Optimal constrained integral sliding mode control design for fuzzy-based nonlinear systems

Abstract

This study introduces a novel H∞ optimal constrained integral sliding mode control (OCISMC) for nonlinear systems due to the matched/unmatched external disturbances based on Takagi–Sugeno (TS) fuzzy models. Based on the Lyapunov function, the appropriate conditions are provided to reach the sliding mode from any initial condition and robustness against the matched disturbances is guaranteed. The optimal nominal part of the proposed OCISMC is designed based on an online optimization problem. To reach robustness against the unmatched disturbances and constrained controller, the H∞ performance and the limitations of the control signal are included in the design procedure of the suggested OCISMC. Furthermore, by considering a non-quadratic Lyapunov function (NQLF), a new linear matrix inequality problem with less conservatism is derived. Finally, two examples are simulated and compared with the existing works to illustrate the capability of the proposed OCISMC.