Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-State Data

TL;DR

This paper introduces a data-driven method for designing dynamic output-feedback controllers for discrete-time LTI systems to ensure dissipativity and $H_2$ performance, using noisy input-state data without requiring a system model.

Contribution

It develops a non-conservative synthesis approach based on LMIs that works with noisy data and unknown system dynamics, focusing on dissipativity and $H_2$ performance.

Findings

The method guarantees desired performance levels from noisy data.

Controller synthesis is formulated as LMIs parametrized by a scalar.

The approach is applicable without full system identification.

Abstract

In this paper we propose dynamic output-feedback controller synthesis methods for discrete-time linear time-invariant systems. The synthesis goal is to achieve dissipativity with respect to a given quadratic supply rate or a given $H_2$ performance level. It is assumed that the model of system dynamics is unknown, expect for the disturbance term. Instead, we have a recorded trajectory of the control input and the state, which can be corrupted by an unknown but bounded disturbance. The state data is used only for the purpose of controller synthesis, while the designed controller is output feedback controller, i.e., the full state is not used for control in real time. The presented synthesis method is formulated in terms of linear matrix inequalities parametrized by a scalar variable. Within the considered setting, the synthesis procedure is non-conservative.