Robust Stackelberg controllability for the Navier--Stokes equations

TL;DR

This paper develops a robust Stackelberg control strategy for the Navier--Stokes equations, enabling effective management of fluid dynamics through hierarchical control and disturbance handling.

Contribution

It introduces a novel Stackelberg control framework for Navier--Stokes equations, combining robust follower control with leader optimization to achieve local null controllability.

Findings

Established a local null controllability result for Navier--Stokes system

Proposed a new hierarchical control scheme incorporating robustness against disturbances

Demonstrated effectiveness of the Stackelberg approach in fluid control problems

Abstract

In this paper we deal with a robust Stackelberg strategy for the Navier--Stokes system. The scheme is based in considering a robust control problem for the "follower control" and its associated disturbance function. Afterwards, we consider the notion of Stackelberg optimization (which is associated to the "leader control") in order to deduce a local null controllability result for the Navier--Stokes system.