Distributed adaptive parameter estimation and control with relaxed excitation conditions

Abstract

Over the years, distributed adaptive parameter estimation/control for multi-agent systems (MASs) has gained a lot of attention in the form of dynamical systems, where the concept of cooperative persistence of excitation (C-PE) is proposed for accurate estimation of unknown parameters. The C-PE condition relaxes the traditional persistence of excitation (PE) condition in the sense that it can be satisfied by incorporating multiple system signals with each of them not necessarily being PE. However, the C-PE condition is still restrictive due to its persistent nature, which is difficult to satisfy in many practical control applications. The main objective of this dissertation is to relax the stringent C-PE condition requirement while still designing efficient distributed adaptive systems by utilizing different network topologies. The research is structured into three key sub-problems - 1 > Developing a relaxed excitation condition based distributed adaptive parameter estimation (DAPE) algorithm considering undirected connected graph network topology along with control application, 2 > Extending the framework to strongly connected directed graph network while also analyzing the effect of communication delay, 3 > Proposing a generalized relaxed excitation condition for DAPE over weakly connected digraph topology along with extremum-seeking control application. We have conceptualized a new condition, called cooperative initial excitation (C-IE), which is milder than the classical C-PE condition. We have proved that the C-IE condition is sufficient to ensure convergence for the proposed distributed adaptive algorithms using a rigorous Lyapunov analysis. Simulation results validate the efficacy of the proposed algorithms.