Approximate Solutions to the Hamilton-Jacobi Equations for Generating Functions

作     者：HAO Zhiwei FUJIMOTO Kenji ZHANG Qiuhua HAO Zhiwei;FUJIMOTO Kenji;ZHANG Qiuhua

作者机构：Department of Astronautical Science and MechanicsHarbin Institute of TechnologyHarbin 150001China Department of Aeronautics and AstronauticsKyoto UniversityC3 Bldg.Kyotodaigaku-katsuraNishikyo-kuKyoto 615-8540Japan 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2020年第33卷第2期

页      面：261-288页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by“the Fundamental Research Funds for the Central Universities”under Grant No.HIT.NSRIF.201620 

主　　题：Generating functions Hamilton-Jacobi equations optimal control Taylor series expansion two-point boundary-value problems 

摘      要：For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this *** algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations ***,the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical *** a generating function is found,it can be used to generate a family of optimal control for different boundary *** the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional *** is useful to online optimal trajectory generation *** examples illustrate the effectiveness of the proposed algorithm.