A Simple Framework for Stability Analysis of State-Dependent Networks of Heterogeneous Agents

TL;DR

This paper introduces a simple framework for analyzing the stability of complex, heterogeneous multi-agent networks with state-dependent switching, applicable to opinion dynamics and game-theoretic scenarios.

Contribution

It provides a novel, unified approach to stability analysis of highly coupled, state-dependent multi-agent systems with heterogeneity and complex environments.

Findings

Lyapunov stability established for opinion dynamics

Analysis of nearest neighbor opinion dynamics introduced

Extended results to game-theoretic multi-agent systems

Abstract

Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems become further complicated once one accounts for asymmetry or heterogeneity of the underlying agents/dynamics. Despite extensive progress in analysis of conventional networked decision systems where the network evolution and state dynamics are driven by independent or weakly coupled processes, most of the existing results fail to address multi-agent systems where the network and state dynamics are highly coupled and evolve based on status of heterogeneous agents. Motivated by numerous applications of such dynamics in social sciences, in this paper we provide a new direction toward analysis of dynamic networks of heterogeneous agents under complex time-varying environments. As a result we show how Lyapunov stability of several challenging problems from opinion dynamics can be established using a simple application of our framework. Moreover, we introduce a new class of asymmetric opinion dynamics, namely nearest neighbor dynamics, and show how our approach can be used to analyze their behavior. In particular, we extend our results to game-theoretic settings and provide new insights toward analysis of complex networked multi-agent systems using exciting field of sequential optimization.