{"title":"通过参数化输入推理实现近似受限随机最优控制","authors":"Shahbaz P. Qadri Syed, He Bai","doi":"10.1016/j.automatica.2024.111978","DOIUrl":null,"url":null,"abstract":"<div><div>Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic Gaussian problems. In this work, we propose an Expectation–Maximization (EM) based inference procedure to generate state-feedback controls for constrained SOC problems. We consider the inequality constraints for the state and controls and also the structural constraints for the controls. We employ barrier functions to address state and control constraints. We show that the expectation step leads to smoothing of the state-control pair while the maximization step on the non-zero subsets of the control parameters allows inference of structured stochastic optimal controllers. We demonstrate the effectiveness of the algorithm on unicycle obstacle avoidance and four-unicycle formation control examples. In these examples, we perform an empirical study on the parametric effect of barrier functions on the state constraint satisfaction. We also present a comparative study of smoothing algorithms on the performance of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximate constrained stochastic optimal control via parameterized input inference\",\"authors\":\"Shahbaz P. Qadri Syed, He Bai\",\"doi\":\"10.1016/j.automatica.2024.111978\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic Gaussian problems. In this work, we propose an Expectation–Maximization (EM) based inference procedure to generate state-feedback controls for constrained SOC problems. We consider the inequality constraints for the state and controls and also the structural constraints for the controls. We employ barrier functions to address state and control constraints. We show that the expectation step leads to smoothing of the state-control pair while the maximization step on the non-zero subsets of the control parameters allows inference of structured stochastic optimal controllers. We demonstrate the effectiveness of the algorithm on unicycle obstacle avoidance and four-unicycle formation control examples. In these examples, we perform an empirical study on the parametric effect of barrier functions on the state constraint satisfaction. We also present a comparative study of smoothing algorithms on the performance of the proposed approach.</div></div>\",\"PeriodicalId\":55413,\"journal\":{\"name\":\"Automatica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.8000,\"publicationDate\":\"2024-10-21\",\"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/S0005109824004722\",\"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/S0005109824004722","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}
Approximate constrained stochastic optimal control via parameterized input inference
Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic Gaussian problems. In this work, we propose an Expectation–Maximization (EM) based inference procedure to generate state-feedback controls for constrained SOC problems. We consider the inequality constraints for the state and controls and also the structural constraints for the controls. We employ barrier functions to address state and control constraints. We show that the expectation step leads to smoothing of the state-control pair while the maximization step on the non-zero subsets of the control parameters allows inference of structured stochastic optimal controllers. We demonstrate the effectiveness of the algorithm on unicycle obstacle avoidance and four-unicycle formation control examples. In these examples, we perform an empirical study on the parametric effect of barrier functions on the state constraint satisfaction. We also present a comparative study of smoothing algorithms on the performance of the proposed approach.
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.