Localization of Control Synthesis Problem for Large-Scale Interconnected System Using IQC and Dissipativity Theories

TL;DR

This paper presents a unified approach using IQC and dissipativity theories to localize control synthesis problems in large-scale interconnected systems, enabling decentralized control and performance certification.

Contribution

It introduces a novel localization concept that reduces global synthesis problems into smaller, manageable local problems for large-scale systems.

Findings

Localization simplifies control synthesis for large systems.

The approach enables decentralized control design.

It provides a feasible certification method for system performance.

Abstract

The synthesis problem for the compositional performance certification of interconnected systems is considered. A fairly unified description of control synthesis problem is given using integral quadratic constraints (IQC) and dissipativity. Starting with a given large-scale interconnected system and a global performance objective, an optimization problem is formulated to search for admissible dissipativity properties of each subsystems. Local control laws are then synthesized to certify the relevant dissipativity properties. Moreover, the term localization is introduced to describe a finite collection of syntheses problems, for the local subsystems, which are a feasibility certificate for the global synthesis problem. Consequently, the problem of localizing the global problem to a smaller collection of disjointed sets of subsystems, called groups, is considered. This works looks promising as another way of looking at decentralized control and also as a way of doing performance specifications for components in a large-scale system.