This article presents a robust model predictive control (MPC) for piecewise constant reference tracking based on a constrained linear model and a terminal constraint defined from the admissible equilibria set. The new robust MPC algorithm based on nominal predictions ensures recursive feasibility and convergence to an optimal target, but the terminal constraint is derived from an admissible equilibria set with a suitable disturbance translation. The computation of the proposed terminal constraint is simple because no subset verification is required and the number of half‐spaces of the proposed terminal constraint is fixed a priori. A zonotope disturbance bound description is used to simplify the computation of the admissible equilibria. Furthermore, it is shown that the proposed strategy can be directly extended to other MPC algorithms based on artificial targets, as a stochastic MPC based on the individual chance constraints, for instance. Two case studies are used to illustrate the usefulness of the proposed robust MPC for piecewise constant set‐point tracking based on nominal predictions.

中文翻译：

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基于可容许均衡集的带界扰动的线性系统的鲁棒MPC

本文提出了一种基于约束线性模型和从可容许平衡集中定义的终端约束的分段恒定参考跟踪的鲁棒模型预测控制（MPC）。基于标称预测的新的鲁棒MPC算法可确保递归的可行性并收敛到最佳目标，但是终端约束是通过具有适当干扰转换的可容许平衡集得出的。提议的终端约束的计算很简单，因为不需要子集验证，并且提议的终端约束的半空间数量事先固定。使用区域干扰扰动描述来简化可容许平衡的计算。此外，结果表明，所提出的策略可以直接扩展到其他基于人工目标的MPC算法，例如基于个体机会约束的随机MPC。通过两个案例研究来说明所提出的鲁棒MPC对基于名义预测的分段恒定设定点跟踪的有用性。