Weak Dynamic Programming for Generalized State Constraints
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.
|Date of creation:||May 2011|
|Date of revision:||Oct 2012|
|Publication status:||Published in SIAM Journal on Control and Optimization, Vol. 50, No. 6, pp. 3344-3373, 2012|
|Contact details of provider:|| Web page: http://arxiv.org/ |
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