Weak Dynamic Programming for Generalized State Constraints

Details Weak Dynamic Programming for Generalized State Constraints Weak Dynamic Programming for Generalized State Constraints

2011-05-04

arxiv.org/abs/1105.0745v1

Mathematics

Optimization and Control

34 pages

Scientific paper

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.

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