A Distributed Observer Approach to the Bipartite Output Regulation of Nonlinear Multi-Agent Systems over Signed Networks

Abstract

This paper investigates the bipartite output regulation problem (BORP) of nonlinear multi-agent systems (MASs) over static signed networks. Unlike conventional cooperative output regulation problem (CORP), antagonistic couplings among agents result in a bipartite tracking objective, where different groups of followers asymptotically approach references with opposite signs. To address the nonlinear exogenous dynamics under signed topologies, a nonlinear distributed observer (NDO) is proposed by incorporating the sign information of inter-agent interactions into the observer update law. It is shown that the resulting observer remains well-posed and achieves exponential convergence to the desired signed reference trajectory. Moreover, the solvability of the nonlinear BORP is analyzed which is based on the solvability of nonlinear regulator equations. Furthermore, a distributed state-feedback protocol is constructed for nonlinear MASs based on the observer estimates, guaranteeing leader-follower bipartite synchronization of the overall closed-loop system. Finally, numerical simulations involving multiple pendulum systems are presented to demonstrate the feasibility and effectiveness of the proposed approach.