Structural Controllability of a Networked Dynamic System with LFT Parameterized Subsystems

TL;DR

This paper investigates the structural controllability of networked dynamic systems with subsystems parameterized by LFT, providing scalable conditions and a heuristic for minimal interconnection links to ensure controllability.

Contribution

It establishes necessary and sufficient conditions for controllability in LFT-parameterized NDSs and proposes a scalable, low-complexity heuristic for minimal interconnection design.

Findings

Controllability is a generic property for LFT-parameterized NDSs.

Derived scalable conditions for structural controllability and uncontrollable modes.

Proposed a heuristic method for minimal interconnection links with provable bounds.

Abstract

This paper studies structural controllability for a networked dynamic system (NDS), in which each subsystem may have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation (LFT). It is proven that controllability keeps to be a generic property for this kind of NDSs. Some necessary and sufficient conditions are then established respectively for them to be structurally controllable, to have a fixed uncontrollable mode, and to have a parameter dependent uncontrollable mode, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and in their verifications, all arithmetic calculations are performed separately on each subsystem. In addition, these conditions also reveal influences on NDS controllability from subsystem input-output relations, subsystem uncontrollable modes and subsystem interconnection topology. Based on these observations, the problem of selecting the minimal number of subsystem interconnection links is studied under the requirement of constructing a structurally controllable NDS. A heuristic method is derived with some provable approximation bounds and a low computational complexity.