Observer-based adaptive control for a class of nonlinear chaotic systems

In this paper, an adaptive observer control is proposed for a class of uncertain chaotic systems. Because the system states are assumed to be unavailable, an observer is designed to estimate those unavailable states. The main advantage of this algorithm can overcome the problem of “explosion of complexity” inherent in the backstepping design. The stability analysis shows that the system is stable in the sense that all signals in the closed-loop system are uniformly ultimately bounded (GUUB) and the system output can track the reference signal to a bounded compact set. Finally, an example is provided to illustrate the effectiveness of the proposed control system.