An optimal hybrid adaptive controller based on the multi-objective evolutionary algorithm for an under-actuated nonlinear ball and wheel system

The present paper introduces an optimal hybrid adaptive robust sliding mode control based on a combination of feedback linearization and a PD controller (ARSMC-PD) to present a general scheme for stabilization of a ball and wheel system. Since the combination of adaptive sliding mode and feedback linearization cannot reduce the control efforts and tracking error, a PD controller is added to enhance the performance and provide sufficient optimal control input. At first, an adaptive mechanism is used to update the parameters of the SMC controller according to the gradient descent method and the chain rule of differentiation to minimize the sliding surface. Then, the strength Pareto evolutionary algorithm (SPEA-II) is utilized to minimize the control effort and the integral time absolute errors of the system response simultaneously in the presence of disturbance. The results prove the efficiency of the proposed controller in two aspects of low tracking error and optimal control input.