Time-Varying Formation Tracking With Prescribed Performance for Uncertain Nonaffine Nonlinear Multiagent Systems

Abstract

Formation tracking is a critical issue in the consensus control of multiagent systems (MASs). This article presents a time-varying formation tracking strategy with predefined performance for a class of uncertain nonaffine nonlinear MASs connected through a directed topology. The nonaffine nonlinear MASs are transformed into affine nonlinear ones with uncertainties via the idea of active disturbance rejection control (ADRC). The uncertainties in the MASs are approximated and compensated by extended state observers (ESOs) in real time. Tracking differentiators (TDs) are introduced to reduce the complexity in the computation of the derivatives of virtual control variables. Employing funnel variables, our strategy guarantees the formation of tracking errors to stay within the desired ranges, thus improving the control performance of the closed-loop system. It is proved that all signals of the system are bounded and the formation errors can be made arbitrarily small within a residue around the origin by appropriate choices of control parameters. Case studies are carried out to demonstrate the effectiveness of the proposed control strategy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this article is to present a time-varying formation tracking strategy with predefined performance for a class of uncertain nonaffine nonlinear MASs within a directed topology. To simplify the process of solving the formation tracking problem, the presented strategy incorporates ADRC with the backstepping technique. Employing ADRC, our strategy approximates the uncertainties of the MAS followers via ESOs. The uncertainties are then compensated through real-time estimations of extended states. Moreover, with ADRC, TDs are used to estimate the derivatives of complex nonlinear functions, eliminating the requirement of the operations of higher order derivatives of virtual control variables. It provides a feasible strategy for industrial applications.