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/).
Cite this article
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 -