Adaptive sliding mode control for chaotic synchronization of oscillator with input nonlinearity

This paper deals with the problem of sliding mode control to achieve chaotic synchronization for the controlled driven system with an input nonlinear term – the term commonly ignored in the published literature. However, the problem does possess importance in practical applications while hardware limits imposed on the actuating devices need to be considered. The major contribution here is the development of a new adaptive control scheme instead of directly computing the magnitudes of overall nonlinear dynamics for compensation as that commonly adopted in the published literature. In the influence of control input nonlinearity, the adaptive sliding mode control scheme, possessing time-varying feedback gains, can compensate unmatched nonlinear dynamics without knowing their magnitudes. In addition, it is unnecessary to determine these time-varying feedback gains in advance but apply adaptive tuning according to suitably updated rules. Based on the Lyapunov stability analysis, a new condition ensuring stable synchronization is established. Case study and numerical simulations are given to verify effectiveness of the presented scheme.