Topology Preservation for Multi-agent Networks: Design and Implementation

Abstract

We consider a network of interconnected systems with discrete-time dynamics. Each system is called agent and we assume that two agents can interact as far as their states are close in a sense defined by an algebraic relation. In this work, we present several implementation strategies answering to different classical problems in multiagent systems. The primary goal of our methodology is to characterize the controllers that preserve a given interconnection subgraph that makes possible the global coordination. The second goal is to choose among these controllers those that ensure an agreement. This is done by solving a convex optimization problem associated to the minimization of a well-chosen cost function. Examples concerning full or partial consensus of agents with double-integrator dynamics illustrate the implementation of the proposed methodology.