hybrid control to approach chaos synchronization of uncertain duffing oscillator systems with external disturbance

this paper proposes a hybrid control scheme for the synchronization of two chaotic duffing oscillator system, subject to uncertainties and external disturbances. the novelty of this scheme is that the linear quadratic regulation (lqr) control, sliding mode (sm) control and gaussian radial basis function neural network (grbfnn) control are combined to chaos synchronization with respect to external disturbances. by lyapunov stability theory, sm control is presented to ensure the stability of the controlled system. grbfnn control is trained during the control process. the learning algorithm of the grbfnn is based on the minimization of a cost function which considers the sliding surface and control effort. simulation results demonstrate the ability of the hybrid control scheme to synchronize the chaotic duffing oscillator systems through the application of a single control signal.