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：我们建议设计一个模型预测控制器(MPC),用于受约束的线性时变变量系统,执行迭接任务。这个系统会受到添加干扰,目的是学会强力地满足状态和输入限制。在每次迭代后,我们使用扰动测量,构建信任支持组,其中含有以给定概率对扰动分布的真正支持。随着数据的收集,信任支持组会聚集到扰动的真正支持上。这样可以设计一个MPC控制器,避免对扰动支持进行保守的估计,同时限制违反的可能性。然后用一个详细的数字示例来证明拟议方法的有效性。