Closed-loop reference model based distributed MRAC using cooperative initial excitation and distributed reference input estimation

Raghavv Goel, tushar garg, Sayan Basu Roy

Abstract: This article proposes a novel closed-loop reference model (CRM) architecture for a distributed model reference adaptive control (DMRAC) algorithm, called CRM-DMRAC. The idea of CRM has been recently conceptualized in the literature for a single agent system where the reference model (leader) receives feedback from the plant (follower) while enabling the use of high gain tuners without adding more transients in the parameter estimation. In this article, a CRM formulation is proposed where the leader receives feedback from a subset of follower agents (which are called neighbors of the leader). The external input to the leader is not shared with any of the followers unlike traditional MRAC algorithms. A novel external input estimator is proposed inspired from dynamic surface control in a hierarchical and cooperative manner. Further, the adaptation scheme is based on a newly defined excitation condition, called cooperative initial excitation (C-IE). The C-IE condition is significantly relaxed as compared to cooperative persistence of excitation, which is required for parameter convergence in traditional distributed adaptive controllers. The closed-loop system using the proposed adaptive controller has proven to be globally uniformly ultimately bounded. As a special case, it is shown that the closed-loop error dynamics will be exponentially converging to zero if the external input is available to all the followers. Numerical simulations validate the proof of concept, which illustrates the superiority in terms of transients response, estimation performance, and control effort for the proposed method over conventional open-loop reference model DMRAC and CRM-DMRAC without C-IE.