Controllability of networked MIMO systems

TL;DR

This paper analyzes how network topology, node dynamics, and inputs jointly influence the controllability of complex networked MIMO systems, revealing that controllability depends on integrated factors beyond individual node properties.

Contribution

It provides a comprehensive analysis of controllability in networked MIMO systems, highlighting the interplay of topology, node dynamics, and inputs, with precise conditions for SISO cases.

Findings

Controllability depends on combined network and node factors.

Uncontrollable topology leads to uncontrollable networked systems.

Necessary conditions include controllability and observability of nodes.

Abstract

In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: 1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology, quite different from the familiar notion of consensus or formation controllability; 2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; 3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient. For a networked system with single-input/single-output (SISO) LTI nodes, we present precise necessary and sufficient conditions for the controllability of a general network topology.