## Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua’s circuit.(English)Zbl 1317.34087

Summary: The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are $$L_{2}$$ signals, an adaptive control incorporated with $$H_{\infty}$$ control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua’s circuits.{
 34C28 Complex behavior and chaotic systems of ordinary differential equations 93B36 $$H^\infty$$-control 34D06 Synchronization of solutions to ordinary differential equations 93C40 Adaptive control/observation systems 93D21 Adaptive or robust stabilization