Adaptive tracking control of Duffing-Holmes chaotic systems with uncertainty

The tracking control problem of Duffing-Holmes chaotic systems containing unknown parameters is studied. Based on the backstepping design method, special barrier functions are employed in Lyapunov synthesis. The derived adaptive robust controller guarantees the closed-loop system globally uniformly ultimate bound, and the tracking error is convergent to a small neighborhood of zero. In addition, the desired performance can be achieved by an appropriate choice of design parameters Simulation results demonstrate that the designed adaptive nonlinear tracking controller owns super robustness and adaptability.