Improved Robust Adaptive Control Law for a Class of Uncertain Nonlinear Systems and Its Application to Chaotic Systems

An adaptive robust control scheme is proposed for a class of unknown nonlinear systems. For achieving this purpose, a class of uncertain nonlinear systems is firstly considered. Then, the regulation and tracking problems are solved with the well-known Lyapunov stability theory. It is shown that although the system dynamic may not be fully or partially known, some adaptive control laws can be mathematically derived by using the proposed control method. Hence, by the proposed control method, the closed-loop system would be globally stabilized in the sense of the Lyapunov stability theory. Finally, the proposed robust adaptive control law is numerically applied into the Lorenz and Van der Pol chaotic systems. The efficiency of the suggested approach is shown by numerical simulation via comparison with an existing method.