{"title":"解决终端最优控制问题的进化Сomputation","authors":"A. Diveev","doi":"10.18698/0236-3933-2023-1-44-59","DOIUrl":null,"url":null,"abstract":"The present article considers the problem of numerical solution of the terminal optimal control problem. The general statement of the terminal optimal control problem and a brief overview of its solving methods are presented. With a direct approach and reduction of the optimal control problem to the finite-dimensional optimization problem, the target functional on the space of desired parameters, regardless of the type of approximation of the control function, may not have the unimodal property. Therefore, it is advisable to use evolutionary algorithms to solve the problem. A general approach to solving the terminal optimal control problem of evolutionary computational algorithms is presented. The paper presents a description of some evolutionary algorithms that were selected as the most effective for solving the optimal control problem. A hybrid evolutionary algorithm based on a combination of several evolutionary algorithms is considered. The computational experiment considers the terminal optimal control problems, for which optimal solutions were found by known classical numerical methods that use the gradient of the target functionality when searching. Comparison of the results obtained by classical and evolutionary methods by functional values and computational costs allows us to conclude that evolutionary algorithms are able to effectively solve the terminal optimal control problems","PeriodicalId":12961,"journal":{"name":"Herald of the Bauman Moscow State Technical University. Series Natural Sciences","volume":"83 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evolutionary Сomputation for Solving the Terminal Optimal Control Problem\",\"authors\":\"A. Diveev\",\"doi\":\"10.18698/0236-3933-2023-1-44-59\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The present article considers the problem of numerical solution of the terminal optimal control problem. The general statement of the terminal optimal control problem and a brief overview of its solving methods are presented. With a direct approach and reduction of the optimal control problem to the finite-dimensional optimization problem, the target functional on the space of desired parameters, regardless of the type of approximation of the control function, may not have the unimodal property. Therefore, it is advisable to use evolutionary algorithms to solve the problem. A general approach to solving the terminal optimal control problem of evolutionary computational algorithms is presented. The paper presents a description of some evolutionary algorithms that were selected as the most effective for solving the optimal control problem. A hybrid evolutionary algorithm based on a combination of several evolutionary algorithms is considered. The computational experiment considers the terminal optimal control problems, for which optimal solutions were found by known classical numerical methods that use the gradient of the target functionality when searching. Comparison of the results obtained by classical and evolutionary methods by functional values and computational costs allows us to conclude that evolutionary algorithms are able to effectively solve the terminal optimal control problems\",\"PeriodicalId\":12961,\"journal\":{\"name\":\"Herald of the Bauman Moscow State Technical University. Series Natural Sciences\",\"volume\":\"83 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Herald of the Bauman Moscow State Technical University. Series Natural Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18698/0236-3933-2023-1-44-59\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Herald of the Bauman Moscow State Technical University. Series Natural Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18698/0236-3933-2023-1-44-59","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Evolutionary Сomputation for Solving the Terminal Optimal Control Problem
The present article considers the problem of numerical solution of the terminal optimal control problem. The general statement of the terminal optimal control problem and a brief overview of its solving methods are presented. With a direct approach and reduction of the optimal control problem to the finite-dimensional optimization problem, the target functional on the space of desired parameters, regardless of the type of approximation of the control function, may not have the unimodal property. Therefore, it is advisable to use evolutionary algorithms to solve the problem. A general approach to solving the terminal optimal control problem of evolutionary computational algorithms is presented. The paper presents a description of some evolutionary algorithms that were selected as the most effective for solving the optimal control problem. A hybrid evolutionary algorithm based on a combination of several evolutionary algorithms is considered. The computational experiment considers the terminal optimal control problems, for which optimal solutions were found by known classical numerical methods that use the gradient of the target functionality when searching. Comparison of the results obtained by classical and evolutionary methods by functional values and computational costs allows us to conclude that evolutionary algorithms are able to effectively solve the terminal optimal control problems
期刊介绍:
The journal is aimed at publishing most significant results of fundamental and applied studies and developments performed at research and industrial institutions in the following trends (ASJC code): 2600 Mathematics 2200 Engineering 3100 Physics and Astronomy 1600 Chemistry 1700 Computer Science.