Adaptive observer-based control for a class of chaotic systems

In this note, the problem of control for a class of chaotic systems is studied. Only partial information of the systems states is known. First, an adaptive observer is designed to ensure the corresponding error system asymptotically stable. Then, based on the states obtained by the above observer, a nonlinear state feedback controller is constructed for the chaotic system, which, according to the input to state stable (ISS) principal, guarantees the closed-loop chaotic system is asymptotically stable. A numerical example is included to show the effectiveness of the proposed techniques.