Distributed Composite Adaptive Synchronization of Multiple Uncertain Euler-Lagrange Systems using Cooperative Initial Excitation

Abstract

This work proposes a distributed composite adaptive synchronization algorithm for multiple uncertain EulerLagrange (EL) systems, where parameter convergence is achieved under a relaxed mathematical condition as compared to the state-of-the-art. Classical adaptive controllers require an analytical condition, called persistence of excitation (PE), to ensure parameter convergence, which results in better transient performance and robustness to disturbance. The PE condition is extended to Cooperative-PE (C-PE) condition for distributed adaptive controllers with cooperative estimation strategies. The PE and C-PE conditions are restrictive in nature since these conditions are not satisfied in most practical applications. Recent literature in adaptive control has relaxed the PE condition to Initial Excitation (IE), which is shown to be sufficient for parameter convergence. The IE condition is argued to be significantly milder than PE and can be satisfied in many practical setting. The proposed result further extends the IE condition to Cooperative-IE (C-IE) condition in distributed adaptive control architecture in the context of synchronizing multiple EL systems. It is established that the C-IE condition is milder than PE, IE, and C-PE conditions. Two-tier filter based estimation algorithm with strategic switching ensures parameter convergence under the C-IE condition and thereby provides exponential convergence of tracking and parameter estimation error to zero. Simulation results validate the efficacy of the proposed algorithm as compared to conventional distributed adaptive controllers in terms of superior tracking and estimation performance.