This paper addresses a robust tube based model predictive control (RTBMPC) strategy for tracking problem of piecewise affine (PWA) linear systems. The core idea of the RTBMPC strategy is to robustly control an uncertain system through its nominal system and an additional feedback term which rejects a bounded additive disturbance. In tracking problem, RTBMPC strategy should be capable to steer the uncertain system to a given setpoint fulfilling the constraints. But if the setpoint changes, the controller may not success due to the loss of feasibility of the optimization problem. This paper employs several novel features to deal with tracking problem. First, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function. Then, the feasibility region is enlarged for given setpoint without increasing the prediction horizon by changing the terminal constraint set at different steps of RTBMPC problem solving. Simulation examples, including two different case studies, are presented to illustrate the effectiveness of the proposed RTBMPC.

本文针对分段仿射 (PWA) 线性系统的跟踪问题提出了一种鲁棒的基于管的模型预测控制 (RTBMPC) 策略。RTBMPC 策略的核心思想是通过其标称系统和一个附加反馈项来稳健地控制不确定系统，该反馈项拒绝有界加性扰动。在跟踪问题中，RTBMPC 策略应该能够将不确定系统引导到满足约束的给定设定点。但是如果设定值发生变化，由于优化问题的可行性丧失，控制器可能不会成功。本文采用了几个新颖的特征来处理跟踪问题。首先，通过引入一个称为调节名义系统的额外系统，将跟踪问题转化为调节问题，该系统的约束从跟踪转化为调节。它导致目标函数复杂度的降低。然后，通过在 RTBMPC 问题求解的不同步骤更改终端约束集，在不增加预测范围的情况下，针对给定的设定点扩大可行性区域。模拟示例，包括两个不同的案例研究，用于说明所提出的 RTBMPC 的有效性。