Sliding Mode Preview Repetitive Control for Interconnected Nonlinear Systems

This paper designs a decentralized sliding mode preview repetitive control (SMPRC) for interconnected nonlinear systems. First, an augmented error system, which is composed of the derivative equation of the available future reference dynamics, the output of the modified repetitive controller and the tracking error dynamics, is constructed. Next, an integral switching surface is designed to verify the robust asymptotic stability of the considered system subject to nonlinearity. Then, the preview repetitive-control (PRC) law design problem is transformed into the stability problem of the augmented system considering the nominal conditions. Thereafter, a sliding mode control (SMC) law cooperates with the PRC law with the purpose to ensure the robustness of the interconnected systems in the presence of nonlinearity. Further, the required stability conditions are derived on the basis of a Lyapunov analysis, linear matrix inequalities (LMI) and the singular-value-decomposition (SVD) technique. Finally, the numerical simulation results demonstrate the effectiveness of the proposed method.