A Youla Operator State-Space Framework for Stably Realizable Distributed Control

TL;DR

This paper introduces a Youla operator state-space framework for designing distributed controllers that are stably realizable over networks, unifying various linear system classes and enabling convex optimization for stability and performance.

Contribution

It develops a novel operator-based Youla parameterization for structured distributed control, allowing convex synthesis and stable realization over networks.

Findings

Framework applies to LTI, LTV, and switched systems.

Control synthesis reduces to convex optimization problems.

Structured controllers can be stably realized over the network.

Abstract

This paper deals with the problem of distributed control synthesis. We seek to find structured controllers that are stably realizable over the underlying network. We address the problem using an operator form of discrete-time linear systems. This allows for uniform treatment of various classes of linear systems, e.g., Linear Time Invariant (LTI), Linear Time Varying (LTV), or linear switched systems. We combine this operator representation for linear systems with the classical Youla parameterization to characterize the set of stably realizable controllers for a given network structure. Using this Youla Operator State-Space (YOSS) framework, we show that if the structure satisfies certain subspace like assumptions, then both stability and performance problems can be formulated as convex optimization and more precisely as tractable model-matching problems to any a priori accuracy. Furthermore, we show that the structured controllers found from our approach can be stably realized over the network and provide a generalized separation principle.