{"title":"LIE-POISSON REDUCTION FOR OPTIMAL CONTROL OF LEFT-INVARIANT CONTROL SYSTEMS WITH SUBGROUP SYMMETRY","authors":"Leonardo Colombo, Efstratios Stratoglou","doi":"10.1016/S0034-4877(23)00015-0","DOIUrl":null,"url":null,"abstract":"<div><p>We study the reduction by symmetries for optimality conditions in optimal control problems of left-invariant affine control systems with partial symmetry breaking cost functions. We recast the optimal control problem as a constrained problem with a partial symmetry breaking Hamiltonian and we obtain the reduced optimality conditions for normal extrema from Pontryagin's Maximum Principle and a Lie--Poisson bracket on the reduced state space. We apply the results to an energy-minimum obstacle avoidance problems.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"91 1","pages":"Pages 131-141"},"PeriodicalIF":1.0000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487723000150","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 1
Abstract
We study the reduction by symmetries for optimality conditions in optimal control problems of left-invariant affine control systems with partial symmetry breaking cost functions. We recast the optimal control problem as a constrained problem with a partial symmetry breaking Hamiltonian and we obtain the reduced optimality conditions for normal extrema from Pontryagin's Maximum Principle and a Lie--Poisson bracket on the reduced state space. We apply the results to an energy-minimum obstacle avoidance problems.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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