Weak Dynamic Programming for Generalized State Constraints

Nutz, Marcel; Bouchard, Bruno

Nutz, Marcel; Bouchard, Bruno (2012), Weak Dynamic Programming for Generalized State Constraints, SIAM Journal on Control and Optimization, 50, 6, p. 3344-3373. http://dx.doi.org/10.1137/110852942

Type

Article accepté pour publication ou publié

Date

2012

Nom de la revue

SIAM Journal on Control and Optimization

Volume

Numéro

Éditeur

SIAM

Pages

3344-3373

Résumé (EN)

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints.

Mots-clés

Comparison theorem; Viscosity solution; Hamilton-Jacobi-Bellman equation; Expectation constraint; State constraint; Weak dynamic programming