American Institute of Mathematical Sciences

Advanced
July  2014, 10(3): 929-943. doi: 10.3934/jimo.2014.10.929

Finite-time optimal consensus control for second-order multi-agent systems

Rui Li 1, and  Yingjing Shi 2,

1. 

School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, China
2. 

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, China

Received  June 2012 Revised  July 2013 Published  November 2013

We propose an optimal consensus design method for solving a finite-time optimal control problem involving a second-order multi-agent system. With this method, the optimal consensus problem can be modeled as an optimal parameter selection problem with continuous state inequality constraints and free terminal time. By virtue of the constraint transcription method and a time scaling transform method, a gradient-based optimization algorithm is developed to solve this optimal parameter selection problem. Furthermore, a new consensus protocol is designed, by which the consensus value of the system velocity can be chosen to be an arbitrary value. For illustration, simulation studies are carried out to demonstrate the proposed method.
Keywords: multi-agent system, optimal parameter selection problem, Finite time consensus, gradient-based optimization algorithm..
Mathematics Subject Classification: Primary: 58E25; Secondary: 49N9.
Citation: Rui Li, Yingjing Shi. Finite-time optimal consensus control for second-order multi-agent systems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 929-943. doi: 10.3934/jimo.2014.10.929
References:
[1]

E. A. Blanchard, R. C. Loxton and V. Rehbock, A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations,, Applied Mathematics and Computation, 219 (2013), 8738.  doi: 10.1016/j.amc.2013.02.070.  Google Scholar

[2]

Y. C. Cao and W. Ren, Optimal linear-consensus algorithms: An LQR perspective,, IEEE Transactions on Systems, 40 (2010), 810.   Google Scholar

[3]

R. Carli, G. Como, P. Frasca and F. Garin, Distributed averaging on digital erasure networks,, Automatica J. IFAC, 47 (2011), 115.  doi: 10.1016/j.automatica.2010.10.015.  Google Scholar

[4]

T. Dierks, Formation Control of Mobile Robots and Unmanmed Aerial Vehicles,, Ph.D thesis, (2009).   Google Scholar

[5]

J. Fax and M. Murray, Information flow and cooperative control of vehicle formations,, IEEE Transactions on Automatic Control, 49 (2004), 1465.  doi: 10.1109/TAC.2004.834433.  Google Scholar

[6]

V. Gazi and K. M. Passino, Stability analysis of social foraging swarms,, IEEE Transactions on Systems Man Cybernet., 34 (2004), 539.  doi: 10.1109/TSMCB.2003.817077.  Google Scholar

[7]

V. Gupta, V. Hassibi and R. M. Murray, On sensor fusion in the presence of packet-dropping communication channels,, in 44th IEEE Conference on Decision and Control, (2005), 3547.  doi: 10.1109/CDC.2005.1582712.  Google Scholar

[8]

D. Jakovetic, J. Xavier and J. M. F. Moura, Cooperative convex optimization in networked systems: Augmented Lagrangian algorithms with directed Gossip communication,, IEEE Transactions on Signal Processing, 59 (2011), 3889.  doi: 10.1109/TSP.2011.2146776.  Google Scholar

[9]

C. H. Jiang, Q. Lin, C. J. Yu, K. L. Teo and G.-R. Duan, An exact penalty method for free terminal time optimal control problem with continuous inequality constraints,, J. Optim. Theory Appl., 154 (2012), 30.  doi: 10.1007/s10957-012-0006-9.  Google Scholar

[10]

P. Lin and Y. M. Jia, Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,, Automatica J. IFAC, 45 (2009), 2154.  doi: 10.1016/j.automatica.2009.05.002.  Google Scholar

[11]

Y. Liu and K. M. Passino, Stable social foraging swarms in a noisy environment,, IEEE Transactions on Automatic Control, 49 (2004), 30.  doi: 10.1109/TAC.2003.821416.  Google Scholar

[12]

R. C. Loxton, K. L. Teo and V. Rehbock, Computational method for a class of switched system optimal control problems,, IEEE Transactions on Automatic Control, 54 (2009), 2455.  doi: 10.1109/TAC.2009.2029310.  Google Scholar

[13]

R. C. Loxton, K. L. Teo, V. Rehbock and K. F. C. Yiu, Optimal control problems with a continuous inequality constraint on the state and control,, Automatica J. IFAC, 45 (2009), 2250.  doi: 10.1016/j.automatica.2009.05.029.  Google Scholar

[14]

R. C. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints,, Automatica J. IFAC, 44 (2008), 2923.  doi: 10.1016/j.automatica.2008.04.011.  Google Scholar

[15]

R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems,, Proceedings of IEEE, 95 (2007), 215.  doi: 10.1109/JPROC.2006.887293.  Google Scholar

[16]

R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays,, IEEE Transactions on Automatic Control, 49 (2004), 1520.  doi: 10.1109/TAC.2004.834113.  Google Scholar

[17]

R. Olfati-Saber and J. S. Shamma, Consensus filters for sensor networks and distributed sensor fusion,, in 44th IEEE Conference on Decision and Control, (2005), 6698.  doi: 10.1109/CDC.2005.1583238.  Google Scholar

[18]

W. Ren and R. Beard, Consensus seeking in multi-agent systems under dynamically changing interaction topologies,, IEEE Transactions on Automatic Control, 50 (2005), 655.  doi: 10.1109/TAC.2005.846556.  Google Scholar

[19]

W. Ren, R. W. Beard and E. M. Atkins, Information consensus in multivehicle cooperative control: Collective group behavior through local interaction,, IEEE Control System Magazine, 27 (2007), 71.   Google Scholar

[20]

H. Sayyaadi and M. R. Doostmohammadian, Finite-time consensus in directed switching network topologies and time-delayed communications,, Scientia Iranica, 18 (2011), 75.  doi: 10.1016/j.scient.2011.03.010.  Google Scholar

[21]

E. Semsar and K. Khorasani, Optimal control and game theoretic approaches to cooperative control of a team of multi-vehicle unmanned systems,, in Proceedings of the 2007 IEEE International Conference on, (2007), 628.  doi: 10.1109/ICNSC.2007.372852.  Google Scholar

[22]

A. Tahbaz-Salehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks,, IEEE Transactions on Automatic Control, 53 (2008), 791.  doi: 10.1109/TAC.2008.917743.  Google Scholar

[23]

K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems,, Journal of the Australian Mathematical Society, 40 (1999), 314.  doi: 10.1017/S0334270000010936.  Google Scholar

[24]

K. L. Teo, C. J. Goh and K. H. Wong, A unified computational approach to optimal control problems,, in World Congress of Nonlinear Analysts '92, (1996), 2763.  doi: 10.1515/9783110883237.2763.  Google Scholar

[25]

L. Wang and F. Xiao, Finite-time consensus problems for networks of dynamic agents,, IEEE Transactions on Automatic Control, 55 (2010), 950.  doi: 10.1109/TAC.2010.2041610.  Google Scholar

[26]

X. L. Wang and Y. G. Hong, Finite-time consensus for multi-agent networks with second-order agent dynamics,, in Proceedings of the 17th IFAC World Congress, (2008), 15185.   Google Scholar

[27]

F. Xiao and L. Wang, Consensus protocols for discrete-time multi-agent systems with time-varying delays,, Automatica J. IFAC, 44 (2008), 2577.  doi: 10.1016/j.automatica.2008.02.017.  Google Scholar

[28]

L. Xiao and S. Boyd, Fast linear iterations for distributed averaging,, Systems Control Letters, 53 (2004), 65.  doi: 10.1016/j.sysconle.2004.02.022.  Google Scholar

[29]

W. Zhang and J. H. Hu, Optimal multi-agent coordination under tree formation constraints,, IEEE Transactions on Automatic Control, 53 (2008), 692.  doi: 10.1109/TAC.2008.919855.  Google Scholar

show all references

References:
[1]

E. A. Blanchard, R. C. Loxton and V. Rehbock, A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations,, Applied Mathematics and Computation, 219 (2013), 8738.  doi: 10.1016/j.amc.2013.02.070.  Google Scholar

[2]

Y. C. Cao and W. Ren, Optimal linear-consensus algorithms: An LQR perspective,, IEEE Transactions on Systems, 40 (2010), 810.   Google Scholar

[3]

R. Carli, G. Como, P. Frasca and F. Garin, Distributed averaging on digital erasure networks,, Automatica J. IFAC, 47 (2011), 115.  doi: 10.1016/j.automatica.2010.10.015.  Google Scholar

[4]

T. Dierks, Formation Control of Mobile Robots and Unmanmed Aerial Vehicles,, Ph.D thesis, (2009).   Google Scholar

[5]

J. Fax and M. Murray, Information flow and cooperative control of vehicle formations,, IEEE Transactions on Automatic Control, 49 (2004), 1465.  doi: 10.1109/TAC.2004.834433.  Google Scholar

[6]

V. Gazi and K. M. Passino, Stability analysis of social foraging swarms,, IEEE Transactions on Systems Man Cybernet., 34 (2004), 539.  doi: 10.1109/TSMCB.2003.817077.  Google Scholar

[7]

V. Gupta, V. Hassibi and R. M. Murray, On sensor fusion in the presence of packet-dropping communication channels,, in 44th IEEE Conference on Decision and Control, (2005), 3547.  doi: 10.1109/CDC.2005.1582712.  Google Scholar

[8]

D. Jakovetic, J. Xavier and J. M. F. Moura, Cooperative convex optimization in networked systems: Augmented Lagrangian algorithms with directed Gossip communication,, IEEE Transactions on Signal Processing, 59 (2011), 3889.  doi: 10.1109/TSP.2011.2146776.  Google Scholar

[9]

C. H. Jiang, Q. Lin, C. J. Yu, K. L. Teo and G.-R. Duan, An exact penalty method for free terminal time optimal control problem with continuous inequality constraints,, J. Optim. Theory Appl., 154 (2012), 30.  doi: 10.1007/s10957-012-0006-9.  Google Scholar

[10]

P. Lin and Y. M. Jia, Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,, Automatica J. IFAC, 45 (2009), 2154.  doi: 10.1016/j.automatica.2009.05.002.  Google Scholar

[11]

Y. Liu and K. M. Passino, Stable social foraging swarms in a noisy environment,, IEEE Transactions on Automatic Control, 49 (2004), 30.  doi: 10.1109/TAC.2003.821416.  Google Scholar

[12]

R. C. Loxton, K. L. Teo and V. Rehbock, Computational method for a class of switched system optimal control problems,, IEEE Transactions on Automatic Control, 54 (2009), 2455.  doi: 10.1109/TAC.2009.2029310.  Google Scholar

[13]

R. C. Loxton, K. L. Teo, V. Rehbock and K. F. C. Yiu, Optimal control problems with a continuous inequality constraint on the state and control,, Automatica J. IFAC, 45 (2009), 2250.  doi: 10.1016/j.automatica.2009.05.029.  Google Scholar

[14]

R. C. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints,, Automatica J. IFAC, 44 (2008), 2923.  doi: 10.1016/j.automatica.2008.04.011.  Google Scholar

[15]

R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems,, Proceedings of IEEE, 95 (2007), 215.  doi: 10.1109/JPROC.2006.887293.  Google Scholar

[16]

R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays,, IEEE Transactions on Automatic Control, 49 (2004), 1520.  doi: 10.1109/TAC.2004.834113.  Google Scholar

[17]

R. Olfati-Saber and J. S. Shamma, Consensus filters for sensor networks and distributed sensor fusion,, in 44th IEEE Conference on Decision and Control, (2005), 6698.  doi: 10.1109/CDC.2005.1583238.  Google Scholar

[18]

W. Ren and R. Beard, Consensus seeking in multi-agent systems under dynamically changing interaction topologies,, IEEE Transactions on Automatic Control, 50 (2005), 655.  doi: 10.1109/TAC.2005.846556.  Google Scholar

[19]

W. Ren, R. W. Beard and E. M. Atkins, Information consensus in multivehicle cooperative control: Collective group behavior through local interaction,, IEEE Control System Magazine, 27 (2007), 71.   Google Scholar

[20]

H. Sayyaadi and M. R. Doostmohammadian, Finite-time consensus in directed switching network topologies and time-delayed communications,, Scientia Iranica, 18 (2011), 75.  doi: 10.1016/j.scient.2011.03.010.  Google Scholar

[21]

E. Semsar and K. Khorasani, Optimal control and game theoretic approaches to cooperative control of a team of multi-vehicle unmanned systems,, in Proceedings of the 2007 IEEE International Conference on, (2007), 628.  doi: 10.1109/ICNSC.2007.372852.  Google Scholar

[22]

A. Tahbaz-Salehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks,, IEEE Transactions on Automatic Control, 53 (2008), 791.  doi: 10.1109/TAC.2008.917743.  Google Scholar

[23]

K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems,, Journal of the Australian Mathematical Society, 40 (1999), 314.  doi: 10.1017/S0334270000010936.  Google Scholar

[24]

K. L. Teo, C. J. Goh and K. H. Wong, A unified computational approach to optimal control problems,, in World Congress of Nonlinear Analysts '92, (1996), 2763.  doi: 10.1515/9783110883237.2763.  Google Scholar

[25]

L. Wang and F. Xiao, Finite-time consensus problems for networks of dynamic agents,, IEEE Transactions on Automatic Control, 55 (2010), 950.  doi: 10.1109/TAC.2010.2041610.  Google Scholar

[26]

X. L. Wang and Y. G. Hong, Finite-time consensus for multi-agent networks with second-order agent dynamics,, in Proceedings of the 17th IFAC World Congress, (2008), 15185.   Google Scholar

[27]

F. Xiao and L. Wang, Consensus protocols for discrete-time multi-agent systems with time-varying delays,, Automatica J. IFAC, 44 (2008), 2577.  doi: 10.1016/j.automatica.2008.02.017.  Google Scholar

[28]

L. Xiao and S. Boyd, Fast linear iterations for distributed averaging,, Systems Control Letters, 53 (2004), 65.  doi: 10.1016/j.sysconle.2004.02.022.  Google Scholar

[29]

W. Zhang and J. H. Hu, Optimal multi-agent coordination under tree formation constraints,, IEEE Transactions on Automatic Control, 53 (2008), 692.  doi: 10.1109/TAC.2008.919855.  Google Scholar

[1]

Giulia Cavagnari, Antonio Marigonda, Benedetto Piccoli. Optimal synchronization problem for a multi-agent system. Networks & Heterogeneous Media, 2017, 12 (2) : 277-295. doi: 10.3934/nhm.2017012
[2]

Zhiyong Sun, Toshiharu Sugie. Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems. Numerical Algebra, Control & Optimization, 2019, 9 (3) : 297-318. doi: 10.3934/naco.2019020
[3]

Zhongkui Li, Zhisheng Duan, Guanrong Chen. Consensus of discrete-time linear multi-agent systems with observer-type protocols. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 489-505. doi: 10.3934/dcdsb.2011.16.489
[4]

Yibo Zhang, Jinfeng Gao, Jia Ren, Huijiao Wang. A type of new consensus protocol for two-dimension multi-agent systems. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 345-357. doi: 10.3934/naco.2017022
[5]

Brendan Pass. Multi-marginal optimal transport and multi-agent matching problems: Uniqueness and structure of solutions. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1623-1639. doi: 10.3934/dcds.2014.34.1623
[6]

Hong Man, Yibin Yu, Yuebang He, Hui Huang. Design of one type of linear network prediction controller for multi-agent system. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 727-734. doi: 10.3934/dcdss.2019047
[7]

Daniela Saxenhuber, Ronny Ramlau. A gradient-based method for atmospheric tomography. Inverse Problems & Imaging, 2016, 10 (3) : 781-805. doi: 10.3934/ipi.2016021
[8]

Tyrone E. Duncan. Some partially observed multi-agent linear exponential quadratic stochastic differential games. Evolution Equations & Control Theory, 2018, 7 (4) : 587-597. doi: 10.3934/eect.2018028
[9]

K. Schittkowski. Optimal parameter selection in support vector machines. Journal of Industrial & Management Optimization, 2005, 1 (4) : 465-476. doi: 10.3934/jimo.2005.1.465
[10]

Min Zhang, Gang Li. Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1413-1426. doi: 10.3934/dcdss.2019097
[11]

Jinyuan Zhang, Aimin Zhou, Guixu Zhang, Hu Zhang. A clustering based mate selection for evolutionary optimization. Big Data & Information Analytics, 2017, 2 (1) : 77-85. doi: 10.3934/bdia.2017010
[12]

Zhong Wan, Chaoming Hu, Zhanlu Yang. A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1157-1169. doi: 10.3934/dcdsb.2011.16.1157
[13]

Cristian Barbarosie, Anca-Maria Toader, Sérgio Lopes. A gradient-type algorithm for constrained optimization with application to microstructure optimization. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019249
[14]

Ming-Jong Yao, Tien-Cheng Hsu. An efficient search algorithm for obtaining the optimal replenishment strategies in multi-stage just-in-time supply chain systems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 11-32. doi: 10.3934/jimo.2009.5.11
[15]

Wenlian Lu, Fatihcan M. Atay, Jürgen Jost. Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays. Networks & Heterogeneous Media, 2011, 6 (2) : 329-349. doi: 10.3934/nhm.2011.6.329
[16]

Sie Long Kek, Mohd Ismail Abd Aziz, Kok Lay Teo, Rohanin Ahmad. An iterative algorithm based on model-reality differences for discrete-time nonlinear stochastic optimal control problems. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 109-125. doi: 10.3934/naco.2013.3.109
[17]

Haibo Jin, Long Hai, Xiaoliang Tang. An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-26. doi: 10.3934/jimo.2018188
[18]

Ali Fuat Alkaya, Dindar Oz. An optimal algorithm for the obstacle neutralization problem. Journal of Industrial & Management Optimization, 2017, 13 (2) : 835-856. doi: 10.3934/jimo.2016049
[19]

Sie Long Kek, Mohd Ismail Abd Aziz, Kok Lay Teo. A gradient algorithm for optimal control problems with model-reality differences. Numerical Algebra, Control & Optimization, 2015, 5 (3) : 251-266. doi: 10.3934/naco.2015.5.251
[20]

Michel Cristofol, Jimmy Garnier, François Hamel, Lionel Roques. Uniqueness from pointwise observations in a multi-parameter inverse problem. Communications on Pure & Applied Analysis, 2012, 11 (1) : 173-188. doi: 10.3934/cpaa.2012.11.173

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences