Stochastic Optimal Control Problems

Michał Kisielewicz
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Michał Kisielewicz: University of Zielona Góra

Chapter Chapter 8 in Set-Valued Stochastic Integrals and Applications, 2020, pp 249-258 from Springer

Abstract: Abstract This chapter contains some optimal control problems for systems described by stochastic differential inclusions. The existence of optimal controls and optimal solutions for such systems is a consequence of the weak compactness in distribution of the set Z D x ( F , G ) $$\,\mathcal {Z}^x_D(F,\mathcal {G})$$ defined in Remark 6.3.1 of Chapter 6 , by the set of all weak solutions to (equivalence classes to) S D I ( F , G ) $$\,SDI(F,\mathcal {G})\,$$ satisfying the initial condition x 0 = x with x ∈ D ⊂ ℝ d $$x\in D\subset \mathbb {R}^d$$ . We begin with an introductory remark dealing with stochastic optimal control problems for systems described by stochastic differential equations depending on stochastic control parameters.

Date: 2020
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DOI: 10.1007/978-3-030-40329-4_8

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