mathbb{R}^3\to \mathbb{R}^3\) are smooth functions. The right-hand side \(f(x)\equiv(a(x_2-x_1),-x_1 x_3 +c x_2, x_1 x_2 - x_3)^T\) corresponds to the Lü system, which was suggested in [Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 659--661 (2002; Zbl 1063.34510)]. The parameter \(a\) is assumed to be unknown. The authors suggest a control law, i.e., a function \(g\), and a parameter update law \(da/dt\) such that the systems are synchronized, that is, \(| x(t)-y(t)| \to 0\) as \(t\to \infty\) for all initial conditions.
scientific article; zbMATH DE number 2093271