Roust Controller Design for a Class of Nonlinear Time-Varying Systems with Optimality Approach

:In this paper, a novel controller is presented with an optimal approach for asymptotic stabilizing of a class of nonlinear time-varying systems in presence of model uncertainties and external disturbances. The proposed controller has two nominal and robust parts and there are new ideas in designing of both of them. In the first part, a new ccontrol Lyapunov function is presented for the nominal controller design. The suggested structure of the proposed control Lyapunov function is different from the common versions. This function is designed in a way that a sliding surface equation is appeared in it directly and therefore, provides the possibility of combining the robust part (which is designed based on sliding mode control technique) with nominal one. This combination leads to a different sub-optimal control law where its discontinuous part switches based on the moment value of the sliding surface and the continuous terms will be designed based on the optimality approach. At the end of the paper, this controller is applied to a nonlinear time-varying inertia pendulum and the simulation results are given to confirm the performance and efficiency of proposed approach and verifying the theoretical achievements.