Collaborative System Identification via Consensus-Based novel PI-like Parameter Estimator

Abstract

This work proposes a consensus-based novel PI-like parameter estimator for collaborative system identification. Conventional online parameter estimation algorithms, which are used for system identification, require a restrictive condition of persistence of excitation (PE) for the estimates to converge to the true parameters. Some recent works have shown that collaborative system identification using multiple agents can relax the PE condition to a milder condition of collective persistence of excitation (C-PE) for parameter convergence. The C-PE condition implies that the PE condition is cooperatively satisfied by all the agents through sharing information between neighbors using a connected graph architecture, where each individual agent does not require to satisfy the PE condition separately. The proposed work designs a novel collaborative parameter estimator dynamics, which with the help of integral-like component ensures parameter convergence under a further slackened condition; coined as collective Initial Excitation (C-IE). The C-IE condition is an extension of the concept of initial excitation (IE), which is recently proposed in the context of parameter estimation in adaptive control. It has been already established that IE condition is significantly less restrictive than PE. The current work generalizes the concept of IE in a multi-agent settings, where information sharing through connected graph guarantees consensus parameter convergence under the C-IE condition. It can be argued that C-IE condition is milder than all of the other above mentioned conditions of PE, C-PE and IE. Simulation results further validate the efficacy of the proposed estimation algorithm.