Distributed Control of Positive Systems

TL;DR

This paper develops scalable methods for the synthesis and verification of distributed controllers for positive systems, leveraging their structure for simplified stability and performance analysis, with applications in transportation, vehicle formations, and power systems.

Contribution

It introduces new scalable synthesis and verification techniques for distributed control of positive systems, including a stronger Kalman-Yakubovich-Popov lemma and frequency domain analysis methods.

Findings

Verification complexity scales linearly with interconnections

New stronger KYP lemma for positive systems

Applications demonstrated in transportation, vehicle formations, power systems

Abstract

A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage functions can be used instead of quadratic ones. This paper shows how such methods can be used for synthesis of distributed controllers. It also shows that stability and performance of such control systems can be verified with a complexity that scales linearly with the number of interconnections. Several results regarding scalable synthesis and verfication are derived, including a new stronger version of the Kalman-Yakubovich-Popov lemma for positive systems. Some main results are stated for frequency domain models using the notion of positively dominated system. The analysis is illustrated with applications to transportation networks, vehicle formations and power systems.