Distributed fixed-time average-tracking for multi-agent systems with mismatched and matched disturbances

Abstract

In this paper, distributed fixed-time average-tracking problem is discussed for second-order multi-agent systems (MASs) with mismatched and matched disturbances. To address this issue, we first propose a novel distributed fixed-time average estimator for each agent to estimate the average value of multiple time-varying reference signals (TVRSs). Then, to tackle with the case in the presence of external mismatched and matched disturbances, a disturbance observer is constructed to estimate them in a fixed time. Finally, based on the disturbance observer, a fixed-time average-tracking protocol is designed to drive each agent to track the average value of multiple TVRSs within a fixed time. Simulation experiments are conducted to verify the effectiveness of the proposed fixed-time anti-disturbance average-tracking algorithm.

Fixed-Time Average Consensus for Delayed Multi-Agent Systems with Discontinuous Dynamics under Fixed and Switching Topology

“…Corollary 1. Under Assumptions 1, 2, and control protocol (28), for the given undirected and connected interaction topology g, if the inequalities (7), (8), and (9) hold, then, MAS (1) can reach finite-time average consensus and…”

“…7)-( 9) hold. It can be verify that Corollary 1 can be used to realize finite-time consensus under control protocol (28). Set the initial value as ζ(0)=[(0.9, −2.5), (1.5, 0), (0.2, −1), (0, 1.5), (−1.5, 3), (−0.65, 1.75), (2.3, 0.8)] T .…”

“…Compared with finitetime consensus, fixed-time consensus control has greater robustness and gives an analytical expression of the settling time independent of initial conditions. Thus, more and more control schemes are established to realize the fixed-time control problem [25][26][27][28]. For example, based on a class of special auxiliary matrices, a fixed-time synchronization problem of coupled neural networks is resolved in [26].…”

“…The problem of fixed-time stabilization for generic linear systems is considered in [27] using a proper control protocol. In [28], a control protocol is studied using a signed function to achieve fixed-time average consensus for MASs.…”

“…For example, it is often advantageous to model nonlinear chaotic systems with high slopes using a system of differential equations with a discontinuous right-hand side [29]. In addition, the control protocols studied in [25][26][27][28] cannot be directly utilized to tackle the problem.…”