Multi-objective control for stochastic parabolic equations with dynamic boundary conditions

TL;DR

This paper develops a hierarchical multi-objective control framework for stochastic parabolic equations with dynamic boundary conditions, employing Nash and Stackelberg strategies combined with Carleman estimates and control duality.

Contribution

It introduces a novel approach to control stochastic parabolic equations with dynamic boundaries using hierarchical strategies and advanced estimates.

Findings

Achieved null controllability for leaders.

Controlled states to prescribed targets in observation regions.

Combined Nash and Stackelberg strategies effectively.

Abstract

This paper deals with a hierarchical multi-objective control problem for forward stochastic parabolic equations with dynamic boundary conditions. The controls are divided into two classes: leaders and followers. The goal of the leaders is of null controllability type while the followers are in charge of letting the state close to prescribed targets in fixed observation regions. To solve the problem, Nash and Stackelberg strategies are used. To implement these strategies, we combine some appropriate Carleman estimates and the well-known control duality approach.