Robust control of chaos in Chua’s circuit based on internal model principle

Abstract

Abstract The paper treats the question of robust control of chaos in Chua’s circuit based on the internal model principle. The Chua’s diode has polynomial non-linearity and it is assumed that the parameters of the circuit are not known. A robust control law for the asymptotic regulation of the output (node voltage) along constant and sinusoidal reference trajectories is derived. For the derivation of the control law, the non-linear regulator equations are solved to obtain a manifold in the state space on which the output error is zero and an internal model of the k -fold exosystem ( k = 3 here) is constructed. Then a feedback control law using the optimal control theory or pole placement technique for the stabilization of the augmented system including the Chua’s circuit and the internal model is derived. In the closed-loop system, robust output node voltage trajectory tracking of sinusoidal and constant reference trajectories are accomplished and in the steady state, the remaining state variables converge to periodic and constant trajectories, respectively. Simulation results are presented which show that in the closed-loop system, asymptotic trajectory control, disturbance rejection and suppression of chaotic motion in spite of uncertainties in the system are accomplished.