引用本文

徐君, 张国良, 曾静, 杜柏阳, 贾枭. 高阶离散多智能体系统在参数不确定和带外部干扰下的鲁棒H∞一致性控制. 自动化学报, 2017, 43(10): 1850-1857. doi: 10.16383/j.aas.2017.e160115

Xu Jun, Zhang Guoliang, Zeng Jing, Du Boyang, Jia Xiao. Robust H∞ Consensus Control for High-order Discrete-time Multi-agent Systems With Parameter Uncertainties and External Disturbances. ACTA AUTOMATICA SINICA, 2017, 43(10): 1850-1857. doi: 10.16383/j.aas.2017.e160115

http://www.aas.net.cn/cn/article/doi/10.16383/j.aas.2017.e160115

关键词

外部干扰，多智能体系统，参数不确定，鲁棒一致性控制 

摘要

研究了高阶离散多智能体系统的在参数不确定和带外部干扰下的H∞鲁棒一致性控制问题，同时提出线性分布式一致性协议.首先将该问题转化为一组不确定系统的H∞鲁棒控制问题.其次推导出线性矩阵不等式在参数为γ的H∞鲁棒一致性意义下的充分条件.第三，给出了所提出一致性协议在不带外部干扰，参数不确定的高阶离散线性多智能体系统中的收敛效果.最后，通过包含和不包含参数不确定系统的对比仿真实验说明了理论结果的正确性和有效性.

文章导读

In recent years, distributed coordination of multi-agent systems (MASs) has received great attention from many researchers due to its broad applications on MASs in many areas including formation control [1], [2], flocking [3], [4], distributed filtering [5], [6], synchronization of coupled chaotic oscillators [7]-[9]. Consensus is an essential problem of distributed coordination of MASs, which is to make each agent agree on some common values of interest through feedback of local information from neighboring agents.

The theoretical framework for posing and solving the consensus problem for MASs was first introduced in [10]-[12]. Their work mostly focused on the first-order and second-order consensus in MASs. Furthermore, the consensus problem of MASs has obtained a tremendous surge of interest and extensive development. These works can be generally divided into two categories depending on whether the agent models are continuous-time or discrete-time. The union of interaction topologies must contain a spanning tree if MASs are expected to achieve consensus asymptotically [13]. A framework of high-dimensional state space for the consensus problems of MASs was studied in [14], and then the consensus problems of high order or more general linear MASs models were discussed in [15]-[17]. The consensus problem of discrete-time MASs (D-MASs) based on general linear models was investigated in [18], [19]. The leader-following consensus problem of D-MASs based on general linear models was studied in [20]. The robust guaranteed cost consensus problem of general linear D-MASs models with parameter uncertainties and time-varying delays was investigated in [21].

With the development of the research, the H_∞ consensus control problem of MASs subject to external disturbances was considered in [22]-[24]. Robust H_∞ consensus control problems of first-order MASs with external disturbances and model uncertainties are discussed in [22]. The second-order robust H_∞ consensus control problem of MASs with measurement noises and asymmetric delays is studied in [23]. Distributed and H_∞ consensus control problems are investigated in [24] for MASs with linear dynamics subject to external disturbances. The robust H_∞ consensus control problem of high-order linear MASs with parameter uncertainties and external disturbances was studied in [25], which also considered the time-delay and switching topology simultaneously. Specifically, the aforementioned works were based on continuous-time models, while the study of discrete-time model cases is more widely applied in practice. In [26], H_∞ synchronization and state estimation problems were considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. The robust H_∞ consensus control problem of high-order linear time-varying D-MASs with uncertainties/disturbances and missing measurements was investigated in [27]. The event-based H_∞ consensus control problem for high-order linear time-varying D-MASs over a finite horizon was studied in [28]. Nevertheless, although the robust H_∞ control consensus problem of high-order D-MASs with parameter uncertainties and external disturbances was addressed in [26]-[28], the final convergence value was not provided in these studies.

Motivated by the above, in this paper, the robust H_∞ control consensus problem of high-order D-MASs with parameter uncertainties and external disturbances is investigated by state space decomposition approach. We consider the leaderless consensus of the uncertain high-order D-MASs with fixed topologies. In this problem, if an appropriate consensus protocol is applied, the D-MASs should converge to a common value. Comparing with the existing works, the contribution of this paper is two-fold. On one hand, by state space decomposition approach, a sufficient linear matrix inequality (LMI) condition is given to guarantee that, high-order D-MASs subject to parameter uncertainties and external disturbances achieve robust consensus with a H_∞ performance index γ. On the other hand, with ω_x(k)≡ 0 or ω_x(k) interpreted as deterministic l₂ signal, final consensus values of high-order D-MASs with parameter uncertainties and external disturbances, which are first provided in this paper for the first time.

The rest of the paper is organized as follows. The problem formulation is presented in Section 2. In Section 3, the robust H_∞ consensus control problem of MASs (1) is transformed to a robust H_∞ control problem of a set of independent uncertain systems, and a sufficient LMI condition insuring the robust consensus, and a final consensus value of MASs (1) with protocol (4) are given. A numerical example is provided in Section 4 to verify the theoretical analysis. Some conclusions are finally drawn in Section 5 which concludes the paper and proposes some possible future directions. The notions of graph theory and Kronecker product that will be used in this paper are summarized in Appendix A and Appendix B, respectively.

图 1  The interaction topology G of 8 agents.

图 2  The state 1 trajectories of D-MASs (1).

图 3  The state 2 trajectories of D-MASs (1).

The robust H_∞ consensus control problem of high-order D-MASs with parameter uncertainties and external disturbances is investigated in this paper. A sufficient LMI condition is obtained to guarantee that D-MASs (1) achieve robust consensus with protocol (4). Meanwhile, the convergence result is given as a final consensus value. Finally, an illustrative example is given to demonstrate the correctness and effectiveness of the theoretical results. Further research will be conducted on the consensus problem of D-MASs with switching topologies and time-delays.

作者简介

Guoliang Zhang

is a Ph.D., Professor at Rocket Force University of Engineering.His research interests include robot technology, advanced control theory and application.E-mail:zhgl@sohu.com

Jing Zeng

is a Ph.D., Associate Professor at Rocket Force University of Engineering.Her research interests include robot technology, military operation research.E-mail:moulai@163.com

DU Bo-Yang 

is a Ph.D., candidate at Rocket Force University of Engineering.His research interests include multi-agent collaborative navigation and control.E-mail:duboyangepgc@163.com

JIA Xiao 

is a Ph.D.candidate at Rocket Force University of Engineering.His research interests include multi-agent collaborative navigation and control.E-mail:15091281454@163.com

Jun Xu 

is a Ph.D.candidate at Rocket Force University of Engineering, Xi'an, China.His research interests include multiagent collaborative navigation and control.Corresponding author of this paper.E-mail:Junxu1021@126.com