Stabilizing terminal constraint-free nonlinear MPC via sliding mode-based terminal cost

Abstract

It is well-known that terminal state constraints play an instrumental role in ensuring the feasibility and stability of the nonlinear model predictive control (MPC). Yet, they inherently and largely limit the size of the feasible region and restrict the use of MPC to practical applications. In this paper, a terminal cost characterized by an implicit sliding mode control (SMC) law is proposed for developing a stabilizing constrained MPC scheme. This SMC law developed for the linearized model helps compensate the model mismatch between the linearization and the original nonlinear system model. Thanks to it, the proposed MPC strategy can stabilize the constrained nonlinear system of which the corresponding linearization around the equilibrium is non-stabilizable. Moreover, by appropriately tuning the sliding mode parameters, the conventional terminal constraints and large prediction horizon typically used in the literature are no longer required. We establish the conditions of ensuring the recursive feasibility and asymptotic stability of the closed-loop system. Finally, numerical comparison results on two examples of dynamic systems are reported to demonstrate the effectiveness of the developed strategy.