Structured H-infinity control of infinite dimensional systems

TL;DR

This paper introduces a frequency-based H-infinity control method for infinite-dimensional LTI systems that avoids reduction techniques, using a trust-region approach to compute practical controllers with guaranteed stability.

Contribution

It presents a novel approach that directly handles infinite-dimensional systems without reduction, utilizing frequency response data and a non-smooth optimization method.

Findings

Successfully applied to PDE boundary control problems

Achieves exponential stability with locally optimal controllers

Demonstrates versatility across various infinite-dimensional systems

Abstract

We develop a novel frequency-based H-infinity control method for a large class of infinite-dimensional Linear-Time-Invariant systems in transfer function form. Major benefits of our approach is that reduction or identification techniques are not needed thereby avoiding possible distortions. It can exploit either transfer function models or input/output frequency response data when available. It computes simple practical controllers of any size and structure. We use a non-smooth trust-region method to compute arbitrarily structured locally optimal H-infinity controllers for a frequency sampled approximation of the underlying infinite-dimensional H-infinity problem in such a way that exponential stability in closed-loop is guaranteed, and the optimal value of the approximation captures the value of the infinite-dimensional problem within a prior tolerance level. We demonstrate the versatility and practicality of our method on a variety of infinite-dimensional H-infinity synthesis problems, including distributed and boundary control of PDEs, control of dead time and delay systems, and using a rich testing set.