Distributed Stabilization of Interconnected Multiagent Systems using Structurally Nonsymmetric Control Layers

Abstract

Recently, graph theoretic distributed protocols have been introduced for the stabilization of interconnected multiagent systems with separate agent and control layers. For the case of unstable local agent dynamics, the existing results focus on only the matched interconnections. Further, except for a multiagent system of first- and second-order agents, the existing results are limited to the structurally symmetric control layers based on the undirected communication among controllers. We aim to relax these restrictions for multiagent systems with partially known unmatched or matched interconnections. We propose two step-by-step procedures to design robust distributed stabilization gains for the candidate nonsymmetric control layers in the presence of agent- and multiagent system-level modeling uncertainties. Combined with an optimal control formulation, we develop a matrix algebraic approach for the unmatched scenario and a Lyapunov-based approach for the matched case. In each case, we prove that all state trajectories of the two-layer interconnected multiagent system exponentially converge to the origin. We examine the feasibility of the proposed ideas in simulation.