Optimal Selection of Interconnections in Composite Systems for Structural Controllability

TL;DR

This paper develops a polynomial-time algorithm to identify the minimal set of interconnections needed to ensure structural controllability in composite systems of identical subsystems.

Contribution

It introduces an optimal algorithm for selecting the smallest interconnection set to maintain controllability in composite systems.

Findings

Algorithm finds minimal interconnection set efficiently.

Ensures structural controllability with fewer links.

Applicable to systems with identical subsystem patterns.

Abstract

In this paper, we study structural controllability of a linear time invariant (LTI) composite system consisting of several subsystems. We assume that the neighbourhood of each subsystem is unconstrained, i.e., any subsystem can interact with any other subsystem. The interaction links between subsystems are referred as interconnections. We assume the composite system to be structurally controllable if all possible interconnections are present, and our objective is to identify the minimum set of interconnections required to keep the system structurally controllable. We consider structurally identical subsystems, i.e., the zero/non-zero pattern of the state matrices of the subsystems are the same, but dynamics can be different. We present a polynomial time optimal algorithm to identify the minimum cardinality set of interconnections that subsystems must establish to make the composite system structurally controllable.