We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The system dynamics matrices are not known exactly, leading to parametric model mismatch. We also consider the presence of an additive disturbance. Set based bounds for each component of the model uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC controller in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example.

中文翻译：

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用于具有参数和附加不确定性的线性系统的鲁棒 MPC：一种新的约束紧缩方法

我们提出了一种新颖的方法来为受约束的不确定线性系统设计一个鲁棒的模型预测控制器 (MPC)。系统动力学矩阵不准确，导致参数模型不匹配。我们还考虑了附加干扰的存在。假设模型不确定性的每个分量的基于设置的界限是已知的。我们围绕利用这些边界的预测标称轨迹制定了一种新的基于优化的约束收紧策略。通过适当设计的终端成本函数和约束集，我们证明了在具有不确定系统的闭环中产生的 MPC 控制器强加约束的鲁棒性满足，以及原点状态稳定性的输入。我们通过一个数值例子强调了我们提出的方法的有效性。