Fixed-Time Output Consensus Tracking for High- Order Multi-Agent Systems With Directed Network Topology and Packet Dropout Junkang Ni, Peng Shi, Fellow, IEEE, Yu Zhao, Member, IEEE, and Zhonghua Wu Abstract—This paper studies the problem of fixed-time output consensus tracking for high-order multi-agent systems (MASs) with directed network topology with consideration of data packet dropout. First, a predictive compensation based distributed observer is presented to compensate for packet dropout and estimate the leader’s states. Next, stability analysis is conducted to prove fixed time convergence of the developed distributed observer. Then, adaptive fixed-time dynamic surface control is designed to counteract mismatched disturbances introduced by observation error, and stabilize the tracking error system within a fixed time, which overcomes explosion of complexity problem and singularity problem. Finally, simulation results are provided to verify the effectiveness and superiority of the consensus tracking strategy proposed. The contribution of this paper is to provide a fixed-time distributed observer design method for high-order MAS under directed graph subject to packet dropout, and a novel fixed-time control strategy which can handle mismatched disturbances and overcome explosion of complexity and singularity problem. Index Terms—Directed graph, fixed-time control, multi-agent system, output consensus tracking, packet dropout.   I. Introduction R ECENTLY, increasing attention has been given to coordinated control of MAS since the MAS exhibits many useful and important features worthy of research [1]– [5]. As a fundamental behavior of MAS, consensus tracking means all the followers can reach consensus on the leader’s trajectory. There are two kinds of consensus tracking, i.e., full-state consensus tracking and output consensus tracking. Full-state consensus tracking requires that all the states of each follower track the leader’s trajectory, which is often suitable for first-order and second-order MAS. Output consensus tracking implies that the output of each follower tracks the output of the leader, which is often suitable for high-order MAS. Consensus tracking has been applied in many fields, such as, mobile robots, unmanned aerial vehicles, autonomous underwater vehicles, and microgrids. In practical MAS, due to oversaturated communication link, channel fading, actuator suspension, noise interference, excessive distance between transmitter and receiver, sensor failure and network attacks, packet dropout is inevitable. Most of the existing consensus tracking protocols rely on reliable information transmission and they may lose effectiveness in the event of packet dropout. Packet dropout changes the communication topology stochastically, introduces consensus tracking error, reduces control performance and even causes instability. Therefore, it is necessary to take packet dropout into account when designing consensus tracking protocol. Recently, fruitful results have been reported on consensus tracking with consideration of packet dropout. References [6]–[8] modeled packet dropout as a Bernoulli distribution stochastic process and used the previous states of its neighbors to construct the current control strategy when packet dropout occurs. In [9]–[14], packet dropout was modeled as time- varying connection strength subject to Bernoulli distribution, i.e., the connection strength will become zero if packet dropout occurs in the communication link. In [15], a stochastically perturbed communication channel was used to describe packet dropout. Based on historical data, the predictive compensation method was presented in [16], [17] to replace missing data when packet dropout occurred. Reference [18] considered deterministic packet dropout and applied switched system with stable and unstable subsystem to develop a zero input packet dropout consensus tracking protocol. Wen et al. [19] treated packet dropout as intermittent communication. In [20], the effect of packet dropout was modeled as a multiply of the transmitted signal and packet dropout rate. In [21], packet dropout was modeled as a Markov chain. These results developed consensus tracking protocols and proved the asymptotical convergence of the presented control strategy using Lyapunov approach, stochastic analysis and stability property of system matrix. Manuscript received September 8, 2020; accepted November 28, 2020. This work was supported in part by the National Natural Science Foundation of China (61903302, 61973252, 61903126), the Natural Science Basic Research Plan in Shaanxi Province of China (2019JQ-035), the Fundamental Research Funds for the Central Universities (31020180QD076, ZDHXYKYYW201914), Key R&D and Promotion Projects in Henan Province (202102210130), Key Scientific Research Projects of Universities in Henan Province-20A590001. Recommended by Associate Editor Hongyi Li. (Corresponding author: Junkang Ni.) Citation: J. K. Ni, P. Shi, Y. Zhao, and Z. H. Wu, “Fixed-time output consensus tracking for high-order multi-agent systems with directed network topology and packet dropout,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 817–836, Apr. 2021. J. K. Ni and Y. Zhao are with the School of Automation, Northwestern Polytechnical University, Xi’an 710072, China (e-mail: max12391@126.com; yuzhao5977@gmail.com). P. Shi is with the School of Electrical and Electronic Engineering, University of Adelaide, SA 5005, Australia (e-mail: peng.shi@adelaide. edu.au). Z. H. Wu is with the College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China (e-mail: wuzhonghua@hpu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2021.1003916 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 4, APRIL 2021 817