Stochastic Optimal Control Problems

  • Michał Kisielewicz
Part of the Springer Optimization and Its Applications book series (SOIA, volume 80)


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.


Weak Solution Optimal Control Problem Stochastic Differential Equation Stochastic Control Admissible Pair 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Michał Kisielewicz
    • 1
  1. 1.Faculty of MathematicsUniversity of Zielona GóraZielona GóraPoland

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