On Exponential Almost Sure Stability of Consensus Algorithm in State Dependent and Switching Networks

Sabato Manfredi(1*), Paris Pennesi(2)

(1) Departement of Electrical Engineering and Information Technology, University of Napoli, Federico II, Italy
(2) HSBC Location, London, United Kingdom, Financial Services, United Kingdom
(*) Corresponding author


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


In many network applications the connectivity between nodes can be state dependent (i.e. in wireless and swarming networks the strength of node interaction depends on the distance between the agents) or can be switching (i.e. due to link failure or link creation). This note is concerned with the analysis of consensus problem and the design of network/protocol parameters in networks with Markov switching topology and state dependent connectivity. In particular a sufficient condition for exponential almost sure stability of consensus protocol is given. The stability condition validation is presented by numerical simulations.
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Consensus Problems; Directed Graphs; Markov-Switching Topology

Full Text:

PDF


References


Saber R.O., Murray R.M., Consensus Problems in Networks of Agents with Switching Topology and Time-Delays IEEE Transactions on Automatic Control, Vol 49, 9, 2004.

Horn R.A. and Johnson C.R., Topics in Matrix Analysis Cambridge University Press 1995.

Z. Lin, M. Brouke, and B. Francis, Local control strategies for groups of mobile autonomous agents., Transactions on Automatic Control, 49, vol 4, pages: 622–629, 2004.

V. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis, Convergence in multiagent coordination, consensus, and flocking, 44th IEEE Conference on Decision and Control and European Control Conference, pages 2996–-3000, 2005.

J. N. Tsitsiklis, D. P. Bertsekas, M. Athans, Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms, Transactions on Automatic Control, pages. 803-–812, 1986.

L. Moreau, Stability of multi-agent systems with time-dependent communication links, IEEE Transactions on Automatic Control, vol. 50, pages: 169–182, February 2005

A. Jadbabaie, J. Lin and A.S. Morse, Coordination of groups of mobile agents using nearest neighbor rules., IEEE Transactions on Automatic Control, 48 , Vol. 6, pages 988-–1001. 2003

A. Tahbaz-Salehi, A. Jadbabaie, Consensus Over Ergodic Stationary Graph Processes., IEEE Transactions on Automatic Control, 55,1, pp. 225-230, 2009.

B. Liu, W. Lu, T. Chen Reaching Lp consensus in a network of multiagents with stochastically switching topologies., Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, December 16-18, 2009.

Lin, B. Francis and M. Maggiore, State agreement for continuous-time coupled nonlinear systems., SIAM Journal on Control and Optimization 46, Vol. 1, pp: 288-–307. 2007

Y. Hong, L. Gao, D. Cheng and J. Hu, Lyapunov-based approach to multi-agent systems with switching jointly connected interconnection., IEEE Transactions on Automatic Control, 52, pages: 943–948. 2007

Guodong Shia, and Yiguang Honga, Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies., Automatica Vol. 45, 5, pp. 1165–1175, 2009

H.G. Tanner, A. Jadbabaie and G.J. Pappas, Flocking in fixed and switching networks., IEEE Transactions on Automatic Control 52, 5, 2007, pp: 863-–868. 2007.

Y. Hatano and M. Mesbahi, Agreement over random networks., IEEE Transactions on Automatic Control 50, vol. 11, pages: 1867-–1872. 2005

Manfredi, S. On Global and Local Consensusability of Multi-Agent Systems with Input Constraint and Uncertain Initial Conditions. Proceedings of the American Control Conference. pp 6102-6107, ISSN: 0743-1619, Washington, DC, USA, 17-19 June, 2013.

Ya Zhanga and Yu-Ping Tian, Consentability and protocol design of multi-agent systems with stochastic switching topology., Automatica, 45, 5, pp. 1195–1201. 2009.

Yang Shi and Bo Yu, Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains, IEEE Transactions on Automatic Control 54, 7, pp: 1668-–1674. 2009

A. Köpke, A. Willig, and H. Karl, Chaotic Maps as Parsimonious Bit Error Models of Wireless Channels, Proc. of IEEE INFOCOM, San Francisco, California, March 2003.

F. Cucker, S. Smale, Emergent Behavior in Flocks, IEEE Transactions on Automatic Control 52, Vol. 5, pp: 852-–862. 2007

V. D. Blondel, J.M. Hendrickx, J.N.Tsitsiklis, On Krause’s Multi-Agent Consensus Model With State-Dependent Connectivity., IEEE Transactions on Automatic Control 54, 11, pp: 2586-–2597. 2009

A. Tahbaz-Salehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks., IEEE Transactions on Automatic Control 53, 3, pp: 791-–795. 2008

Patterson, S., Bamieh, B., Abbadi, A. E., Distributed average consensus with stochastic communication failures., Proceedings of the IEEE conference on decision and control, pp: 4215–4220. 2007

C.W. Wu, Synchronization and convergence of linear dynamics in random directed networks., IEEE Transactions on Automatic Control 51, 7, pp: 1207–1210.. 2010

C. C. Cheaha, S. P. Houa, and J. J. E. Slotine, Region-based shape control for a swarm of robots., Automatica, 45, 10, pp: 2406-–2411. 2009

Olfati-Saber, R., Shamma, J. S, Consensus filters for sensor networks and distributed sensor fusion., In Proc. of the 44th IEEE conference on decision and control and the European control conference. pp: 3551–3556. 2005

Ren, W., Collective Motion From Consensus with Cartesian Coordinate Coupling ., IEEE Transactions on Automatic Control. Vol. 54, 6, pages: 1330–1335. 2009

M. Fiedler, Algebraic connectivity of Graphs., Czechoslovak Mathematical Journal, Vol. 23, 98, 1973.

Chai Wah Wu, On Rayleigh–Ritz ratios of a generalized Laplacian matrix of directed graphs., Linear Algebra and its Applications, Vol. 402, pages: 207–227. 2005

Xuerong Mao, Stability of Stochastic Differential Equations with Markovian Switching., Stochastic Processes and their Applications, Vol. 79, 1, 1999 , pages. 45–67

Xuerong Mao, Exponential stability of stochastic delay interval systems with Markovian switching., IEEE Transactions on Automatic Control, 47, 10, pages: 1604–1612, 2002.

Michael J. Barclay, Terrence Hendershott and D. Timothy McCormick, Competition among Trading Venues: Information and Trading on Electronic Communications Networks., The Journal of Finance, Vol. 58, Issue 6, pages: 2637-–2666, 2003.

Joel Hasbrouck, One Security, Many Markets: Determining the Contributions to Price Discovery, The Journal of Finance, L, 4, 1995.

G. Miaoa, S. Xua & Y. Zoua, Necessary and sufficient conditions for mean square consensus under Markov switching topologies, The International Journal of Systems Science, 44, 1, 2013

R. Tron and R. Vidal. Distributed Algorithms for Camera Sensor Networks. IEEE Signal Processing Magazine, 2011

S. Manfredi, A Reliable and Energy Efficient Cooperative Routing Algorithm for Wireless Monitoring Systems, IET Wireless Sensor Systems, Vol.2, 2, 128-135, DOI: 10.1049/iet-wss.2011.0103 , ISSN: 2043-6386, 2012

Ben Khaled, R., Mnasri, C., Gasmi, M., Adaptive fuzzy decentralized control for nonlinear large scale systems in strict feedback form, (2013) International Review of Automatic Control (IREACO), 6 (3), pp. 346-357.

Queen, M.P.F., Kumar, M.S., Aurtherson, P.B., Repetitive learning controller for six degree of freedom robot manipulator, (2013) International Review of Automatic Control (IREACO), 6 (3), pp. 286-293.

Vesely, V., Puleva, T., Osusky, J., Gain scheduling control design for hydro generator, (2013) International Review of Automatic Control (IREACO), 6 (3), pp. 241-246.

S. Manfredi, Decentralized Queue balancing and Differentiated Service scheme based on Cooperative Control Concept, IEEE Transaction on Industrial Informatics, DOI: 10.1109/TII.2013.2265879, ISSN :1551-3203, accepted for publication, 2013

Manfredi, S., Angeli, D., Frozen state conditions for asymptotic consensus of time-varying cooperative nonlinear networks, accepted at IEEE 52nd Conference on Decision and Control, Firenze, 2013.

Manfredi, S. Design of a multi-hop dynamic consensus algorithm over wireless sensor networks. Control Engineering Practice, Vol 21, 4, pp. 381-394, DOI: dx.doi.org/10.1016/j.conengprac. 2012.12.001, 2013.

Manfredi, S., A consensus based rate control scheme for ATM networks, International Journal of Control, Automation and Systems, 10, 4, pp. 817-823, DOI: 10.1007/s12555-012-0418-1, ISSN: 1598-6446, 2012.

S. Manfredi, A Theoretical Analysis of Multihop Consensus Algorithms for Wireless Networks:trade off among Reliability, Responsiveness and Delay Tolerance, Ad Hoc Networks, in press, DOI information: 10.1016/j.adhoc.2011.05.005, 2011

Dchich, K., Zaafouri, A., Chbeb, A., Jemli, M., Position sensorless robust control of PMSM using the Extended Kalman Filter algorithm, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 380-386.

Cherifi, D., Miloud, Y., Tahri, A., A luenberger state observer for stator resistance estimation in sensorless induction motor drives, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 360-369.

A. Frezzetti, S. Manfredi, M. Pagano, A PV-model based design of a MPPT controller for Energy Harvested Wireless Sensor Nodes, 2 IFAC Workshop on Convergence of Information Technologies and Control Methods with Power Systems-ICPS’13, Cluj-Napoca, Romania, May 22-24, Vol.2, Part.1, ISBN:978-3-902823-32-8, ISSN:1474-6670 DOI:10.3182/20130522-3-RO-4035.00015, pp:101-106, 2013

A. Frezzetti, S. Manfredi, M. Pagano, An Implementation of a Smart Maximum Power Point Tracking Controller to Harvest Renewable Energy of Wireless Sensor Nodes, IEEE International Conference on Clean Electrical Power-ICCEP, Alghero (Italy), 11-13 June 2013, pp. 503-508, Print ISBN: 978-1-4673-4429-6, DOI:10.1109/ICCEP.2013.6586900.

S. Manfredi, An algorithm for fast rendezvous seeking of wireless networked robotic systems, Ad Hoc Networks, 11, 7, pp. 1942-1950, DOI:10.1016/j.adhoc.2012.06.010, 2013

Manfredi, S. A reliable cooperative and distributed management for wireless industrial monitoring and control, International Journal of Robust and Nonlinear Control, 20, 2, pp. 123-139, doi: 10.1002/rnc.1453, 2010.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2020 Praise Worthy Prize