Differential and Integral Equations

Boundary-control problems with convex cost and dynamic programming in infinite dimension. I. The maximum principle

Silvia Faggian

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Abstract

This is the first of two papers on boundary optimal control problems with linear state equation and convex cost arising from boundary control of PDEs and the associated Hamilton--Jacobi--Bellman equation. In this paper we study necessary and sufficient conditions of optimality (Pontryagin maximum principle), and study the properties of a family of approximating problems that will be useful both in this paper and in the sequel. In the second paper we will apply dynamic programming to show that the value function of the problem is a solution of an integral version of the HJB equation, and moreover that it is the pointwise limit of classical solutions of approximating equations.

Article information

Source
Differential Integral Equations Volume 17, Number 9-10 (2004), 1149-1174.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060317

Mathematical Reviews number (MathSciNet)
MR2082463

Zentralblatt MATH identifier
1150.49008

Subjects
Primary: 49K15: Problems involving ordinary differential equations
Secondary: 35B37 35K20: Initial-boundary value problems for second-order parabolic equations 35K90: Abstract parabolic equations 49K27: Problems in abstract spaces [See also 90C48, 93C25]

Citation

Faggian, Silvia. Boundary-control problems with convex cost and dynamic programming in infinite dimension. I. The maximum principle. Differential Integral Equations 17 (2004), no. 9-10, 1149--1174. https://projecteuclid.org/euclid.die/1356060317.


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