Observer‐predictor feedback for consensus of discrete‐time multiagent systems with both state and input delays

Abstract

This article is concerned with the consensus problem for discrete-time multiagent systems with both state and input delays. Single observer-predictor-based protocols and multiple observer-predictors feedback protocols are simultaneously established to predict the future state such that the input delay that can be arbitrarily large yet bounded is completely compensated. It is shown that the consensus of the multiagent system can be achieved by the single/multiple observer-predictors feedback protocol. Moreover, sufficient conditions guaranteeing the consensus of the multiagent system are provided in terms of the stability of some simple observer-error systems, and the separation principle is discovered. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approaches. K E Y W O R D Sconsensus, input delay compensation, multiagent systems, observer-predictor feedback, state and input delays INTRODUCTIONIn recent years, distributed coordination of networks of dynamic agents has attracted several researchers due to its broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles, formation control, 1 flocking, 2 and distributed sensor networks. 3 However, consensus problems have attracted significant interests from the control theory community and has been intensively investigated in the literature. 4-8 Many early results on consensus problem are based on single integrators or second-order dynamics (see, References 1,9,10 and the references therein). Afterward, the consensus problem for high-order linear multiagent systems was studied. 11 For example, the consensus problem of multiagent systems with delays was investigated in Reference 12 by discrete-time predictor feedback, and the consensus problem of multiagent systems with a time-invariant communication topology and consensus disturbance rejection of network-connected dynamic systems were discussed in References 13 and 14, respectively. Generally, time-delays are inevitable in the consensus control. Therefore, consensus of multiagent systems with communication/input delays has been extensively investigated in the literature. For example, the consensus problem for multiagent systems with input and communication delays was studied in Reference 15, both the leaderless consensus problem and the leader-following consensus problem for linear discrete-time multiagent systems under switching network topology were studied in Reference 16, the consensus problem of multiagent systems with nonuniform time-delays and dynamically changing topologies was considered in Reference 17, the consensus and quasi-consensus problems in Int J Robust Nonlinear Control. 2020;30:4003-4021.wileyonlinelibrary.com/journal/rnc

Predictor-based control of time-delay systems: a survey

“…In (Jiang, Peng, Rahmani, Hu, & Wen, 2018;Liu, 2020), the observation-predictor-based controllers were proposed for continuous-time perturbed LTI MASs and discrete-time MASs with state and input delays, respectively. Hereafter, the observation-predictor-based consensus control of LTI MASs simultaneously subject to input delay and communication delay was tackled in (Jiang, Chen, & Charalambous, 2020).…”

Discrete time‐delay multiagent networks: Pseudo‐predictor, full‐order, and reduced‐order observer

“…Whereafter, for multiagent networks with time delays in the state, input and communication, a nested predictor feedback (NPF) protocol and full‐order/reduced‐order observer based NPF protocol were proposed in Reference 32 to consider the consensus problem. The single/multiple observer‐predictor feedback protocol was presented in Reference 33, wherein the consensus problem was settled by means of the stability of the simple linear time‐delay system.…”

“…The PPF protocol proposed in this article not only overcome the shortcomings of the NPF protocol, but also it is easier to implement. On the other hand, the PPF protocol makes use of the closed‐loop dynamics to predict the future states, which is completely different from the NPF protocol 32 and the observer‐predictor feedback protocol 33 utilizing the open‐loop dynamics and the observer to predict the future states. Additionally, only full‐order observer based feedback protocol was established in Reference 33.…”

“…It is disclosed that the convergence rate of the states is fastest under the PPF protocol. Unlike the NPF protocol that is connected with the history information of input and the summations terms of the neighboring agents, 32,33 which may cause considerable calculation burden. The PPF protocol proposed in this article not only overcome the shortcomings of the NPF protocol, but also it is easier to implement.…”

Nonlinear Fractional Active Disturbance Rejection Speed Control for Stabilization of Hydraulic Turbine Regulating Systems With Mechanical Delay

“…The phenomenon of delays has a great influence on uncertain nonlinear systems. The research on time-delay compensator has also developed rapidly [22][23][24][25], such as the output feedback compensator [22], and the predictor compensator [25]. The existing research primarily focuses on linear ADRC, such as the stability analysis of linear ADRC [26], analysis of ADRC for systems with uncertainty and delay [27], and exponential stability analysis of a closed-loop system [28].…”