Robust adaptive control design for chaotic continuous-time systems

This paper presents a new nonlinear robust adaptive control design for continuous-time chaos systems in the presence of disturbances. The scheme of adaptation is based on the concept of dynamic certainty equivalence (DyCE) and incorporates the design of a fixed(non-adaptive) compensator in the error feedback loop. The fixed compensator is used to realize the high performance of a tracking. The key features of our control design are: (1) use of H_∞ minimization design for the fixed compensator, and (2) use of a robust high-order estimator with dead-zone. By using our proposed nonlinear adaptive controller, it can be shown that the chaotic signal of the system dynamics tends to be driven into a well controlled periodic state or a steady state, and conversely, the periodic signal asymptotically converges to chaotic signal. Then it can be seen that our scheme is one of the unified approaches for controlling chaos. The mathematical proof of stability for the total closed loop system is guaranteed. Finally in order to verify the effectiveness of the proposed method, numerical simulations are shown.