This paper proposes a robust tube-based model predictive control for polytopic linear parameter varying systems subject to bounded additive disturbances. In the proposed method, the future scheduling evolutions are described by a known nominal trajectory and some constant uncertainty sets around the nominal signals. Then, by using the notion of polar dual set, a cross-section varying tube parameterization is constructed to robustly satisfy the state and control constraints. Additionally, in contrast to the classical robust MPC problems with a priory known and fixed disturbance set, the shape and size of the additive disturbance set is maximized online through the MPC optimization problem. Therefore, at each time step, the control sequence and the largest allowable disturbance set can be computed simultaneously by solving a single constrained optimal control problem. Numerical simulation demonstrates the efficacy of the proposed approach.

本文提出了一种基于管的鲁棒模型预测控制受到有界加性扰动影响的多位线性参数变化系统。在所提出的方法中，未来的调度演化由已知的标称轨迹和标称信号周围的一些恒定不确定性来描述。然后，通过使用极对偶集的概念，构造了横截面可变的管参数，以稳健地满足状态和控制约束。此外，与具有先验已知和固定扰动集的经典鲁棒MPC问题相比，通过MPC优化问题可在线最大化加性扰动集的形状和大小。因此，在每个时间步，可以通过解决一个约束最优控制问题来同时计算控制序列和最大允许扰动集。