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.

众所周知，终端状态约束在确保非线性模型预测控制(MPC)的可行性和稳定性方面发挥着重要作用。然而，它们本质上并在很大程度上限制了可行区域的大小，并将 MPC 的使用限制在实际应用中。在本文中，提出了一种以隐式滑模控制 (SMC) 定律为特征的终端成本，用于开发稳定约束 MPC 方案。为线性化模型开发的 SMC 定律有助于补偿线性化与原始非线性系统之间的模型失配模型。多亏了它，所提出的 MPC 策略可以稳定受约束的非线性系统，该系统的平衡周围的相应线性化是不稳定的。此外，通过适当调整滑模参数，不再需要文献中通常使用的传统终端约束和大预测范围。我们建立了保证闭环系统递归可行和渐近稳定性的条件。最后，报告了两个动态系统示例的数值比较结果，以证明所开发策略的有效性。