Elsevier

Neurocomputing

Volume 364, 28 October 2019, Pages 219-226
Neurocomputing

Finite-horizon distributed H-consensus control of time-varying multi-agent systems with Round-Robin protocol

https://doi.org/10.1016/j.neucom.2019.07.013Get rights and content

Abstract

This paper takes into account the H-consensus control problem for a class of uncertain discrete time-varying multi-agent systems which is constrained by Round-Robin scheduling protocol and measurement saturations. In the multi-agent system under consideration, all the system parameters are time-varying to better reflect the practical engineering. The Round-Robin protocol is utilized to alleviate the communication congestion in a shared constrained network by scheduling the information transmission among agents, where an agent can receive one neighbor’s information at each time instant and the transmission order of neighboring agents is regulated. The aim of the research is to design consensus controller for each agent over an assigned finite horizon such that the closed-loop multi-agent systems with saturated measurement outputs can satisfy the H disturbance attenuation level. Next, a sufficient condition is derived to ensure the H-consensus performance constraint based on the Lyapunov stability theory. Then, the controller parameters can be obtained by solving recursively a linear matrix inequality at every time instant. Finally, a numerical example is provided to show the effectiveness of the developed consensus control scheme.

Introduction

The multi-agent systems (MASs) have become the main research objectives by degrees during the past two decades due to their widespread applications in various areas such as multi-robots systems, air vehicles, formation control, swarms and flocks [2], [22], [24], [32], [37]. As is well known, the main purpose of MASs research is to complete the complex tasks through the distributed cooperative and coordinated control with all agents, which is the application foundation of MASs, the key to give play to the advantages of MASs and the embodiment of the intelligence of the whole system.

The consensus control, as the basis of the cooperative coordinated control between agents, has important practical significance and theoretical value. The so-called consensus refers to that the state of all agents in a MAS tends to keep consistent with the evolution of time. In recent years, the research on the consensus problem has been developed rapidly in the fields including biological science, physical science, system and control science, computer science and many others, which has brought out in-depth analysis from different levels [5], [7], [8], [14], [19], [23], [36]. For instance, [19] and [14] have concerned with the H-consensus control issue for second-order MASs. The network-based leader-follower consensus issue has been investigated in [7] for MASs via distributed impulsive control. In [5], the consensus control issue has been studied for stochastic MASs with state-dependent noises and event-triggered scheme.

Up to now, most existing research work on consensus control problems has assumed the MAS has time-invariant parameters. Actually, this hypothesis is very restrictive as almost all the system parameters are time-varying in practical engineering process [1]. It is worthwhile noting that, for such systems with time-varying parameters, a controller over finite-horizon is recommendable as it can supply better transient performance for the system to be studied. As a result, it is significant to study the control issues for a system with time-varying parameters over a finite horizon. Some results have been achieved on this problem, for example [6], [20]. An observer-based reliable controller has been designed in [20] for the discrete systems with time-varying parameters, time-delays, quantization effects and parameter uncertainties. However, there have been scattered research results for the consensus control of time-varying MASs, since it is difficult to quantify the consensus performance within a finite time domain [21], [31], [33]. To date, the consensus control issue for time-varying multi-agent systems over a finite time domain has not been explored in depth, which leads to one motivation of our research.

Most of the MASs work has supposed that there is an ideal communication channel among agents, that is, each agent can access its neighboring agents’ state information accurately and timely. Obviously, this is only an ideal approximation for real communication channels. In fact, the limited communication capacity among agents is an unavoidable issue [6], [33], which motivates many researchers to study the consensus control problem with various communication protocols. For instance, the H-consensus control issue has been discussed in [39] for a number of MASs with time-varying parameters subject to the stochastic communication protocol (SCP). As an important scheduling strategy, Round-Robin (RR) protocol has been used in [26], [27], [29], [34], [40] for state estimation. In this paper, the RR protocol is used to determine which neighboring agent’s information can be sent to an agent in the MASs at each time instant, so that the problems of packet dropouts or channel congestion can be effectively avoided. In addition, an agent cannot send/receive signals with unlimited amplitude due to the design or technical constraints [4], [11], [30], [35]. The measurement saturation is a kind of accidental phenomena, which will have important impact on the performance of the consensus control of the MASs. As such, it is more significant to take the measurement saturation into account when dealing with the consensus control issue for MASs with time-varying parameters and RR protocol, which remains as an ongoing research issue.

Based on the aforementioned arguments, in this paper, we are motivated to study the H-consensus control issue for a kind of MASs with time-varying parameters subject to RR protocol and measurement saturations. The main contributions of our research can be summarized as below: (1) the time-varying parameters and measurement saturations are introduced to the considered multi-agent systems, which is closer to practical applications; (2) the RR protocol is used to schedule the information transmission among the neighboring agents to avoid communication collisions; (3) by using Lyapunov stability theory, the sufficient condition is obtained in the form of recursive linear matrix inequalities (RLMIs) to ensure the desirable H-consensus control performance.

The remaining of this article is arranged as below. In Section 2, some preparations are briefly outlined and a class of discrete time-varying MASs with RR protocol and measurement saturation are introduced. In Section 3, the design issue of the consensus control scheme is studied, the sufficient condition is constructed for the existence of the consensus controllers and the controller gains of the H-consensus controllers are solved by means of the solution to the RLMIs. In addition, a numerical example is provided in Section 4 to show the usefulness of the proposed method in this paper. At last, in Section 5, some conclusions are summarized.

Notation: The notations used in this paper is fairly standard except where otherwise stated. MT represents the transpose of M. Rx represents the x dimensional Euclidean space and Rx×y is the set of all x × y real matrices. The notation Q > 0 means that Q is a real, positive definite matrix. The notation diag{A1,A2,,An} stands for a block-diagonal matrix. * always denotes the symmetric block in a symmetric matrix. mod(x, y) denotes the unique nonnegative remainder on division of the integer x by the positive integer y. δ(x) is a binary function which equals to 1 for x=0 and equals to 0 for x ≠ 0. The operator ⊗ represents the Kronecker product. ∘ denotes the Hadamard product operation. 1n × n denotes an n × n matrix with all elements being 1. The N-dimensional identity matrix is denoted as IN or simply I, if no confusion is caused.

Section snippets

Problem formulation

The MAS concerned in this paper has S agents with the communication topology described by a directed graph D. Let D=(J,O,A) be a graph of order S where J={1,2,,S} is the set of agents, O=J×J is the set of edges, and A=[aij] is the weighted adjacency matrix. The adjacency elements related to the edges of graph D are non-negative, i.e. aij>0(i,j)O, which means that agent j is a neighboring agent of agent i and agent i can obtain information form agent j. Obviously, aij=0(i,j)O means that

Main results

Before further processing, the lemmas listed below are introduced for facilitating the derivation of our research results.

Lemma 3

(S-procedure)[3]

Let A=AT, B, C and D be real matrices of appropriate dimensions with C satisfying CTC ≤ I, then A+BCD+DTCTBT<0, if and only if there exists a positive scalar ϵ > 0 such that A+ϵ1BBT+ϵDTD<0 or equivalently,[A**BTϵI*ϵD0ϵI]<0.

Lemma 4

[9]

For a full-column rank matrix B(k)Rnx×nu (nx > nu), there always exist two orthogonal matrices Q(k)Rnx×nx and N(k)Rnu×nu satisfyB(k)=Q(k)[k0]NT(k)=[

An illustrative example

In this section, a simulation example is provided to demonstrate the usefulness of the proposed H-consensus controller design algorithm for MASs in the presence of RR protocol, measurement saturation and parameter uncertainties simultaneously.

Take into account of a MAS with three agents whose communication topology is expressed by a directed graph D=(J,O,A) with the set of nodes J={1,2,3} and the corresponding adjacency matrix A preset as below:[011101110].

Consider the system (2) with the

Conclusion

In this paper, the distributed H-consensus controller design issue has been studied for a kind of discrete MASs with time-varying parameters and uncertainties, measurement saturation and RR communication protocol. The RR protocol has been employed under which only one neighboring agent is determined to obtain access to the agent at one time step. Sufficient conditions have been derived such that the MAS under study satisfies the H performance constraint. According to the Lyapunov stability

Declaration of competing interest

None.

Acknowledgement

This work was supported in part by the National Natural Science Foundation of China under Grants 61873148 and 61873058, the China Postdoctoral Science Foundation under Grant 2017M621242, the PetroChina Innovation Foundation under Grant 2018D-5007-0302, the Fundamental Research Funds for Undergraduate Universities affiliated to Heilongjiang Province under Grant 2018QNL-05, the Natural Science Foundation of Heilongjiang Province of China under Grant F2018005 and the Alexander von Humboldt

Jinbo Song received her M.Sc. degree in Automation in 2007 from Northeast Petroleum University, Daqing, China. She is currently working toward the Ph.D. degree in Petroleum and Natural Gas Engineering at the Northeast Petroleum University, Daqing, China. Her research interests include multi-agent systems, oil gas information and control engineering.

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    Jinbo Song received her M.Sc. degree in Automation in 2007 from Northeast Petroleum University, Daqing, China. She is currently working toward the Ph.D. degree in Petroleum and Natural Gas Engineering at the Northeast Petroleum University, Daqing, China. Her research interests include multi-agent systems, oil gas information and control engineering.

    Fei Han received the B.Sc. degree in mathematics and applied mathematics from China University of Ming and Technology, Xuzhou, China, in 2003 and the M.Sc. degree in applied mathematics from Henan Normal University, Xinxiang, China, in 2009, and the Ph.D. degree in system analysis and integration from University of Shanghai for Science and Technology, Shanghai, China, in 2017. From March 2018 to June 2018, he was a Senior Research Assistant in the Department of Electronic Engineering, the City University of Hong Kong. He is currently an Associate Professor with the Institute of Complex Systems and Advanced Control, Northeast Petroleum University, Daqing, China. His current research interests include distributed control and filtering.

    Haijing Fu was born in Inner Mongolia, China, in 1993. She received the B.Sc. degree from school of mechanical engineering, Inner Mongolia University of Science and Technology, Inner Mongolia, China, in 2018. She is currently pursing the M.S. degree with the Institute of Complex Systems and Advanced Control, Northeast Petroleum University, Daqing, China.

    Hongjian Liu received his B.Sc. degree in applied mathematics in 2003 from Anhui University, Hefei, China and the M.Sc. degree in detection technology and automation equipments in 2009 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in control theory and control engineering in 2018 from Donghua University, Shanghai, China. In 2016, he was a Research Assistant with the Department of Mathematics, Texas A&M University at Qatar, Doha, Qatar, for two months. From March 2017 to March 2018, he was a Visiting Scholar in the Department of Information Systems and Computing, Brunel University London, UK. He is currently an Associate Professor in the School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China. His current research interests include filtering theory, memristive neural networks and network communication systems. He is a very active reviewer for many international journals.

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