Duality and Stability in Complex Multiagent State-Dependent Network Dynamics
share
Many of the current challenges in science and engineering are related to complex networks and distributed multiagent network systems are currently the focal point of many new applications. Such applications relate to the growing popularity of social networks, the analysis of large network data sets, and the problems that arise from interactions among agents in complex political, economic, and biological systems. Despite extensive progress for stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings to address multiagent systems with highly coupled state-network dynamics. Motivated by numerous applications of such dynamics, in our previous work [1], we initiated a new direction for stability analysis of such systems using a sequential optimization framework. Building upon that, in this paper we complete our results by providing another angle to multiagent network dynamics from a duality perspective which allows us to view the network structure as dual variables of a constrained convex program. Leveraging this idea, we show that the evolution of the coupled state-network multiagent dynamics can be viewed as iterates of a primal-dual algorithm to a static constrained optimization/saddle-point problem. This bridges the Lyapunov stability of state-dependent network dynamics and frequently used optimization techniques such as block coordinated descent, mirror descent, Newton method, and subgradient method. As a result, we develop a systematic framework to analyze the Lyapunov stability of state-dependent network dynamics using well-known techniques from nonlinear optimization.
READ FULL TEXT