Multi-objective Control for Stochastic Parabolic Equations with Dynamic Boundary Conditions

Omar Oukdach (), Said Boulite (), Abdellatif Elgrou () and Lahcen Maniar ()
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Omar Oukdach: University of Meknes
Said Boulite: Cadi Ayyad University
Abdellatif Elgrou: Cadi Ayyad University
Lahcen Maniar: Cadi Ayyad University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 20, 31 pages

Abstract: Abstract This paper deals with a hierarchical multi-objective control problem for forward stochastic parabolic equations with dynamic boundary conditions. Viewed as a game, the players (the controls) are divided into two classes: leaders and followers. The leaders aim to drive the system to rest, while the followers are in charge of letting the state close to prescribed targets in fixed observation regions. The problem is solved using Nash–Stackelberg strategies as follows: for fixed leaders, we first establish the existence and uniqueness of the Nash equilibrium and characterize it by a backward system. The problem is then reduced to the classical null controllability property for a forward–backward coupled system, which is obtained using some new Carleman estimates.

Keywords: Stochastic parabolic equations; Stackelberg–Nash strategy; Observability inequality; Null controllability; Carleman estimates; Dynamic boundary conditions; Primary 93E20; 35Q91; Secondary 93B05; 93B07 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02623-6

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