Pré-Publication, Document De Travail Année : 2025

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.

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Dates et versions

hal-04588106 , version 1 (25-05-2024)
hal-04588106 , version 2 (30-05-2024)
hal-04588106 , version 3 (03-06-2024)
hal-04588106 , version 4 (15-09-2025)

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  • HAL Id : hal-04588106 , version 4

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Manish Kumar, Subrata Majumdar. A Hierarchical control problem for the Benney-Lin equation using Stackelberg-Nash strategy. 2025. ⟨hal-04588106v4⟩
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