Vibrational Stabilization of Complex Network Systems

TL;DR

This paper investigates vibrational control as an open-loop stabilization method for complex network systems, especially when system states are difficult to measure, providing theoretical conditions and control placement strategies.

Contribution

It introduces a graph-theoretic condition for structural vibrational stabilizability and offers a method for control placement and input design in network systems.

Findings

Derived a sufficient condition for vibrational stabilizability

Proposed a control placement and input design approach

Numerical results validate theoretical findings

Abstract

Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on stabilization assume that network systems states can be measured online so that feedback control strategies can be used. However, in many real-world scenarios, systems states, e.g., neuronal activity in the brain, are often difficult to measure. In this paper, we take this situation into account and study the stabilization problem of linear network systems with an open-loop control strategy (vibrational control). We derive a graph-theoretic sufficient condition for structural vibrational stabilizability, under which network systems can always be stabilized. We further provide an approach to select the locations in the network for control placement and design corresponding vibrational inputs to stabilize systems that satisfy this condition. Finally, we provide some numerical results that demonstrate the validity of our theoretical findings.