Synthesis of Dissipative Systems Using Input-State Data

TL;DR

This paper presents a data-driven method for synthesizing controllers that ensure dissipativity in linear systems using finitely many noisy data samples, with conditions for informativity and controller design via linear matrix inequalities.

Contribution

It introduces the concept of informativity for closed-loop dissipativity and provides necessary and sufficient conditions for data-based controller synthesis in dissipative systems.

Findings

Provided conditions for data informativity for dissipativity.

Developed a data-based controller design method using linear matrix inequalities.

Illustrated the approach with an example achieving strict passivity.

Abstract

This paper deals with the data-driven synthesis of dissipative linear systems in discrete time. We collect finitely many noisy data samples with which we synthesise a controller that makes all systems that explain the data dissipative with respect to a given quadratic supply rate. By adopting the informativity approach, we introduce the notion of informativity for closed-loop dissipativity. Under certain assumptions on the noise and the system, with the help of tools for quadratic matrix inequalities, we provide necessary and sufficient conditions for informativity for closed-loop dissipativity. We also provide a recipe to design suitable controllers by means of data-based linear matrix inequalities. This main result comprises two parts, to account for both the cases that the output matrices are known or unknown. Lastly, we illustrate our findings with an example, for which we want to design a data-driven controller achieving (strict) passivity.