Weak Dynamic Programming for Generalized State Constraints
arXiv:1105.0745 · doi:10.1137/110852942
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.
36 pages;forthcoming in 'SIAM Journal on Control and Optimization'