Optimal Boundary Control for Cascaded Parabolic PDEs with Constraints

DOI

10.2991/icence-16.2016.62How to use a DOI?

Keywords

Optimal boundary control; Cascaded PDEs; Control constraints; Adjoint equation

Abstract

In this paper, the optimal boundary control problem in finite time horizon for linear parabolic partial differential equations cascaded through Robin boundary condition is addressed. Firstly, the well-posedness of the solution for the cascaded system is presented. Secondly, with the existence of the optimal control, the adjoint equation and the first-order sufficient and necessary condition are derived. Also, the well-posedness of the adjoint equation is guaranteed. Thirdly, to implement the optimal control, the optimal system consisting of a forward-in-time state equation and a backward-in-time adjoint equation coupled with the optimal boundary control is derived. Finally, a numerical example is presented to illustrate this method.

Copyright

© 2016, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Chao He
AU  - Junmin Li
PY  - 2016/09
DA  - 2016/09
TI  - Optimal Boundary Control for Cascaded Parabolic PDEs with Constraints
BT  - Proceedings of the 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016)
PB  - Atlantis Press
SP  - 304
EP  - 309
SN  - 2352-538X
UR  - https://doi.org/10.2991/icence-16.2016.62
DO  - 10.2991/icence-16.2016.62
ID  - He2016/09
ER  -