Indirect Adaptive MPC for Discrete-Time LTI Systems With Parametric Uncertainties

• 成果类型: Article
• 署名作者: Dhar, Abhishek; Bhasin, Shubhendu
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Delhi
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3050446
• 发表日期: 2021
• 页码: 5498-5505
• 关键词: uncertainty; Linear systems; Parameter Estimation; Adaptation models; uncertain systems; Closed loop systems; stability analysis; Adaptive control; constrained system; discrete-time system; model predictive control (MPC); uncertain linear time-invariant (LTI) system

摘要

This article addresses the problem of controlling discrete-time linear time-invariant systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed gradient-descent-based indirect adaptive controller, used to handle parametric uncertainties, is combined with a model predictive control (MPC) algorithm, which guarantees constraint satisfaction. An estimated model of the actual uncertain plant is used for predictions of the future states. The parameters of the estimated model are updated using a gradient-descent-based adaptive update law. The errors arising due to the model mismatch between the estimated plant model and the actual uncertain plant are accounted for using a constraint tightening method in the MPC algorithm. The proposed adaptive MPC strategy is proved to be recursively feasible and the closed-loop system is proved to be bounded at all instants and asymptotically converging to the origin.