Evaluation of a PSO Approach for Optimum Design of a First-Order Controllers for TCP/AQM Systems

This paper presents a Particle Swarm Optimization (PSO) method for determining the optimal parameters of a first-order controller for TCP/AQM system. The model TCP/AQM is described by a second-order system with time delay. First, the analytical approach, based on the D-decomposition method and Lemma of Kharitonov, is used to determine the stabilizing regions of a firstorder controller. Second, the optimal parameters of the controller are obtained by the PSO algorithm. Finally, the proposed method is implemented in the Network Simulator NS-2 and compared with the PI controller.

Authors:

• Sana Testouri
• Karim Saadaoui
• Mohamed Benrejeb

Keywords:

• AQM
• first-order controller
• time delay
• stability
• PSO.

References:

[1] V. Jacobson, "Congestion avoidance and control," Proceeding of
SIGOMM-88,ACM,1998.
[2] S. Floyd and V. Jacobson, "Random Early Detection Gateways for
Congestion Avoidance," IEEE/ACM Transactions on Networking, vol.
1, August 1993, pp. 397-413.
[3] C.V Hollot, V.Misra D. Towsley, W. Gong ,"Analysis and design of
controllers for AQM routers supporting TCP flows," IEEE Trans on
Automatic Control, vol.47, June 2002, pp. 945-959.
[4] J. S. Sun, G.C .K.T .Ko, S.Chan and M. Zukerman, "PD-controller: A
New Active Queue Management Scheme," In Proc. IEEE Global
Telecommunications Conference GLOBE-COM , December 2003.
[5] K.B.Kim , "Design of feedback controls supporting TCP base on the
state-space approach," IEEE Trans. Automatic Control, 51(7),2002, pp.
1086-1099.
[6] J.W.Yang, G. Dan-Ying, Z. Wei-Dong," An analytical design method of
PID controller based on AQM/ARQ," Journal of Software,
17(9),2006, pp 1989-1995.
[7] R. N. Tantaris, L. H. Keel, and S. P. Bhattacharyya, "Stabilizing of
continuous-time systems by first order controllers," Proceedings of the
10th Mediterranen Conference on Control and Automation, Lisbon,
Portugal, July 2002.
[8] K. Saadaoui and A. B. Ozguler, " On the set of all stabilizing firstorder
controllers, " in Proceedings of American Control Conference
Denver, Colorado USA, 2003.
[9] K. Saadaoui and A. B. ¨ Ozg¨uler," A new method for the computation
of all stabilizing controllers of a given order, " International Journal of
Control, vol. 78, 2005, pp. 14-28.
[10] R. N. Tantaris, L. H. Keel, and S. P. Bhattacharyya, "Stabilization of
discrete-time systems by first-order controllers," IEEE Trans Automat.
Cont., vol. 48, 2003, pp. 858-860.
[11] C .V. Hollot, V. Misra, D. Towsley and W. Gong , "A Control
Theoretic Analysis of RED," Proceedings of IEEE Infocom2001.
[12] S. Kunniyur and R. Srikant, "Analysis and design of an Adaptive
Virtual Queue (AVQ) algorithm for Active Queue Management,"
Proceedings of ACM SIGCOMM, August 2001, pp. 123- 134.
[13] Y.Fan,F. Ren and C. Lin, "Design a pid controller for active queue
Management," In IEEE International Symposium on Computers and
Communication (ISCC), volume 2, 2003, pp. 985- 990.
[14] D. Agrawal and F. Granelli, "Redesigning an active queue management
system," In IEEE Globecom, volume 2, December 2004, pp 702-706.
[15] V. Misra., W. Gong and D. Towsley, "Fluid-based analysis of a network
of AQM routers supporting TCP flows with an application to RED,". In
ACM SIGCOMM, August, 2000,pp.151-160.
[16] NS-2 Simulator, available at http://www.isi.edu/nsnam/ns/
[17] G. J. Silva, A. Datta, and S.P Bhattacharyya, "PI stabilization of first -
order systems with time delay," Automatica, vol. 37, 2001, pp. 2025-
2031.
[18] V. L Kharitonov, S. Niculescu, J. Moreno and W. Michiel, "Static
output stabilization: Necessary conditions for multiple delay
controllers," IEEE Trans Automat. Control, 2005.
[19] K. Saadaoui, S. Testouri and M. Benrejeb,"Robust stabilizing first -
order controllers for a class of time delay systems," ISA Transactions
vol. 49, 2010, pp. 277-282.
[20] E.N. Gryazina, and B.T. Polyak."Stability regions in the parameter
space : D-decomposition revisited," Automatica 2006, pp 13-26.
[21] J. Kennedy and R. Eberhart, "Particle swarm optimization," in Proc.
IEEE Int. Conf. Neural Networks, vol. IV, Perth, Australia, 1995, pp.
1942-1948.
[22] R. C. Eberhart and Y. Shi, "Comparison between genetic algoritms and
particle swarm optimization," in Proc. IEEE Int.Conf. Evol.Comput.,
Anchorage, AK, May 1998, pp. 611-616.
[23] H. Yoshida, K. Kawata, and Y. Fukuyama, "A particle swarm
optimization for reactive power and voltage control considering
voltage security assessment," IEEE Trans. Power Syst., vol. 15, ,
Nov..2000, pp. 1232-1239.
[24] Z.-L. Gaing, "A particle swarm optimization approach for
optimumdesign of PID controller in AVR system," IEEE
Trans.EnergyConversion, vol. 19, , June 2004, pp. 384-391.
[25] L.G Zwe, "A Particle Swarm Optimization approach for
optimumdesign of PID controller in AVR system," IEEE Transactions
on Energy Conversion, vol.19, June, 2004, pp. 384-391.
[26] S. Testouri, K. Saadaoui, and M. Benrejb, "A Particle Swarm
Optimization for Optimum Design of First-Order Controllers in
TCP/AQM Network Systems," International Journal of Computer
Application (IJCA),vol.45,n┬░7, May,2012, pp-31-38.