Journal Article

Approximation of exact controllability problem involving parabolic differential equations

Mohan C. Joshi and Anil Kumar

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 3, pages 350-363
Published in print September 2005 | ISSN: 0265-0754
Published online September 2005 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni032
Approximation of exact controllability problem involving parabolic differential equations

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In this paper we examine computation of optimal control u* of the exact controllability problem (referred to as the constraint problem) governed by the following type of linear parabolic differential equations:

(∂y/∂t) + Ay = u in Q

y = 0 on ∑

y(0) = y0 on Ω

where A is the second-order elliptic differential operator, Ω is a bounded domain in ℝk with smooth boundary ∂Ω, Q = (0, T) × Ω, ∑ = (0, T) × ∂Ω and T > 0. This is achieved by approximating u* through a sequence {un} of controls corresponding to unconstrained problems involving a penalty function arising from the controllability constraint.

Keywords: optimal control; exact controllability; parabolic equation; penalty function

Journal Article.  0 words. 

Subjects: Mathematics

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