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 results are the proof of a directional C1-regularity for the value function and the feedback characterization of optimal controls. © 2014 Society for Industrial and Applied Mathematics.
Federico S., Tacconi E. (2014). Dynamic programming for optimal control problems with delays in the control variable?. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 52(2), 1203-1236 [10.1137/110840649].
Dynamic programming for optimal control problems with delays in the control variable?
Federico S.;
2014
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 results are the proof of a directional C1-regularity for the value function and the feedback characterization of optimal controls. © 2014 Society for Industrial and Applied Mathematics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
