A Feedback Design For Numerical Solution To Optimal Control Problems Based On Hamilton-Jacobi-Bellman Equation

Zhen Zhen Tao; Bing Sun

doi:10.3934/era.2021046

A Feedback Design For Numerical Solution To Optimal Control Problems Based On Hamilton-Jacobi-Bellman Equation

Zhen Zhen Tao^*, Bing Sun

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 viscosity solution (DPVS) approach. Dierent 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 numerical results.

Original language	English
Pages (from-to)	3429-3447
Number of pages	19
Journal	Electronic Research Archive
Volume	29
Issue number	5
DOIs	https://doi.org/10.3934/era.2021046
Publication status	Published - Nov 2021

Keywords

Dynamic programming
Hamilton-Jacobi-Bellman equation
interpolation
optimal feedback control
upwind Finite difference scheme
viscosity solution

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abstract = "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 viscosity solution (DPVS) approach. Dierent 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 numerical results.",

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author = "Tao, {Zhen Zhen} and Bing Sun",

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AU - Sun, Bing

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N2 - 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 viscosity solution (DPVS) approach. Dierent 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 numerical results.

AB - 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 viscosity solution (DPVS) approach. Dierent 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 numerical results.

KW - Dynamic programming

KW - Hamilton-Jacobi-Bellman equation

KW - interpolation

KW - optimal feedback control

KW - upwind Finite difference scheme

KW - viscosity solution

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ER -

A Feedback Design For Numerical Solution To Optimal Control Problems Based On Hamilton-Jacobi-Bellman Equation

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Keywords

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