Weak Dynamic Programming for Generalized State Constraints
Optimization and Control
2012-12-21 v2 Systems and Control
Analysis of PDEs
Probability
Risk Management
Abstract
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.
Cite
@article{arxiv.1105.0745,
title = {Weak Dynamic Programming for Generalized State Constraints},
author = {Bruno Bouchard and Marcel Nutz},
journal= {arXiv preprint arXiv:1105.0745},
year = {2012}
}
Comments
36 pages;forthcoming in 'SIAM Journal on Control and Optimization'