A Hierarchical control problem for the Benney-Lin equation using Stackelberg-Nash strategy
Résumé
The goal of this article is to study a control problem for the Benney-Lin equation with multiple objectives, by means of localized interior controls. The primary objective is to steer the solution to a given control-free trajectory, along with a secondary goal of solving a non-cooperative/competitive optimization problem associated with the solution of the underlying control system. To study such a multi-objective hierarchical control problem, we employ a well-known Stackelberg–Nash strategy. More precisely, assuming the existence of a control (referred to as {\em leader}) responsible for driving the solution to a free trajectory, we characterize the other two controls (referred to as {\em followers}) which solve the non-cooperative optimization problem under study. The characterization of the followers is influenced by the choice of the leader, leading to a coupled optimality system. Consequently, this multi-objective control problem for the Benney–Lin equation simplifies to a single-objective control problem for the optimality system.
Mots clés
- Mathematics Subject Classification. 35Q30 35Q53 93B05 93B07 93C10 91A65 49J20 Fifth-order Korteweg-de Vries equation Benney-Lin type equation Hierarchical controls Exact controllability Carleman estimate
- Mathematics Subject Classification. 35Q30
- 35Q53
- 93B05
- 93B07
- 93C10
- 91A65
- 49J20 Fifth-order Korteweg-de Vries equation
- Benney-Lin type equation
- Hierarchical controls
- Exact controllability
- Carleman estimate
Domaines
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