Distributed Adaptive Control of Disturbed Interconnected Systems with High-Order Tuners

TL;DR

This paper develops distributed adaptive control algorithms for interconnected linear systems with disturbances, focusing on achieving consensus in multi-agent networks with various topologies using high-order tuners.

Contribution

It introduces a novel high-order tuner-based distributed control method for leader-follower networks with disturbances, improving convergence and robustness.

Findings

Modified high-order tuner outperforms other algorithms.

Increasing agents can reduce errors in some networks.

Network topology influences convergence and error patterns.

Abstract

This paper addresses the challenge of network synchronization under limited communication, involving heterogeneous agents with different dynamics and various network topologies, to achieve consensus. We investigate the distributed adaptive control for interconnected unknown linear subsystems with a leader and followers, in the presence of input-output disturbance. We enhance the communication within multi-agent systems to achieve consensus under the leadership's guidance. While the measured variable is similar among the followers, the incoming measurements are weighted and constructed based on their proximity to the leader. We also explore the convergence rates across various balanced topologies (Star-like, Cyclic-like, Path, Random), featuring different numbers of agents, using three distributed algorithms, ranging from first- to high-order tuners to effectively address time-varying regressors. The mathematical foundation is rigorously presented from the network designs of the unknown agents following a leader, to the distributed methods. Moreover, we conduct several numerical simulations across various networks, agents and tuners to evaluate the effects of sparsity in the interaction between subsystems using the $L_2-$norm and $L_\infty-$norm. Some networks exhibit a trend where an increasing number of agents results in smaller errors, although this is not universally the case. Additionally, patterns observed at initial times may not reliably predict overall performance across different networks. Finally, we demonstrate that the proposed modified high-order tuner outperforms its counterparts, and we provide related insights along with our conclusions.