Duality and stability in complex multiagent state-dependent network dynamics

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Despite significant progress on stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings in addressing multiagent systems with highly coupled state-network dynamics. Motivated by numerous applications of such dynamics, in our previous work [SIAM J. Control Optim., 57 (2019), pp. 1757-1782], we initiated a new direction for stability analysis of such systems that uses a sequential optimization framework. Building upon that, in this paper, we extend our results by providing another angle on multiagent network dynamics from a duality perspective, which allows us to view the network structure as dual variables of a constrained nonlinear program. Leveraging that idea, we show that the evolution of the coupled state-network multiagent dynamics can be viewed as iterates of a primal-dual algorithm for a static constrained optimization/saddle-point problem. This view bridges the Lyapunov stability of state-dependent network dynamics and frequently used optimization techniques such as block coordinated descent, mirror descent, the Newton method, and the subgradient method. As a result, we develop a systematic framework for analyzing the Lyapunov stability of state-dependent network dynamics using techniques from nonlinear optimization. Finally, we support our theoretical results through numerical simulations from social science.

Original languageEnglish (US)
Pages (from-to)3062-3091
Number of pages30
JournalSIAM Journal on Control and Optimization
Issue number6
StatePublished - 2020


  • Block coordinate descent
  • Lyapunov stability
  • Multiagent systems
  • Newton method
  • Nonlinear optimization
  • Saddle-point dynamics
  • State-dependent network dynamics

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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