Distributed adaptive estimation without persistence of excitation: An online optimization perspective

Abstract

SummaryThis work proposes a distributed adaptive estimation algorithm for multi‐agent system (MAS) architecture using online measurements in a continuous‐time setting. Classical adaptive parameter estimation algorithms demand to satisfy persistence of excitation (PE) or its distributed variant cooperative persistent of excitation (C‐PE) for parameter convergence. PE, C‐PE, are restrictive in nature since it requires excitation (richness of information content) over the entire time span of the signal/data, making it unrealistic in most real‐world applications, especially in robotics and cyber‐physical systems. Unlike past literature, the proposed work ensures parameter convergence under a slackened condition, coined as cooperative initial excitation (C‐IE), which demands information richness only in the initial time‐window (transient period) suitable for practical scenarios. A distributed differential parameter estimator algorithm is designed, which with the help of stable closed‐loop filter dynamics and strategic switching guarantees global exponential stability (GES) of the parameter estimation error dynamics in the sense of Lyapunov. The formulation is further augmented by providing an online optimization perspective. A novel cost function is constructed in such a way that the proposed distributed parameter estimator acts as a distributed continuous‐time gradient‐descent algorithm based on the cost function and the true uncertain parameter vector is the global minima of the cost function. Simulation results validate the efficacy of the proposed algorithm in contrast to the PE/C‐PE based methods.