Adaptive variable structure control for chaos suppression of unified chaotic systems
The paper investigates the chaos suppression problem for the chaotic system \[ \begin{cases} x'= (25\alpha + 10)(y-x), \\ y'=(28-35\alpha) x +(29\alpha -1)y - xz, \\ z'=xy-\frac{8+\alpha}{3} z, \end{cases} \] where \(x\), \(y\) and \(z\) are states variables and \(\alpha\in [0,1]\) is a parameter. For \(\alpha\in [0,0.8)\) this is the Lorenz chaotic system, it is Lü's chaotic system for \(\alpha=0.8\) and Chen's chaotic system for \(\alpha\in (0.8,1]\). The authors consider the variable structure control technique which involves two major phases: first to select an appropriate switching surface for the system such that the sliding motion on this surface be asymptotically stable and second, design a control law to drive the system towards the surface even with unknown system parameters and control input nonlinearity. In particular, for this second step, the paper provides an scheme and a theorem that by means of the Lyapunov stability theory, the chaos suppression and the overall stability is proved. Finally the paper ends with some numerical results that validate the robustness of the proposed adaptive control scheme in any of Lorenz (\(\alpha=0\) is chosen), Lü and Chen (\(\alpha=1\) is chosen) chaotic systems.
scientific article; zbMATH DE number 5534874
scientific article