{"title":"基于路径拟合变分积分器的机械系统优化控制","authors":"Xinlei Kong, Shiyu Yu, Huibin Wu","doi":"10.1115/1.4064360","DOIUrl":null,"url":null,"abstract":"\n In view of the crucial importance of optimal control in many application areas and the improved performance of path-fitted variational integrators, the paper links these two aspects and presents a methodology to find optimal control policies for mechanical systems. The main process of the methodology is employing path-fitted variational integrators to discretize the forced mechanical equations and further taking the obtained discrete equations as equality constraints for the final optimization problem. Simultaneously, the discretization also provides a reasonable way to approximate the objective functional and incorporate the boundary conditions. With the transformation of optimal control problems into nonlinear optimization problems, all the benefits of path-fitted variational integrators are inherited by the presented methodology, mainly expressed in giving more faithful optimizations and thus more accurate solutions, providing greater possibility of global optimality, as well as conserving computed control efforts. These superiorities, verified by the optimal control of an overhead crane, indicate that the methodology has high potential application in industrial control field.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"35 5","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Control of Mechanical Systems Based On Path-Fitted Variational Integrators\",\"authors\":\"Xinlei Kong, Shiyu Yu, Huibin Wu\",\"doi\":\"10.1115/1.4064360\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In view of the crucial importance of optimal control in many application areas and the improved performance of path-fitted variational integrators, the paper links these two aspects and presents a methodology to find optimal control policies for mechanical systems. The main process of the methodology is employing path-fitted variational integrators to discretize the forced mechanical equations and further taking the obtained discrete equations as equality constraints for the final optimization problem. Simultaneously, the discretization also provides a reasonable way to approximate the objective functional and incorporate the boundary conditions. With the transformation of optimal control problems into nonlinear optimization problems, all the benefits of path-fitted variational integrators are inherited by the presented methodology, mainly expressed in giving more faithful optimizations and thus more accurate solutions, providing greater possibility of global optimality, as well as conserving computed control efforts. These superiorities, verified by the optimal control of an overhead crane, indicate that the methodology has high potential application in industrial control field.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":\"35 5\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-12-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Nonlinear Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4064360\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4064360","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Optimal Control of Mechanical Systems Based On Path-Fitted Variational Integrators
In view of the crucial importance of optimal control in many application areas and the improved performance of path-fitted variational integrators, the paper links these two aspects and presents a methodology to find optimal control policies for mechanical systems. The main process of the methodology is employing path-fitted variational integrators to discretize the forced mechanical equations and further taking the obtained discrete equations as equality constraints for the final optimization problem. Simultaneously, the discretization also provides a reasonable way to approximate the objective functional and incorporate the boundary conditions. With the transformation of optimal control problems into nonlinear optimization problems, all the benefits of path-fitted variational integrators are inherited by the presented methodology, mainly expressed in giving more faithful optimizations and thus more accurate solutions, providing greater possibility of global optimality, as well as conserving computed control efforts. These superiorities, verified by the optimal control of an overhead crane, indicate that the methodology has high potential application in industrial control field.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.