Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods

Mohsen Mehrali-Varjani; Mostafa Shamsi; Alaeddin Malek

Kybernetika (2018)

  • Volume: 54, Issue: 4, page 629-647
  • ISSN: 0023-5954

Abstract

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This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem is computed. In addition, to get more efficient and accurate method, the domain decomposition strategy is proposed with the pseudospectral spatial discretization. Five numerical examples are presented to demonstrate the efficiency and accuracy of the proposed hybrid method.

How to cite

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Mehrali-Varjani, Mohsen, Shamsi, Mostafa, and Malek, Alaeddin. "Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods." Kybernetika 54.4 (2018): 629-647. <http://eudml.org/doc/294663>.

@article{Mehrali2018,
abstract = {This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem is computed. In addition, to get more efficient and accurate method, the domain decomposition strategy is proposed with the pseudospectral spatial discretization. Five numerical examples are presented to demonstrate the efficiency and accuracy of the proposed hybrid method.},
author = {Mehrali-Varjani, Mohsen, Shamsi, Mostafa, Malek, Alaeddin},
journal = {Kybernetika},
keywords = {nonlinear optimal control; pseudospectral method; Hamilton–Jacobi–Bellman equation},
language = {eng},
number = {4},
pages = {629-647},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods},
url = {http://eudml.org/doc/294663},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Mehrali-Varjani, Mohsen
AU - Shamsi, Mostafa
AU - Malek, Alaeddin
TI - Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 4
SP - 629
EP - 647
AB - This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem is computed. In addition, to get more efficient and accurate method, the domain decomposition strategy is proposed with the pseudospectral spatial discretization. Five numerical examples are presented to demonstrate the efficiency and accuracy of the proposed hybrid method.
LA - eng
KW - nonlinear optimal control; pseudospectral method; Hamilton–Jacobi–Bellman equation
UR - http://eudml.org/doc/294663
ER -

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