Distributed Model Predictive Control and Optimization for Linear Systems With Global Constraints and Time-Varying Communication

• 成果类型: Article
• 署名作者: Jin, Bo; Li, Huiping; Yan, Weisheng; Cao, Ming
• 署名单位: Northwestern Polytechnical University; University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3021528
• 发表日期: 2021
• 页码: 3393-3400
• 关键词: Optimization; communication networks; Heuristic algorithms; Prediction algorithms; Predictive control; CONVERGENCE; Linear systems; distributed model predictive control (DMPC); global constraints; gossip-based push-sum algorithm; push-sum dual gradient (PSDG) algorithm; time-varying directed graphs

摘要

In the article, we study the distributed model predictive control (DMPC) problem for a network of linear discrete-time systems, where the system dynamics are decoupled, the system constraints are coupled, and the communication networks are described by time-varying directed graphs. A novel distributed optimization algorithm called the push-sum dual gradient (PSDG) algorithm is proposed to solve the dual problem of the DMPC optimization problem in a fully distributed way. We prove that the sequences of the primal, and dual variables converge to their optimal values. Furthermore, to solve the implementation issues, stopping criteria are designed to allow early termination of the PSDG Algorithm, and the gossip-based push-sum algorithm is proposed to check the stopping criteria in a distributed manner. It is shown that the optimization problem is iteratively feasible, and the closed-loop system is exponentially stable. Finally, the effectiveness of the proposed DMPC approach is verified via an example.