This paper, which is the natural continuation of part I [S. Federico, B. Goldys, and F. Gozzi, SIAM J. Control Optim., 48 (2010), pp. 4910-4937], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In part I the problem is embedded in a suitable Hilbert space H and the regularity of the associated Hamilton-Jacobi-Bellman equation is studied. The goal of the present paper is to exploit the regularity result of part I to prove a verification theorem and find optimal feedback controls for the problem. While it is easy to define a feedback control formally following the classical case, the proof of its existence and optimality is hard due to lack of full regularity of V and to the infinite dimensionality of the problem. The theory developed is applied to study economic problems of optimal growth for nonlinear time-to-build models. In particular, we show the existence and uniqueness of optimal controls and their characterization as feedbacks. © 2011 Society for Industrial and Applied Mathematics.

Federico, S., Goldys, B., Gozzi, F. (2011). HJB equations for the optimal control of differential equations with delays and state constraints, ii: Verification and optimal feedbacks. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 49(6), 2378-2414 [10.1137/100804292].

HJB equations for the optimal control of differential equations with delays and state constraints, ii: Verification and optimal feedbacks

FEDERICO, SALVATORE;
2011-01-01

Abstract

This paper, which is the natural continuation of part I [S. Federico, B. Goldys, and F. Gozzi, SIAM J. Control Optim., 48 (2010), pp. 4910-4937], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In part I the problem is embedded in a suitable Hilbert space H and the regularity of the associated Hamilton-Jacobi-Bellman equation is studied. The goal of the present paper is to exploit the regularity result of part I to prove a verification theorem and find optimal feedback controls for the problem. While it is easy to define a feedback control formally following the classical case, the proof of its existence and optimality is hard due to lack of full regularity of V and to the infinite dimensionality of the problem. The theory developed is applied to study economic problems of optimal growth for nonlinear time-to-build models. In particular, we show the existence and uniqueness of optimal controls and their characterization as feedbacks. © 2011 Society for Industrial and Applied Mathematics.
2011
Federico, S., Goldys, B., Gozzi, F. (2011). HJB equations for the optimal control of differential equations with delays and state constraints, ii: Verification and optimal feedbacks. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 49(6), 2378-2414 [10.1137/100804292].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1003436
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