{"title":"通过假设-保证合同的凸优化实现线性系统的组合合成","authors":"","doi":"10.1016/j.automatica.2024.111816","DOIUrl":null,"url":null,"abstract":"<div><p>We take a divide and conquer approach to design controllers for reachability problems given large-scale linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. We treat the couplings as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. The main contribution of this paper is a method to derive the contracts via a novel parameterization and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems. We present numerical examples, including a scalability study on a system with tens of thousands of dimensions, and a simple case study on applying our method to a distributed Model Predictive Control (MPC) problem in a power system.</p></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Compositional synthesis for linear systems via convex optimization of assume-guarantee contracts\",\"authors\":\"\",\"doi\":\"10.1016/j.automatica.2024.111816\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We take a divide and conquer approach to design controllers for reachability problems given large-scale linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. We treat the couplings as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. The main contribution of this paper is a method to derive the contracts via a novel parameterization and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems. We present numerical examples, including a scalability study on a system with tens of thousands of dimensions, and a simple case study on applying our method to a distributed Model Predictive Control (MPC) problem in a power system.</p></div>\",\"PeriodicalId\":55413,\"journal\":{\"name\":\"Automatica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.8000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Automatica\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0005109824003108\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824003108","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Compositional synthesis for linear systems via convex optimization of assume-guarantee contracts
We take a divide and conquer approach to design controllers for reachability problems given large-scale linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. We treat the couplings as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. The main contribution of this paper is a method to derive the contracts via a novel parameterization and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems. We present numerical examples, including a scalability study on a system with tens of thousands of dimensions, and a simple case study on applying our method to a distributed Model Predictive Control (MPC) problem in a power system.
期刊介绍:
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.