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 $C^1$-regularity for the value function and the feedback characterization of optimal controls
Dynamic programming for optimal control problems with delays in the control variable / S. Federico, E. Tacconi. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 52:2(2014), pp. 1203-1236. [Epub ahead of print] [10.1137/110840649]
Dynamic programming for optimal control problems with delays in the control variable
S. FedericoPrimo
;
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 $C^1$-regularity for the value function and the feedback characterization of optimal controlsFile | Dimensione | Formato | |
---|---|---|---|
110840649.pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Dimensione
610.01 kB
Formato
Adobe PDF
|
610.01 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.