Friday, 16:15 - 16:40 h, Room: MA 144

 

Tony Huschto
Solving stochastic optimal control problems by a polynomial chaos approach

Coauthor: Sebastian Sager

 

Abstract:
In optimal control problems driven by stochastic differential equations, the detection of optimal (Markovian) decision rules is a very challenging task. Explicit solutions can be found in only very few cases by considering the corresponding Hamilton-Jacobi-Bellman equation. Thus numerical methods, e.g., based on Markov chains, have attracted great interest.
In this contribution, we introduce a new methodology for solving continuous finite-horizon stochastic optimal control problems. We utilize ideas for approximating stochastic differential equations within the framework of Polynomial Chaos and expand this to reformulate stochastic optimal control problems directly into deterministic ones. This allows us to use Bock's direct multiple shooting method, a state of the art simultaneous method to solve optimization and simulation tasks at the same time. We implement different approaches to preserve the feedback character of the optimal decision rules. Numerical examples illustrate this new methodology and show the validity of the developed reformulations.

 

Talk 3 of the invited session Fri.3.MA 144
"PDE constrained stochastic optimization" [...]
Cluster 22
"Stochastic optimization" [...]

 

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