State-constrained porous media control systems with application to stabilization

TL;DR

This paper investigates how to control stochastic porous media systems within constraints, using internal controls and quasi-tangency conditions to achieve exponential stabilization.

Contribution

It introduces a novel characterization of control capabilities for constrained stochastic porous media systems using a quasi-tangency approach.

Findings

Conditions for exponential asymptotic stabilizability established

Quasi-tangency method applied to control characterization

Use of system component as asymptotic supervisor

Abstract

We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency local-in-time condition in the spirit of Euler approximation schemes. In particular, by employing one of the components of the system as asymptotic supervisor, we give conditions guaranteeing the exponential asymptotic stabilizability of controlled porous media equations.