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Stochastic Optimal Control Problems

In: Stochastic Differential Inclusions and Applications

Author

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  • Michał Kisielewicz

    (University of Zielona Góra)

Abstract

This chapter contains some optimal control problems for systems described by stochastic functional and partial differential inclusions. The existence of optimal controls and optimal solutions for such systems is a consequence of the weak compactness of the set $$\mathcal{X}_{sx}(F,G)$$ of all weak solutions of (equivalence classes of) SFI(F, G) satisfying an initial condition x s = x, measurable selection theorems, and stochastic representation theorems for solutions of partial differential inclusions presented in Chap. 6. We begin with introductory remarks dealing with optimal control problems of systems described by stochastic differential equations.

Suggested Citation

  • Michał Kisielewicz, 2013. "Stochastic Optimal Control Problems," Springer Optimization and Its Applications, in: Stochastic Differential Inclusions and Applications, edition 127, chapter 0, pages 253-273, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-6756-4_7
    DOI: 10.1007/978-1-4614-6756-4_7
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