Discrete Approximations of the Hamilton-Jacobi Equation for an Optimal Control Problem of a Differential-Algebraic System

J. Frederic Bonnans (1) , Philippe Chartier (2) , Hasnaa Zidani (1, 3)

1 SYDOCO - Dynamic systems, optimisation and optimal command
2 ALADIN - Algorithms Adapted to Intensive Numerical Computing
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Domaines: Autre [cs.OH]; Optimisation et contrôle [math.OC]

J. Frederic Bonnans, Philippe Chartier, Hasnaa Zidani. Discrete Approximations of the Hamilton-Jacobi Equation for an Optimal Control Problem of a Differential-Algebraic System. [Research Report] RR-4265, INRIA. 2001. ⟨inria-00072322⟩