Consensus and synchronization in multi-agent coordination

Abstract

This thesis considers mainly two topics in the area of multi-agent coordination. The first topic is the consensus and synchronization problem and its extension, where the widely considered models and algorithms in existing studies are revisited. More specifically, for agents with double-integrator dynamics, we consider the design and analysis of the consensus algorithms in a more general framework that agents interact under independent position and velocity network topologies. Both the cases with fixed and switching topologies are considered. While for agents modeled by generic linear system dynamics with static feedback controller, we work on switching interaction topologies. The first of our efforts is trying to relax and extend the assumptions/conditions proposed in existing studies to guarantee the synchronization; the second of our efforts is made towards the specification of the convergence rate under the weakest possible interaction topologies; finally, we attempt to extend the notions of consensus and synchronization as well as containment to the general coordination behavior inherent in networks of diffusively coupled homogeneous agents with arbitrary interaction topology. The second topic is consensus and synchronization for multiple interacting clusters of agents, termed group or cluster consensus and synchronization in existing studies. For this topic, we first revisit the group consensus problem for single-integrator dynamics and try to work out the weakest possible conditions that are necessary to guarantee the group or cluster consensus. We then extend the cooperative and competitive coupling scheme to deal with agents with double-integrator dynamics, for which different group consensus algorithms are proposed to account for different settings in practical applications. That includes agents interacting under respectively the same and different position and velocity interactions, leaderless and leader-following consensus, as well as leaders of constant and time-varying velocities. Finally, we consider the cluster synchronization control for agents with generic linear system dynamics via pinning control techniques under both fixed and switching coupling topologies. Different methodologies, based mainly on the exploration of tools from stability theory for linear systems, algebraic graph theory, as well as matrix analysis, are employed to analyze the algorithms that are proposed in different frameworks. For all such frameworks, we aim at addressing the following two concerns of both theoretical and practical interests: - Whether group or cluster consensus and synchronization can be achieved if the underlying topology of each cluster only has a directed spanning tree and further, the intra-cluster couplings, as compared to the inter-cluster ones, are sufficiently strong? If yes, then how to quantitatively specify the strength? - Under what kind of coupling topologies the group or cluster consensus and synchronization behaviors are irrelevant to the magnitudes of the coupling strengths among the agents?