HJB equations for the optimal control of differential equations with delay in the control variable

Abstract : We study a class of optimal control problems with state constraint, where the state equation is a differential equation with delays in the control variable. This class of problems arises in some economic applications, in particular in optimal advertising problems. The optimal control problem is embedded in a suitable Hilbert space and the associated Hamilton- Jacobi-Bellman (HJB) equation is considered in this space. It is proved that the value function is continuous with respect to a weak norm and that it solves in the viscosity sense the associated HJB equation. The main result is the proof of a directional C1 regularity for the value function. This result represents the starting point to define a feedback map in classical sense going towards a verification theorem and the construction of optimal feedback controls for the problem.
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Preprints, Working Papers, ...
2011
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https://hal.archives-ouvertes.fr/hal-00596717
Contributor : Salvatore Federico <>
Submitted on : Sunday, May 29, 2011 - 7:18:01 PM
Last modification on : Tuesday, October 11, 2016 - 2:10:49 PM
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Salvatore Federico, Elisa Tacconi. HJB equations for the optimal control of differential equations with delay in the control variable. 2011. <hal-00596717>

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