Hierarchical Control for the Oldroyd Equation in Memoriam to Professor Luiz Adauto Medeiros

TL;DR

This paper develops a hierarchical control framework for the Oldroyd equation with non-regular coefficients, establishing existence, uniqueness, and controllability results within a Stackelberg-Nash strategic setting.

Contribution

It introduces a novel hierarchical control approach for the Oldroyd equation with measurable coefficients, including Nash equilibrium characterization and controllability analysis.

Findings

Existence and uniqueness of Nash equilibrium established.

Approximate controllability with respect to the leader control proven.

Optimality system for leader control derived.

Abstract

This manuscript deals with a hierarchical control problem for Oldroyd equation under the Stackelberg-Nash strategy. The Oldroyd equation model is defined by non-regular coefficients, that is, they are bounded measurable functions. We assume that we can act in the dynamic of the system by a hierarchy of controls, where one main control (the leader) and several additional secondary control (the followers) act in order to accomplish their given tasks: controllability for the leader and optimization for followers. We obtain the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability with respect to the leader control, and the optimality system for leader control.