Designing L1 Adaptive Control for stabilizing Chaotic Systems with Uncertainty in the model

In this paper, L1 adaptive control strategy for stabilizing chaotic systems in the presence of model uncertainty is proposed. In order to design controller, first, system dynamics is divided into two linear and nonlinear parts. The linear part is converged by placement feedback to the reference model behavior. The uncertain nonlinear part is compensated through adaptive control based on projection adaptive algorithm. This part includes a unknown vector multiplied at infinity norm of state vector and a vector as offset. A state observer also describes reference model behavior. In addition, first order pre-filters with unity gain are used to increase the stability margin. The main property of L1 adaptive control is encountering both parametric and nonparametric uncertainties. Stability analysis of the closed loop system is presented based on Lyapunov theory, and the control system performance is compared and evaluated with one of the conventional adaptive control methods. The results indicate the desirable performance of the proposed method for stabilizing the chaotic system in the presence of model uncertainty.