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669. Optimal control of a generalized Fokker-Planck equation
Invited abstract in session TD-33: Optimal control theory, stream Optimal Control Theory and Applications.
Tuesday, 14:30-16:00Room: 42 (building: 303A)
Authors (first author is the speaker)
| 1. | Stefana-Lucia Anita
|
| Octav Mayer Institute of Mathematics of the Romanian Academy |
Abstract
Our talk concerns an optimal control problem (P) related to a generalized Fokker-Planck (FP) equation. First we establish some properties of the solutions to the generalized FP equation using a semigroup approach in an appropriate Sobolev space. Problem (P) is proven to be deeply related to a stochastic optimal control problem (PS) for a McKean-Vlasov equation. We prove next the existence of an optimal control for the deterministic problem (P) and the existence of an optimal control for an approximating optimal control problem (Ph) related to a backward Euler approximation of the generalized FP equation (with a constant discretization step h). Finally, we show that under additional hypotheses "(Ph) converges to (P)" in a certain sense. First order necessary optimality conditions for (Ph) are derived as well.
Keywords
- Optimal Control
- Control Theory
Status: accepted
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