We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain the true support of the disturbance distribution with a given probability. As more data is collected, the Confidence Supports converge to the true support of the disturbance. This enables design of an MPC controller that avoids conservative estimate of the disturbance support, while simultaneously bounding the probability of constraint violation. The efficacy of the proposed approach is then demonstrated with a detailed numerical example.

翻译：我们提出了一种针对执行迭代任务的约束线性时不变系统设计模型预测控制器的方法。系统受到加性扰动的影响，目标是学习鲁棒地满足状态和输入约束。利用每次迭代后的扰动测量，我们构建置信支撑集，该集合以给定概率包含扰动分布的真实支撑域。随着更多数据的收集，置信支撑集将收敛至扰动的真实支撑域。这使得设计的MPC控制器能够避免对扰动支撑域的保守估计，同时约束违反约束的概率。最后，通过详细的数值示例验证了所提方法的有效性。