Hierarchic Controllability for a nonlinear parabolic equation in one dimension

TL;DR

This paper investigates hierarchical control strategies for one-dimensional nonlinear parabolic equations using Stackelberg-Nash frameworks, focusing on null controllability and equilibrium solutions.

Contribution

It introduces a novel approach combining Stackelberg and Nash strategies for controlling nonlinear parabolic equations in one dimension.

Findings

Established null controllability results for linear and nonlinear cases

Developed a hierarchical control framework with leader-follower dynamics

Analyzed equilibrium solutions in a bi-objective control setting

Abstract

This paper deals with the hierarchical control of the parabolic equation.We use Stackelberg{Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem, then, we look for a leader that solves null controllability e with trajectories problem. We consider linear and nonlinear equations in dimension 1.