Set-membership estimation is commonly used in adaptive/learning-based control algorithms that require robustness over the model uncertainty sets, e.g., online robustly stabilizing control and robust adaptive model predictive control. Despite having broad applications, non-asymptotic estimation error bounds in the stochastic setting are limited. This paper provides such a non-asymptotic bound on the diameter of the uncertainty sets generated by set membership estimation on linear dynamical systems under bounded, i.i.d. disturbances. Further, this result is applied to robust adaptive model predictive control with uncertainty sets updated by set membership. We numerically demonstrate the performance of the robust adaptive controller, which rapidly approaches the performance of the offline optimal model predictive controller, in comparison with the control design based on least square estimation's confidence regions.

该研究提供了在线构建并考虑模型不确定性集合的集合成员估计的非渐进边界，并将其应用于更新模型预测控制的不确定性集合。通过与基于最小二乘估计置信区域的控制设计相比较，数值结果表明了鲁棒自适应控制器的性能与离线最优模型预测控制器逼近的速度。

通过集合成员关系学习控制动力学的不确定性集合：非渐进性分析