{"title":"Minimization of an Integral Quadratic Estimate of the Controlled Variable in Systems with Distributed Parameters","authors":"Yu. E. Pleshivtseva, E. Ya. Rapoport","doi":"10.1134/s1064230724700084","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A constructive method for solving the linear-quadratic problem of the optimal control of a parabolic-type system with distributed parameters is proposed under the condition of the uniform estimation of the target sets. The optimality criterion takes the form of an integral quadratic estimate of the controlled state function in the spatiotemporal domain of its definition. A parameterized representation of the control inputs is given with the required accuracy within special intervals of the optimal process, where the control inputs cannot be determined using first-order analytical optimality conditions. The proposed approach is based on the previously developed alternance method for constructing parameterized algorithms of programmed control, which heavily relies on the fundamental regularities of the subject area. It is demonstrated that the equations of the optimal regulators within the special intervals are reduced to the linear feedback algorithms based on the measured states of the objects. These algorithms are supplemented with switches at the boundary points to apply the admissible control inputs corresponding to the calculated values of the controlled variable.</p>","PeriodicalId":50223,"journal":{"name":"Journal of Computer and Systems Sciences International","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and Systems Sciences International","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s1064230724700084","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
A constructive method for solving the linear-quadratic problem of the optimal control of a parabolic-type system with distributed parameters is proposed under the condition of the uniform estimation of the target sets. The optimality criterion takes the form of an integral quadratic estimate of the controlled state function in the spatiotemporal domain of its definition. A parameterized representation of the control inputs is given with the required accuracy within special intervals of the optimal process, where the control inputs cannot be determined using first-order analytical optimality conditions. The proposed approach is based on the previously developed alternance method for constructing parameterized algorithms of programmed control, which heavily relies on the fundamental regularities of the subject area. It is demonstrated that the equations of the optimal regulators within the special intervals are reduced to the linear feedback algorithms based on the measured states of the objects. These algorithms are supplemented with switches at the boundary points to apply the admissible control inputs corresponding to the calculated values of the controlled variable.
期刊介绍：
Journal of Computer and System Sciences International is a journal published in collaboration with the Russian Academy of Sciences. It covers all areas of control theory and systems. The journal features papers on the theory and methods of control, as well as papers devoted to the study, design, modeling, development, and application of new control systems. The journal publishes papers that reflect contemporary research and development in the field of control. Particular attention is given to applications of computer methods and technologies to control theory and control engineering. The journal publishes proceedings of international scientific conferences in the form of collections of regular journal articles and reviews by top experts on topical problems of modern studies in control theory.
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