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

^*此作品的通讯作者

数学学院

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	3429-3447
页数	19
期刊	Electronic Research Archive
卷	29
期	5
DOI	https://doi.org/10.3934/era.2021046
出版状态	已出版 - 11月 2021

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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.",

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

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

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AU - Tao, Zhen Zhen

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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