Discrete approximations of the Hamilton-Jacobi equation for an optimal control problem of a differential-algebraic system

J. Frédéric Bonnans; Philippe Chartierand; Housnaa Zidani

Discrete approximations of the Hamilton-Jacobi equation for an optimal control problem of a differential-algebraic system

J. Frédéric Bonnans
, Philippe Chartierand
, Housnaa Zidani

École Polytechnique

INRIA Rocquencourt
INRIA Institut National de Recherche en Informatique et en Automatique

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

3 Citations (Scopus)

Abstract

This paper discusses the numerical resolution of the Hamilton-Jacobi-Bellman equation associated with optimal control problem when the state equation is of algebraic differential type. We discuss two numerical schemes. The first reduces to the standard framework, while the second does not suppose any knowledge of the Jacobian of the data. We obtain some error estimates, and display numerical results obtained on a simple test problem.

Original language	English
Pages (from-to)	33-55
Number of pages	23
Journal	Control and Cybernetics
Volume	32
Issue number	1
Publication status	Published - 14 Oct 2003

Keywords

Approximation schemes
Differential-algebraic system
Dynamic programming
Finite differences
Hamilton-Jacobi-Bellman equation
Optimal control
Viscosity solutions

Cite this

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title = "Discrete approximations of the Hamilton-Jacobi equation for an optimal control problem of a differential-algebraic system",

abstract = "This paper discusses the numerical resolution of the Hamilton-Jacobi-Bellman equation associated with optimal control problem when the state equation is of algebraic differential type. We discuss two numerical schemes. The first reduces to the standard framework, while the second does not suppose any knowledge of the Jacobian of the data. We obtain some error estimates, and display numerical results obtained on a simple test problem.",

keywords = "Approximation schemes, Differential-algebraic system, Dynamic programming, Finite differences, Hamilton-Jacobi-Bellman equation, Optimal control, Viscosity solutions",

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AU - Chartierand, Philippe

AU - Zidani, Housnaa

PY - 2003/10/14

Y1 - 2003/10/14

N2 - This paper discusses the numerical resolution of the Hamilton-Jacobi-Bellman equation associated with optimal control problem when the state equation is of algebraic differential type. We discuss two numerical schemes. The first reduces to the standard framework, while the second does not suppose any knowledge of the Jacobian of the data. We obtain some error estimates, and display numerical results obtained on a simple test problem.

AB - This paper discusses the numerical resolution of the Hamilton-Jacobi-Bellman equation associated with optimal control problem when the state equation is of algebraic differential type. We discuss two numerical schemes. The first reduces to the standard framework, while the second does not suppose any knowledge of the Jacobian of the data. We obtain some error estimates, and display numerical results obtained on a simple test problem.

KW - Approximation schemes

KW - Differential-algebraic system

KW - Dynamic programming

KW - Finite differences

KW - Hamilton-Jacobi-Bellman equation

KW - Optimal control

KW - Viscosity solutions

UR - https://www.scopus.com/pages/publications/0141506927

M3 - Article

AN - SCOPUS:0141506927

SN - 0324-8569

VL - 32

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EP - 55

JO - Control and Cybernetics

JF - Control and Cybernetics

IS - 1

ER -

Discrete approximations of the Hamilton-Jacobi equation for an optimal control problem of a differential-algebraic system

Abstract

Keywords

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