Non-smooth optimization for robust control of infinite-dimensional systems

TL;DR

This paper introduces a non-smooth trust-region method for robust $H_$-control of infinite-dimensional systems, effectively handling distributed and boundary control problems without system reduction.

Contribution

The paper presents a novel non-smooth optimization approach for $H_$-control of infinite-dimensional systems, applicable to PDE-based control problems, avoiding system reduction or identification.

Findings

Successfully applied to reaction-convection-diffusion system

Controlled Van de Vusse reactor effectively

Managed cavity flow control with the proposed method

Abstract

We use a non-smooth trust-region method for $H_\infty$-control of infinite-dimensional systems. Our method applies in particular to distributed and boundary control of partial differential equations. It is computationally attractive as it avoids the use of system reduction or identification. For illustration the method is applied to control a reaction-convection-diffusion system, a Van de Vusse reactor, and to a cavity flow control problem.