A Technique for Designing Stabilizing Distributed Controllers with Arbitrary Signal Structure Constraints

TL;DR

This paper introduces a novel method for designing distributed controllers with arbitrary signal structure constraints by leveraging a partial-structure representation called the dynamical structure function, enabling structured control synthesis.

Contribution

It proposes a sequential design technique for controllers based on the dynamical structure function, allowing arbitrary signal structure constraints and providing stability guarantees.

Findings

The method can construct stabilizing controllers with specified structures.

The approach characterizes richer system structures than traditional sparsity patterns.

It proves that the designed controller is either stabilizing or no such controller exists.

Abstract

This paper presents a new approach to distributed controller design that exploits a partial-structure representation of linear time invariant systems to characterize the structure of a system. This partial-structure representation, called the dynamical structure function, characterizes the {\em signal structure}, or open-loop causal dependencies among manifest variables, capturing a significantly richer notion of structure than the sparsity pattern of the transfer function. The design technique sequentially constructs each link in an arbitrary controller signal structure, and the main result proves that the resulting controller is either stabilizing or no controller with the desired structure can stabilize the system.