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 \(\,\mathcal {Z}^x_D(F,\mathcal {G})\) defined in Remark 6.3.1 of Chapter 6, by the set of all weak solutions to (equivalence classes to) \(\,SDI(F,\mathcal {G})\,\) satisfying the initial condition x 0 = x with \(x\in D\subset \mathbb {R}^d\). We begin with an introductory remark dealing with stochastic optimal control problems for systems described by stochastic differential equations depending on stochastic control parameters.
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References
Ahmed, N.U.: Optimal control of stochastic dynamical systems. Inf. Contr. 22(1), 13–30 (1973)
Kisielewicz, M.: Stochastic Differential Inclusions and Applications. Springer, Berlin (2013)
Øksendal, B.: Stochastionc Differential Equations. Springer, Berlin (1998)
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Kisielewicz, M. (2020). Stochastic Optimal Control Problems. In: Set-Valued Stochastic Integrals and Applications. Springer Optimization and Its Applications, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-030-40329-4_8
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DOI: https://doi.org/10.1007/978-3-030-40329-4_8
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