Adaptive Backstepping Control Scheme for Duffing-Holmes Chaotic System with Unknown Disturbances

Abstract

In this work a modified Duffing-Holmes chaotic system has been developed and an adaptive backstepping control (ABC) scheme has been proposed to tackle the unknown control coefficients and to reject the unknown disturbances simultaneously. The proposed control scheme has also been used to force the closed loop chaotic system to follow a smooth reference trajectory. The adaptation of the estimates of unknown control coefficients and disturbances improves the backstepping control scheme to guarantee the closed loop stability of the Duffing-Holmes system in the sense of Lyapunov theory. To avoid the repeated differentiation of virtual control signals at every step of backstepping controller design, first-order low pass filters have been inserted into the closed loop control configuration. The free parameters of the proposed controller are tuned by employing a stochastic optimization technique, namely particle swarm optimization (PSO). The effectiveness of the proposed control strategy has been validated through the simulation studies of the competing control strategies.