Consensus of heterogeneous linear multi-agent systems: Linear-transformation-based partial stability approach

Abstract

We deal with the state consensus problem of a general heterogeneous linear multi-agent system under a time-invariant and directed communication topology. First we adopt a general linear consensus protocol consisting of two parts. One is a state feedback of the agent for independently regulating its dynamics, and the other is a cooperative term in a generalized feedback form of the relative states between the agents. Then we propose a state-linear-transformation to equivalently transform the state consensus problem into a partial stability problem. Therefore, the result from the partial stability theory is applied to derive a sufficient and necessary algebraic criterion of consensus convergence, which is expressed in terms of the Hurwitz stability of a real matrix constructed from the parameters of both the agents’ models and the protocol. Meanwhile, an analytical formula of the consensus function is presented. Based on the criterion, we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.

Keywords

Heterogeneous linear multi-agent systems state-linear-transformation partial stability criterion of consensus convergence consensus function design of consensus protocol

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References

Chen

Zhang

(2014a) Partial stability approach to consensus problem of linear multi-agent systems, Acta Automatica Sinica 40(11): 1100–1111.

Chen

Guo

et al . (2014b) Output consensus of linear multi-agent systems: Linear-transformation-based partial stability approach. In: 2014 33rd Chinese control conference, Nanjing, China, 28–30 July 2014, pp. 1545–1550.

Fan

Wang

Zhang

et al . (2013) The synchronization of complex dynamical networks with similar nodes and coupling time-delay. Applied Mathematics and Computation 219(12): 6719–6728.

Goh

Safonov

Papavassilopoulos

(1994) A global optimization approach for the BMI problem. In: Proceedings of the 33rd IEEE conference on decision and control 3, Lake Buena Vista, FL, 14–16 December 1994, pp.2009–2014.

Grip

Yang

Saberi

et al . (2012) Output synchronization for heterogeneous networks of non-introspective agents. Automatica 48(10): 2444–2453.

Hassibi

How

Boyd

(1999) A path-following method for solving BMI problems in control. In: Proceedings of the 1999 American control conference 2, San Diego, California, 2–4 June 1999, pp.1385–1389.

Kim

Shim

Seo

(2011) Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Transactions on Automatic Control 56(1): 200–206.

Listmann

Wahrburg

Strubel

et al . (2011) Partial-state synchronization of linear heterogeneous multi-agent systems. In: IEEE conference on decision and control and european control conference (CDC-ECC), Orlando, Florida, 12–15 December 2011, pp.3440–3445.

Liu

(2011) Stationary consensus of heterogeneous MASs with bounded communication delays. Automatica 47(9): 2130–2133.

10.

Lunze

(2012) Synchronization of heterogeneous agents. IEEE Transactions on Automatic Control 57(11): 2885–2890.

11.

Miao

(2015) Output consensus for heterogeneous multi-agent systems with linear dynamics. Applied Mathematics and Computation 271: 548–555.

12.

Rodrigues de Campos

Briñón-Arranz

Seuret

et al . (2012) On the consensus of heterogeneous multi-agent systems: A decoupling approach. Estimation and Control of Networked Systems 3(1): 246–251.

13.

Shaw

Hedrick

(2007a) String stability analysis for heterogeneous vehicle strings. In: Proceedings of the 2007 American control conference, New York, USA, 11–13 July 2007, pp.3118–3125.

14.

Shaw

Hedrick

(2007b) Controller design for string stable heterogeneous vehicle strings. In: Proceedings of the 46th IEEE conference on decision and control, New Orleans, LA, 12–14 December 2007, pp.2868–2875.

15.

Shimomura

Fujii

(2000) Multiobjective control design via successive over-bounding of quadratic terms. In: Proceedings of the 39th IEEE conference on decision and control 3, Sydney, NSW Australia, 12–15 December 2000, pp. 2763–2768.

16.

Huang

(2012) Cooperative output regulation of linear multi-agent systems. IEEE Transactions on Automatic Control 57(4): 1062–1066.

17.

Tian

Zhang

(2012) High-order consensus of heterogeneous multi-agent systems with unknown communication delays. Automatica 48(6): 1205–1212.

18.

Vorotnikov

(1998) Partial Stability and Control. Boston, MA: Birkhauser.

19.

Wahrburg

Adamy

(2011) Observer-based synchronization of heterogeneous multi-agent systems by homogenization. In: Australian control conference (AUCC), Melbourne, Australia, 10–11 November 2011, pp.386–391.

20.

Wieland

Sepulchre

Allgöwer

(2011) An internal model principle is necessary and sufficient for linear output synchronization. Automatica 47(5): 1068–1074.

21.

Shi

Zhong

(2012) Output consensus analysis and design for high-order linear swarm systems: partial stability method. Automatica 48(9): 2335–343.

22.

Yin

Yue

(2013) Distributed event-triggered control of discrete-time heterogeneous multi-agent systems. Journal of the Franklin Institute 350(3): 651–669.

23.

Zheng

Wang

(2012) Consensus of heterogeneous multi-agent systems without velocity measurements. International Journal of Control 85(7): 906–914.