{"title":"非线性二次型跟踪问题最优控制的迭代方法","authors":"Xin Ning, Walter Bomela, Shin Li","doi":"10.23919/ACC45564.2020.9147364","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate an iterative method for computing optimal controls for general affine nonlinear quadratic tracking problems. The control law is computed iteratively by solving a sequence of linear quadratic tracking problems and, in particular, it consists of solving a set of coupled differential equations derived from the Hamilton-Jacobi-Bellman equation. The convergence of the iterative scheme is shown by constructing a contraction mapping and using the fixed-point theorem. The versatility and effectiveness of the proposed method is demonstrated in numerical simulations of three structurally different nonlinear systems.","PeriodicalId":288450,"journal":{"name":"2020 American Control Conference (ACC)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Iterative Method for Optimal Control of Nonlinear Quadratic Tracking Problems\",\"authors\":\"Xin Ning, Walter Bomela, Shin Li\",\"doi\":\"10.23919/ACC45564.2020.9147364\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate an iterative method for computing optimal controls for general affine nonlinear quadratic tracking problems. The control law is computed iteratively by solving a sequence of linear quadratic tracking problems and, in particular, it consists of solving a set of coupled differential equations derived from the Hamilton-Jacobi-Bellman equation. The convergence of the iterative scheme is shown by constructing a contraction mapping and using the fixed-point theorem. The versatility and effectiveness of the proposed method is demonstrated in numerical simulations of three structurally different nonlinear systems.\",\"PeriodicalId\":288450,\"journal\":{\"name\":\"2020 American Control Conference (ACC)\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2020 American Control Conference (ACC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23919/ACC45564.2020.9147364\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 American Control Conference (ACC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23919/ACC45564.2020.9147364","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Iterative Method for Optimal Control of Nonlinear Quadratic Tracking Problems
In this paper, we investigate an iterative method for computing optimal controls for general affine nonlinear quadratic tracking problems. The control law is computed iteratively by solving a sequence of linear quadratic tracking problems and, in particular, it consists of solving a set of coupled differential equations derived from the Hamilton-Jacobi-Bellman equation. The convergence of the iterative scheme is shown by constructing a contraction mapping and using the fixed-point theorem. The versatility and effectiveness of the proposed method is demonstrated in numerical simulations of three structurally different nonlinear systems.