State-constrained control-affine parabolic problems I: first and second order necessary optimality conditions
Abstract
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results.
Cite
@article{arxiv.1906.00237,
title = {State-constrained control-affine parabolic problems I: first and second order necessary optimality conditions},
author = {M. Soledad Aronna and J. Frédéric Bonnans and Axel Kröner},
journal= {arXiv preprint arXiv:1906.00237},
year = {2020}
}
Comments
This is the first part of a work on optimality conditions for a control problem of a semilinear heat equation. More precisely, the full version, available at arXiv:1906.00237v1, has been divided in two, resulting in the current manuscript (that corresponds to Part I) and arXiv:1909.05056 (which is Part II)