Volume 21, Number 3, July-September 2015
|Page(s)||835 - 856|
|Published online||20 May 2015|
Dpto. de Matemática, Universidade Federal da
João Pessoa –
2 Dpto. EDAN and IMUS, University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
3 Dpto. de Matemática, Universidade Federal de Pernambuco, 50740-540 Recife-PE, Brasil
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
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