Containment control of multi-agent systems by exploiting the control inputs of neighbors
Corresponding Author
Shuai Liu
School of Control Science and Engineering, Shandong University, Jinan, China
EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
Correspondence to: Shuai Liu, School of Control Science and Engineering, Shandong University, Jinan, China.
E-mail: [email protected]
Search for more papers by this authorLihua Xie
EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
Search for more papers by this authorHuanshui Zhang
School of Control Science and Engineering, Shandong University, Jinan, China
Search for more papers by this authorCorresponding Author
Shuai Liu
School of Control Science and Engineering, Shandong University, Jinan, China
EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
Correspondence to: Shuai Liu, School of Control Science and Engineering, Shandong University, Jinan, China.
E-mail: [email protected]
Search for more papers by this authorLihua Xie
EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
Search for more papers by this authorHuanshui Zhang
School of Control Science and Engineering, Shandong University, Jinan, China
Search for more papers by this authorSUMMARY
This paper studies the containment control problem for multi-agent systems consisting of multiple leaders and followers connected as a network. The objective is to design control protocols so that the leaders will converge to a certain desired formation while the followers converge to the convex hull of the leaders. A novel protocol is proposed by exploiting the control input information of neighbors. Both continuous-time and discrete-time systems are considered. For continuous-time systems, it is proved that the protocol is robust to any constant delays of the neighbors' control inputs. For discrete-time systems, a sufficient condition on the feedback gain for the containment control is given in terms of the time delay and graph information. Some numerical examples are given to demonstrate the results. Copyright © 2013 John Wiley & Sons, Ltd.
REFERENCES
- 1 Jadbabaie A, Jie L, Morse AS. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control 2003; 48(6): 988–1001.
- 2 Olfati-Saber R, Murray RM. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 2004; 49(9): 1520–1533.
- 3
Ren W,
Beard RW. Distributed Consensus in Multi-Vehicle Cooperative Control. Springer: London, 2008.
10.1007/978-1-84800-015-5 Google Scholar
- 4 Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica 2008; 44(3): 846–850.
- 5 Peng K, Yang Y. Leader-following consensus problem with a varying-velocity leader and time-varying delays. Physica A: Statistical Mechanics and its Applications 2009; 388(2-3): 193–208.
- 6 Ni W, Cheng D. Leader-following consensus of multi-agent systems under fixed and switching topologies. Systems & Control Letters 2010; 59(3-4): 209–217.
- 7 Ma C, Li T, Zhang J. Consensus control for leader-following multi-agent systems with measurement noises. Journal of Systems Science and Complexity 2010; 23(1): 35–49.
- 8 Gustavi T, Dimarogonas DV., Egerstedt M, Hu X. Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks. Automatica 2010; 46(1): 133–139.
- 9 Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O. Novel type of phase transition in a system of self-driven particles. Physical Review Letters 1995; 75(6): 1226.
- 10 Ji M, Ferrari-Trecate G, Egerstedt M, Buffa A. Containment control in mobile networks. IEEE Transactions on Automatic Control 2008; 53(8): 1972–1975.
- 11
Ferrari-Trecate G,
Egerstedt M,
Buffa A,
Ji M,
Hespanha J,
Tiwari A. Laplacian sheep: a hybrid, stop-go policy for leader-based containment control. In Hybrid Systems: Computation and Control, Lecture Notes in Computer Science. Springer: Berlin / Heidelberg, 2006; 212–226.
10.1007/11730637_18 Google Scholar
- 12 Khan UA, Kar S, Moura JMF. Distributed sensor localization in random environments using minimal number of anchor nodes. IEEE Transactions on Signal Processing 2009; 57(5): 2000–2016.
- 13 Hu J-P, Yuan H-W. Collective coordination of multi-agent systems guided by multiple leaders. Chinese Physics B 2009; 18(9): 3777–3782.
- 14 Notarstefano G, Egerstedt M, Haque M. Rendezvous with multiple, intermittent leaders. In Proceedings of the 48th IEEE Conference on Decision and Control/28th Chinese Control Conference, Shanghai, 2009; 3733–3738.
- 15 Shi G, Hong Y. Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies. Automatica 2009; 45(5): 1165–1175.
- 16 Cao Y, Stuart D, Ren W, Meng Z. Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments. IEEE Transactions on Control Systems Technology 2011; 19(4): 929–938.
- 17 Lou Y, Hong Y. Target containment control of multi-agent systems with random switching interconnection topologies. Automatica 2012; 48(5): 879–885.
- 18 Shi G, Hong Y, Johansson KH. Connectivity and set tracking of multi-agent systems guided by multiple moving leaders. IEEE Transactions on Automatic Control 2012; 57(3): 663–676.
- 19 Li Z, Ren W, Liu X, Fu M. Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. International Journal of Robust and Nonlinear Control 2013; 23(5): 534–547.
- 20 Liu S, Xie L, Lewis FL. Synchronization of multi-agent systems with delayed control input information from neighbors. Automatica 2011; 47(10): 2152–2164.
- 21 Cao Y, Ren W. Containment control with multiple stationary or dynamic leaders under a directed interaction graph. Proceedings of the 48th IEEE Conference on Decision and Control/28th Chinese Control Conference, Shanghai, 2009; 3014–3019.
- 22 Notarstefano G, Bullo F. Distributed abstract optimization via constraints consensus: theory and applications. IEEE Transactions on Automatic Control 2011; 56(10): 2247–2261.
- 23 Cao Y, Ren W, Egerstedt M. Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica 2012; 48(8): 1586–1597.
- 24 Liu H, Xie G, Wang L. Necessary and sufficient conditions for containment control of networked multi-agent systems. Automatica 2012; 48(7): 1415–1422.
- 25
Wolfowitz J. Products of indecomposable, aperiodic, stochastic matrices. Proceedings of the American Mathematical Society 1963; 14(5): 733–737.
10.1090/S0002-9939-1963-0154756-3 Google Scholar
- 26 Wei P, Guan Q, Yu W, Wang L. Easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems. Systems & Control Letters 2008; 57(2): 165–174.
- 27
Bensoussan A,
Da Prato G,
Delfour M,
Mitter S. Representation and Control of Infinite Dimensional Systems. Birkhäuser: Verlag Basel, Switzerland, 2007.
10.1007/978-0-8176-4581-6 Google Scholar
- 28 Liu S, Xie L, Zhang H. Distributed consensus for multi-agent systems with delays and noises in transmission channels. Automatica 2011; 47(5): 920–934.
- 29 Liu S, Li T, Xie L. Distributed consensus for multiagent systems with communication delays and limited data rate. SIAM Journal on Control and Optimization 2011; 49(6): 2239–2262.
