Sliding mode model predictive control with terminal constraints

A new model predictive control scheme is proposed, which combines the receding horizon control and sliding mode variable structure control. By predicting the system states, the pre-designed switching function is predicted, then the control law can be found by solving the constrained open-loop optimal control problem based on the given cost function. The current control is implemented, and at the next sampling time the optimizing procedure is repeated. The proposed scheme has advantage of receding horizon control and sliding mode variable structure control, can deal with constraints online, and has strong robustness on the sliding surface. Furthermore, by constraining terminal sliding mode to be zero, the stability of closed-loop systems is guaranteed. Another scheme, which relaxes equality constraints to inequality constraints, is suggested for less calculation. In addition, the proposed method can be extended to nonlinear systems, and a nonlinear sliding mode predictive control scheme is acquired.