Issue |
ESAIM: COCV
Volume 21, Number 3, July-September 2015
|
|
---|---|---|
Page(s) | 835 - 856 | |
DOI | https://doi.org/10.1051/cocv/2014052 | |
Published online | 20 May 2015 |
Stackelberg–Nash exact controllability for linear and semilinear parabolic equations∗,∗∗
1
Dpto. de Matemática, Universidade Federal da
Paraíba, 58051-900
João Pessoa –
PB,
Brasil
fagner@mat.ufpb.br
2
Dpto. EDAN and IMUS, University of Sevilla,
Aptdo. 1160, 41080
Sevilla,
Spain
cara@us.es
3
Dpto. de Matemática, Universidade Federal de
Pernambuco, 50740-540
Recife-PE,
Brasil
mauricio@dmat.ufpe.br
Received:
27
June
2014
Revised:
27
September
2014
This paper deals with the application of Stackelberg–Nash strategies to the control of parabolic equations. We assume that we can act on the system through a hierarchy of controls. A first control (the leader) is assumed to choose the policy. Then, a Nash equilibrium pair (corresponding to a noncooperative multiple-objective optimization strategy) is found; this governs the action of the other controls (the followers). The main novelty in this paper is that, this way, we can obtain the exact controllability to a prescribed (but arbitrary) trajectory. We study linear and semilinear problems and, also, problems with pointwise constraints on the followers.
Mathematics Subject Classification: 34K35 / 49J20 / 35K10
Key words: Controllability / Stackelberg–Nash strategies / Carleman inequalities
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.