On the Optimality and Convergence Properties of the Iterative Learning Model Predictive Controller

• 成果类型: Article
• 署名作者: Rosolia, Ugo; Lian, Yingzhao; Maddalena, Emilio T. T.; Ferrari-Trecate, Giancarlo; Jones, Colin N. N.
• 署名单位: California Institute of Technology; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3148227
• 发表日期: 2023
• 页码: 556-563
• 关键词: Iterative algorithms; Iterative learning control; optimal control; Predictive control

摘要

In this technical article, we analyze the performance improvement and optimality properties of the learning model predictive control (LMPC) strategy for linear deterministic systems. The LMPC framework is a policy iteration scheme where closed-loop trajectories are used to update the control policy for the next execution of the control task. We show that, when a linear independence constraint qualification (LICQ) condition holds, the LMPC scheme guarantees strict iterative performance improvement and optimality, meaning that the closed-loop cost evaluated over the entire task converges asymptotically to the optimal cost of the infinite-horizon control problem. Compared to previous works, this sufficient LICQ condition can be easily checked, it holds for a larger class of systems and it can be used to adaptively select the prediction horizon of the controller, as demonstrated by a numerical example.