A Separation-Based Methodology to Consensus Tracking of Switched High-Order Nonlinear Multi-Agent Systems

TL;DR

This paper introduces a novel separation-based adaptive control methodology for consensus tracking in uncertain high-order nonlinear multi-agent systems with switched dynamics, reducing complexity and high-gain issues.

Contribution

It proposes a new separable function definition enabling a simplified, less complex control design for high-order nonlinear multi-agent systems with switching behaviors.

Findings

Reduced control gain complexity in distributed control laws

Control gains increase only proportionally with system order

Effective consensus tracking achieved despite system uncertainties

Abstract

This work investigates a reduced-complexity adaptive methodology to consensus tracking for a team of uncertain high-order nonlinear systems with switched (possibly asynchronous) dynamics. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping methods successfully developed for low-order systems fail to work. At the same time, even the adding-one power-integrator methodology, well explored for the single-agent high-order case, presents some complexity issues and is unsuited for distributed control. At the core of the proposed distributed methodology is a newly proposed definition for separable functions: this definition allows the formulation of a separation-based lemma to handle the high-order terms with reduced complexity in the control design. Complexity is reduced in a twofold sense: the control gain of each virtual control law does not have to be incorporated in the next virtual control law iteratively, thus leading to a simpler expression of the control laws; the order of the virtual control gains increases only proportionally (rather than exponentially) with the order of the systems, dramatically reducing high-gain issues.