Hao, Zhiwei; Fujimoto, Kenji; Zhang, Qiuhua Approximate solutions to the Hamilton-Jacobi equations for generating functions. (English) Zbl 1447.49050 J. Syst. Sci. Complex. 33, No. 2, 261-288 (2020). Summary: 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 paper. 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 recursively. Furthermore, the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition. Once a generating function is found, it can be used to generate a family of optimal control for different boundary conditions. Since the generating function is computed off-line, the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method. It is useful to online optimal trajectory generation problems. Numerical examples illustrate the effectiveness of the proposed algorithm. MSC: 49M41 PDE constrained optimization (numerical aspects) 35F21 Hamilton-Jacobi equations Keywords:generating functions; Hamilton-Jacobi equations; optimal control; Taylor series expansion; two-point boundary-value problems Software:bvp4c PDFBibTeX XMLCite \textit{Z. Hao} et al., J. Syst. Sci. Complex. 33, No. 2, 261--288 (2020; Zbl 1447.49050) Full Text: DOI References: [1] Locatelli, A., Optimal Control: An Introduction (2001), Basel-Boston-Berlin: Birkhauser Verlag, Basel-Boston-Berlin · Zbl 1096.49500 [2] Keller, H. 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