Output regulation via input-output data

TL;DR

This paper presents a data-driven method for designing feedback controllers that achieve output regulation in MIMO linear systems without requiring explicit system models, using input-output data affected by noise.

Contribution

It introduces a novel approach to solve the output regulation problem directly from input-output data via semidefinite programming, bypassing the need for system identification.

Findings

Controller design is formulated as a semidefinite program.

The method guarantees asymptotic annihilation of the exosignal effect.

The approach is validated through rigorous theoretical analysis.

Abstract

From a multi-input-multi-output (MIMO) discrete-time linear system, we collect input-output data affected by noise in the form of an unknown exosignal and, from these data points (without knowledge of the system model), we design a feedback controller that asymptotically annihilates the effect of that exosignal on the output. This amounts to solving an output regulation problem purely from input-output data, for MIMO linear systems. The design of the controller corresponds to a semidefinite program and is pursued on a suitable auxiliary system. Such design carries over from the auxiliary system to the original one by a rigorous examination of the relation between the solutions of the two systems.