Distributed adaptive parameter estimation over weakly connected digraphs using a relaxed excitation condition

Abstract

In this article, a novel distributed adaptive parameter estimation (DAPE) algorithm is proposed for an multi-agent system over weakly connected digraph networks, where parameter convergence is ensured under a newly coined relaxed excitation condition, called generalized cooperative initial excitation (gC-IE). This is in contrast to the past literature, where such DAPE algorithms demand cooperative persistent of excitation (C-PE) and generalized cooperative persistent of excitation (gC-PE) for strongly connected digraph, and weakly connected digraph networks, respectively, for parameter convergence. The gC-PE and C-PE conditions are restrictive in the sense that they require the richness/excitation of information over the entire time-span of the signal/data, unlike gC-IE condition where excitation is needed only in the initial time-span. The newly coined gC-IE condition is an extension of cooperative initial excitation (C-IE) condition. While the C-IE condition is applicable to a strongly connected digraph, the newly proposed gC-IE condition extends the concept to weakly connected digraph. The proposed algorithm utilizes a novel set of weighted integrator dynamics, which omits the requirement of computationally involved multiples switching mechanisms in past literature, while still ensuring parameter convergence. The proposed algorithm provides global exponential stability of origin of the parameter estimation error dynamics under gC-IE condition. Furthermore, robustness to unmodeled disturbance is also established in the form of input-to-state stability. Simulation results validate the efficacy of the proposed algorithm in contrast to the gC-PE based algorithm.