Consensus of General Linear Multi-Agent Systems With Heterogeneous Input and Communication Delays

Abstract

This paper studies the consensus tracking control for multi-agent systems (MASs) of general linear dynamics considering heterogeneous constant known input and communication delays under a directed communication graph containing a spanning tree. First, for open-loop stable MASs, a distributed predictive observer is proposed to estimate the consensus tracking error and to construct the control input that does not involve any integral term (which is time-efficient in calculation). Then, using the generalized Nyquist criterion, we derive the conditions for asymptotic convergence of the closed-loop system and show that is delay-independent. Subsequently, another observer is designed that allows the MASs to be open-loop unstable. Next, we use the generalized Nyquist criterion to compute the observer's gain matrix. Towards this end, we choose a specific structure with which the problem boils down to computing a single parameter, herein called the predictive observer parameter. Two algorithms are proposed for choosing this parameter: one for general linear systems and one for monotone systems. To the best of the authors' knowledge, this is the first work for which asymptotic convergence of consensus is proven for general linear MASs with arbitrary heterogeneous delays. Finally, the validity of our results is demonstrated via a vehicle platooning example.

Observer-based Control for Vehicle Platooning with a Leader of Varying Speed

“…Since A − BK is Hurwitz, i.e., Re(λ(A − BK)) < 0 and l ii is positive from Assumption 1, inspired by [28], if we design the term BL being non-negative definite, then, there is high possibility that Re(λ(A − BK − l ii BL)) < 0 can be satisfied. Herein, we propose one solution of L as…”

Multi-agent consensus with heterogeneous time-varying input and communication delays in digraphs

“…However, these LMI conditions are not scalable to arbitrarily large networks as the dimension of the LMI increases with the number of agents or the number of the delays. Alternatively, heterogeneous fixed delays can be transformed into the Laplace domain and approaches in the frequency domain (e.g., generalized Nyquist criterion) can be utilized to design controllers for specific dynamics of MASs, i.e., single-input-singleoutput (Münz, Papachristodoulou, & Allgöwer, 2010), first order (Ahmed, Khan, Saeed, & Zhang, 2020) and general linear dynamics (Jiang, Chen, & Charalambous, 2021). However, time-varying delays cannot be transformed and analyzed in the frequency domain.…”

“…There are also some works considering IDs and CDs si-multaneously. For example, for constant IDs and CDs, see (Ahmed et al, 2020;Jiang et al, 2021;Tian & Liu, 2008); for constant IDs but time-varying CDs, see (Xu et al, 2018;Zhou & Lin, 2014). To the authors' best knowledge, there is no work dealing with time-varying IDs and CDs at the same time, which is more realistic in real applications.…”

“…In this paper, time-varying HIDs and HCDs and external disturbances are addressed for multi-agent consensus tracking under a directed graph topology. Instead of designing an observer related to IDs and CDs together as in Jiang et al (2021), the idea is to decouple IDs and CDs during controller construction by designing an only-CD-related observer such that the ID can be dealt with inside each agent separately using the LMI technique. The main contributions are as follows.…”

“…As a result, the receiving node i is able to measure the delay τ cij (t) for a packet arriving from node j. Note that the assumption of known CDs appears in several works in the literature (see, e.g., Hou, Fu, Zhang, and Wu (2017); Jiang et al (2021); Zhou and Lin (2014) and references therein). Assumption 3 Graph G contains a directed spanning tree in which the leader acts as the root node.…”