A dual-mode framework for lifting-based self-triggered model predictive control of linear systems with a guarantee of minimum triggering in steady state
{"title":"A dual-mode framework for lifting-based self-triggered model predictive control of linear systems with a guarantee of minimum triggering in steady state","authors":"Junsoo Kim, Gyunghoon Park","doi":"10.1016/j.jfranklin.2025.107805","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we propose a new self-triggered model predictive control (ST-MPC) that stabilizes a class of linear time-invariant systems, under limited communication resource between plant and controller. A remarkable feature of the ST-MPC presented this work is to trigger as little as possible in steady state, by adopting the lifting method in order to realize the dual-mode paradigm in the ST-MPC formulation. In the lifting-based dual-mode framework, the steady-state requirement on minimum triggering can be achieved by driving the system state into a (maximal) positively invariant set constructed based on a large-sized lifted model, for which a new self-triggering mechanism is also proposed to plan a sequence of moments of triggering in transient (that takes place more frequently than in steady state if needed). The solution of a lifting-based discrete-time algebraic Riccati equation (DARE) plays an essential role in the ST-MPC design, whose existence condition and structural properties are thus intensively studied. The recursive feasibility and closed-loop stability are mathematically analyzed, while the validity of the proposed ST-MPC is verified via computer-aided simulation.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 12","pages":"Article 107805"},"PeriodicalIF":4.2000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003225002984","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose a new self-triggered model predictive control (ST-MPC) that stabilizes a class of linear time-invariant systems, under limited communication resource between plant and controller. A remarkable feature of the ST-MPC presented this work is to trigger as little as possible in steady state, by adopting the lifting method in order to realize the dual-mode paradigm in the ST-MPC formulation. In the lifting-based dual-mode framework, the steady-state requirement on minimum triggering can be achieved by driving the system state into a (maximal) positively invariant set constructed based on a large-sized lifted model, for which a new self-triggering mechanism is also proposed to plan a sequence of moments of triggering in transient (that takes place more frequently than in steady state if needed). The solution of a lifting-based discrete-time algebraic Riccati equation (DARE) plays an essential role in the ST-MPC design, whose existence condition and structural properties are thus intensively studied. The recursive feasibility and closed-loop stability are mathematically analyzed, while the validity of the proposed ST-MPC is verified via computer-aided simulation.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.