This paper deals with a family of stochastic control problems in Hilbert spaces which arises in many engineering/economic/financial applications (in particular the ones featuring boundary control and control of delay equations with delay in the control) and for which it is difficult to apply the dynamic programming approach due to the unboundedness of the control operator and to the lack of regularity of the underlying transition semigroup. We introduce a specific concept of partial derivative, designed for this situation, and we develop a method to prove that the associated HJB equation has a solution with enough regularity to find optimal controls in feedback form.

Stochastic Control Problems with Unbounded Control Operators: Solutions Through Generalized Derivatives / Gozzi, Fausto; Masiero, F.. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 61:2(2023), pp. 586-619. [10.1137/22m1474679]

Stochastic Control Problems with Unbounded Control Operators: Solutions Through Generalized Derivatives

Gozzi F.;
2023

Abstract

This paper deals with a family of stochastic control problems in Hilbert spaces which arises in many engineering/economic/financial applications (in particular the ones featuring boundary control and control of delay equations with delay in the control) and for which it is difficult to apply the dynamic programming approach due to the unboundedness of the control operator and to the lack of regularity of the underlying transition semigroup. We introduce a specific concept of partial derivative, designed for this situation, and we develop a method to prove that the associated HJB equation has a solution with enough regularity to find optimal controls in feedback form.
2023
second order Hamilton-Jacobi-Bellman equations in infinite dimension, smoothing properties of transition semigroups, stochastic boundary control problems, stochastic control of delay equation with delay in the control, unbounded control operator
Stochastic Control Problems with Unbounded Control Operators: Solutions Through Generalized Derivatives / Gozzi, Fausto; Masiero, F.. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 61:2(2023), pp. 586-619. [10.1137/22m1474679]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/234945
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