Full Text:   <2163>

Summary:  <1953>

CLC number: TP273

On-line Access: 2016-02-02

Received: 2015-12-30

Revision Accepted: 2016-01-20

Crosschecked: 2016-01-22

Cited: 1

Clicked: 5515

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yin-qiu Wang

http://orcid.org/0000-0002-1410-9619

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2016 Vol.17 No.2 P.96-109

http://doi.org/10.1631/FITEE.1500490


Optimization of formation for multi-agent systems based on LQR


Author(s):  Chang-bin Yu, Yin-qiu Wang, Jin-liang Shao

Affiliation(s):  1School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China; more

Corresponding email(s):   brad.yu@anu.edu.au, wh6508@gmail.com, jinliangshao@126.com

Key Words:  Linear quadratic regulator (LQR), Formation control, Algebraic Riccati equation (ARE), Optimal control, Multi-agent systems


Chang-bin Yu, Yin-qiu Wang, Jin-liang Shao. Optimization of formation for multi-agent systems based on LQR[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(2): 96-109.

@article{title="Optimization of formation for multi-agent systems based on LQR",
author="Chang-bin Yu, Yin-qiu Wang, Jin-liang Shao",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="17",
number="2",
pages="96-109",
year="2016",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1500490"
}

%0 Journal Article
%T Optimization of formation for multi-agent systems based on LQR
%A Chang-bin Yu
%A Yin-qiu Wang
%A Jin-liang Shao
%J Frontiers of Information Technology & Electronic Engineering
%V 17
%N 2
%P 96-109
%@ 2095-9184
%D 2016
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500490

TY - JOUR
T1 - Optimization of formation for multi-agent systems based on LQR
A1 - Chang-bin Yu
A1 - Yin-qiu Wang
A1 - Jin-liang Shao
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 17
IS - 2
SP - 96
EP - 109
%@ 2095-9184
Y1 - 2016
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1500490


Abstract: 
In this paper, three optimal linear formation control algorithms are proposed for first-order linear multi-agent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.

The authors of this paper provide three algorithms for optimal linear formation control of multi-agent systems. The agents are considered to have single integrator dynamics. In this connection they used LQR method to minimize collective objective of all agents and the individual objective of each agent. Three cases of independent agents, physically bounded agents, and a network of agents with fixed topology are considered. The paper is technically correct and the mathematical derivations are accurate. The results are a bit interesting.

基于线性二次最优化的多智能体编队控制

目的:随着空间技术和计算机技术的发展,空间飞行器协作控制越来越受到重视。多智能体编队控制是研究这一类问题的基础。本文研究了三种情况下单积分器多智能体系统基于线性二次最优性能指标的编队控制问题,并设计相应的控制算法保证多智能体系统在完成编队的基础上使所定义的性能指标达到最优。
创新点:针对三种不同的单积分器多智能体最优编队情况,分别提出相应的网络连接拓扑以及局部反馈矩阵;不同于其他论文不能给出网络拓扑以及局部最优反馈矩阵的具体解析解,本文给出相应的解析解,并且证明解析解与实际物理系统完全相符。
方法:应用代数图论以及矩阵理论的相关知识,针对无物理耦合的多智能体系统,通过求解代数里卡蒂方程,设计智能体之间的网络连接拓扑以及局部反馈矩阵,保证多智能体系统在完成编队的同时相应的LQR指标最优。针对有物理耦合的多智能体系统,同样通过求解代数里卡蒂方程,得到相应的网络连接拓扑以及局部反馈矩阵,保证多智能体系统在完成编队的基础上使相应的LQR指标最优;针对有物理耦合但无法设计网络拓扑的多智能体系统,将最优指标写成局部反馈增益的函数,通过求最优指标的导数,得到最优局部反馈增益。
结论:对于无物理耦合单积分器多智能体的编队问题与有物理耦合单积分器多智能体的编队问题,分别设计网络连接拓扑以及局部反馈矩阵,在多智能体系统完成编队的基础上保证相应的性能指标达到最优。对于有物理耦合但无法改变通讯网络拓扑的单积分器多智能体系统编队问题,设计最优局部反馈增益,在多智能体系统完成编队的同时保证性能指标最优。

关键词:线性二次最优;编队控制;代数里卡蒂方程;最优控制;多智能体系统

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Alefeld, G., Schneider, N., 1982. On square roots of M-matrices. Linear Algebra Appl., 42:119-132.

[2]Altafini, C., 2013. Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Contr., 58(4):935-946.

[3]Anderson, B.D.O., Moore, J.B., 2007. Optimal Control: Linear Quadratic Methods. Dover Publications, USA.

[4]Basiri, M., Bishop, A.N., Jensfelt, P., 2010. Distributed control of triangular formations with angle-only constraints. Syst. Contr. Lett., 59(2):147-154.

[5]Bishop, A.N., 2011. A very relaxed control law for bearing-only triangular formation control. Proc. 18th IFAC World Congress, p.5991-5998.

[6]Borrelli, F., Keviczky, T., 2008. Distributed LQR design for identical dynamically decoupled systems. IEEE Trans. Autom. Contr., 53(8):1901-1912.

[7]Cao, Y., Ren, W., 2010. Optimal linear-consensus algorithms: an LQR perspective. IEEE Trans. Syst. Man Cybern. Part B, 40(3):819-830.

[8]Dimarogonas, D.V., Johansson, K.H., 2010. Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control. Automatica, 46(4):695-700.

[9]Ghadami, R., Shafai, B., 2013. Decomposition-based distributed control for continuous-time multi-agent systems. IEEE Trans. Autom. Contr., 58(1):258-264.

[10]Ghadami, R., Shafai, B., 2014. Distributed observer-based LQR design for multi-agent systems. World Automation Congress, p.520-525.

[11]Godsil, C., Royle, G.F., 2013. Algebraic Graph Theory. Springer, USA.

[12]Guo, J., Lin, Z., Cao, M., et al., 2010. Adaptive control schemes for mobile robot formations with triangularised structures. IET Contr. Theory Appl., 4(9):1817-1827.

[13]Horn, R.A., Johnson, C.R., 1985. Matrix Analysis. Cambridge University Press, USA.

[14]Horn, R.A., Johnson, C.R., 1991. Topics in Matrix Analysis. Cambridge University Press, USA.

[15]Huang, H., Yu, C., Wu, Q., 2010. Distributed LQR design for multi-agent formations. Proc. 49th IEEE Conf. on Decision and Control, p.4535-4540.

[16]Li, Z., Duan, Z., Lewis, F.L., 2014. Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties. Automatica, 50(3):883-889.

[17]Liu, T., Jiang, Z., 2014. Distributed nonlinear control of mobile autonomous multi-agents. Automatica, 50(4):1075-1086.

[18]Movric, K.H., Lewis, F.L., 2014. Cooperative optimal control for multi-agent systems on directed graph topologies. IEEE Trans. Autom. Contr., 59(3):769-774.

[19]Oh, K.K., Park, M.C., Ahn, H.S., 2015. A survey of multi-agent formation control. Automatica., 53(3):424-440.

[20]Qin, J., Gao, H., 2012. A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with nonuniform and time-varying communication delays. IEEE Trans. Autom. Contr., 57(9):2417-2422.

[21]Qin, J., Gao, H., Zheng, W.X., 2011. Second-order consensus for multi-agent systems with switching topology and communication delay. Syst. Contr. Lett., 60(6):390-397.

[22]Ren, W., Beard, R.W., Atkins, E.M., 2007. Information consensus in multivehicle cooperative control. IEEE Contr. Syst. Mag., 27(2):71-82.

[23]Shi, G., Sou, K.C., Sandberg, H., et al., 2014. A graph-theoretic approach on optimizing informed-node selection in multi-agent tracking control. Phys. D, 267:104-111.

[24]Xiao, F., Wang, L., Chen, J., et al., 2009. Finite-time formation control for multi-agent systems. Automatica, 45(11):2605-2611.

[25]Yu, C., Hendrickx, J.M., Fidan, B., et al., 2007. Three and higher dimensional autonomous formations: rigidity, persistence and structural persistence. Automatica, 43(3):387-402.

[26]Yu, C., Anderson, B.D.O., Dasgupta, S., et al., 2009. Control of minimally persistent formations in the plane. SIAM J. Contr. Optim., 48(1):206-233.

[27]Zhang, H., Lewis, F.L., Das, A., 2011. Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Autom. Contr., 56(8):1948-1952.

[28]Zhao, S., Lin, F., Peng, K., et al., 2014. Distributed control of angle-constrained cyclic formations using bearing-only measurements. Syst. Contr. Lett., 63:12-24.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE