Open AccessA feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation
Author(s) -
ZhenZhen Tao,
Bing Sun
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021046
Subject(s) - hamilton–jacobi–bellman equation , viscosity solution , bellman equation , dynamic programming , optimal control , hamilton–jacobi equation , mathematics , fast marching method , mathematical optimization , computation , numerical analysis , computer science , mathematical analysis , algorithm
In this paper, we present a feedback design for numerical solution to optimal control problems, which is based on solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. An upwind finite-difference scheme is adopted to solve the HJB equation under the framework of the dynamic programming viscosity solution (DPVS) approach. Different from the usual existing algorithms, the numerical control function is interpolated in turn to gain the approximation of optimal feedback control-trajectory pair. Five simulations are executed and both of them, without exception, output the accurate numerical results. The design can avoid solving the HJB equation repeatedly, thus efficaciously promote the computation efficiency and save memory.