Robust and almost perfect periodic tracking of nonlinear systems using repetitive VSC

A repetitive variable structure control (RVSC) approach is originated for the nonlinear system with state-dependent modeling uncertainties and exogenous periodic disturbance. RVSC incorporates repetitive control into VSC. The VSC part ensures the robustness to the uncertain system, and the modeling uncertainties are relaxed to be locally Lipschitz instead of being globally Lipschitz. saturation design to ensures the uniform boundedness of the repetitive control signal. Repetitive control law using directly the VSC signal of the previous cycle for updating is further proposed if a constant bounding function is available. Rigorous proof based on energy function and functional analysis shows that the filtered tracking error converges to zero on the L2 norm, and almost perfect periodic tracking is achieved. Simulation results confirm the effectiveness of the proposed approach