Abstract
A novel active queue management (AQM) approach is considered for a class of TCP network systems in this paper. A sufficient condition is given and the corresponding control is obtained based on integral back-stepping technique (IB) and minimax method. The presented results not only are used to deal with the disturbances produced by UDP flows, but also can shorten the convergent time of the signals. Simulation examples are carried out to verify the effectiveness and superiority of the proposed algorithm.
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S. Floyd and V. Jacobson, “Random early detection gateways for congestion avoidance,” IEEE/ACM Trans. on Networking, vol. 1, no. 4, pp. 397–413, Aug 1993.
F. Kelly, A. Maulloo, and D. Tan, “Rate control for communication networks: shadow prices, proportional fairness and stability,” Journal of the Operational Research Society, vol. 49, no. 3, pp. 237–252, 1998.
F. Kelly, “Mathematical modeling of the internet,” Mathematics Unlimited-2001 and Beyond, pp. 685–702, 2001.
C. Liao and Z. Tian, “Effective adaptive virtual queue: a stabilizing active queue management algorithm for improving responsiveness and robustness,” IET Communications, vol. 5, no. 1, pp. 99–109, 2011.
S. Kunniyur and R. Strikant, “An adaptive virtual queue (AVQ) algorithm for active queue management,” IEEE/ACM Transactions on Networking, vol. 12, no. 2, pp. 286–299, 2004.
S. Athuraliya, S. Low, and Q. Yin, “REM: active queue management,” IEEE Network, vol. 15, no. 3, pp. 48–53, 2001.
V. Misra, W. B. Gong, and D. Towsley, “Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED,” Proceedings of ACM/SIGCOMM00, Sweden, pp. 151–160, 2000.
M. Azadegan, M. T. H. Beheshti, and B. Tavassoli, “Using AQM for performance improvement of net-worked control systems,” International Journal of Control Automation & Systems, vol. 13, no. 3, pp. 764–772, 2015.
Y. Tang, M. Xiao, and G. Jiang, “Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system,” Nonlinear Dynamics, vol. 90, no. 3, pp. 1–14, 2017.
H. Hamidian and M. T. H. Beheshti, “A robust fractionalorder PID controller design based on active queue management for TCP network,” International Journal of Systems Science, vol. 49, no. 1, pp. 211–216, 2018.
R. Zhu, H. Teng, and J. Fu, “A predictive PID controller for AQM router supporting TCP with ECN,” Lecture Notes in Computer Science, vol. 1, pp. 131–136, 2003.
C. W. Feng, L. F. Huang, and C. Xu, “Congestion control scheme performance analysis based on nonlinear RED,” IEEE Systems Journal, vol. 99, pp. 1–8, 2017.
S. Xu, M. Fei, and X. Yang, “AQM scheme design for TCP network via TakagiSugeno fuzzy method,” Complexity, vol. 21, no. S2, pp. 606–612, 2016.
J. M. Kim, B. P. Jin, and Y. H. Choi, “Wavelet neural network controller for AQMin a TCP net-work adaptive learning rates approach,” International Journal of Control Automation & Systems, vol. 6, no. 4, pp. 526–533, 2008.
M. Sheikhan, R. Shahnazi, and E. Hemmati, “Adaptive active queue management controller for TCP communication networks using PSO-RBF models,” Neural Computing and Applications, vol. 22, no. 5, pp. 933–945, 2013.
A. Mozo, J. L. López-Presa, and A. F. Anta, “A distributed and quiescent max-min fair algorithm for network congestion control,” Expert Systems with Applications, vol. 91, pp. 492–512, 2018.
X. Yang, S. Xu, and Z. Li, “Consensus congestion control in multi-router networks based on multi-agent system,” Complexity, vol. 1, pp. 1–10, 2017.
P.Wang, D. Zhu, and X. Lu, “Active queue management algorithm based on data-driven predictive control,” Telecommunication Systems, vol. 64, no. 1, pp. 1–9, 2017.
Y. Liu, X. Liu, and Y. Jing, “Adaptive backstepping H¥ tracking control with prescribed performance for internet congestion,” ISA Transactions, vol. 72, pp. 92–99, 2018.
C. H. Lin, “Nonlinear backstepping control design of LSM drive system using adaptive modified recurrent Laguerre orthogonal polynomial neural network,” International Journal of Control Automation & Systems, vol. 15, no. 2, pp. 905–917, 2017.
M. Wang, Z. Zhang, and Y. Liu, “Adaptive back-stepping control that is equivalent to tuning functions design,” International Journal of Control Automation & Systems, vol. 14, no. 1, pp. 90–98, 2016.
T. Gao, Y. Liu, L. Liu, and D. Li, “Adaptive neural network-based control for a class of nonlinear purefeedback systems with time-varying full state constraints,” IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 5, pp. 923–933, 2018.
D. Zhai, L. An, J. Dong, and Q. Zhang, “Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 585–597, 2018.
L. Liu, Y. Liu, and S. Tong, “Neural networks-based adaptive finite-time fault-tolerant control for a class of strictfeedback switched nonlinear systems,” IEEE Transactions on Cybernetics, pp. 1–10, 2018.
D. Zhai, L. An, D. Ye, and Q. Zhang, “Adaptive reliable H¥ static output feedback control against Markovian Jumping sensor failures,” IEEE Transactions on Neural Networks & Learning Systems, vol. 29, pp. 631–644, 2018.
D. Li and D. Li, “Adaptive neural tracking control for an uncertain state constrained robotic manipulator with unknown time-varying delays,” IEEE Transactions on Systems Man&Cybernetics Systems, vol. 48, no. 12, pp. 2219–2228, Dec. 2018.
F. J. Niroumand, A. Fakharian, and M. S. Seyedsajadi, “Fuzzy integral backstepping control approach in attitude stabilization of a quadrotor UAV,” Pro.c of 13th Iranian Conference on Fuzzy Systems (IFSC), IEEE, pp. 1–6, 2013.
M. Hoshyar and M. Mola, “Full adaptive integral backstepping controller for interior permanent magnet synchronous motors,” Asian Journal of Control, vol. 20, no. 2, pp. 768–779, 2017.
F. Yue, X. Li, and C. Chen, “Adaptive integral backstepping sliding mode control for optoelectronic tracking system based on modified LuGre friction model,” International Journal of Systems Science, vol. 4, pp. 1–8, 2017.
Z. Zhou, C. Yu, and K. L. Teo, “Some new results on integral-type backstepping method for a control problem governed by a linear heat equation,” IEEE Transactions on Automatic Control, vol. 62, no. 7 pp. 3640–3645, 2017.
M. Guisser, A. El-Jouni, and M. Aboulfatah, et al, “Nonlinear MPPT controller for photovoltaic pumping system based on robust integral backstepping approach,” International Review on Modelling & Simulations, vol. 7, no. 3, pp. 481–488, 2014.
M. A. Hamida, J. D. Leon, and A. Glumineau, “High-order sliding mode observers and integral backstepping sensorless control of IPMS motor,” International Journal of Control, vol. 87, no. 10, pp. 2176–2193, 2014.
E. Abolfazli, and V. Shah-Mansouri, “Robust congestion control for TCP/AQM using integral backstepping control,” Proc. of International Symposium on Personal, Indoor, and Mobile Radio Communications, IEEE, pp. 1840–1844, 2015.
M. M. Kogan, “Solution to the inverse problem of minimax control and worst case disturbance for linear continuoustime systems,” IEEE Transaction on Automatic Control, vol. 43, no. 5, pp. 670–674, 1998.
D. Motreanu, “On the proof of a minimax principle,” Le Matematiche, vol. 58, no. 1, pp. 95–99, 2003.
J. Moon and T. Baar, “Minimax control over unreliable communication channels,” Automatica, vol. 59, pp. 182–193, 2015.
N. Jiang and Y. W. Jing, “Non-fragile minimax control of nonlinear systems based on T-S model,” Journal of Systems Engineering, vol. 25, no. 5, pp. 925–928, 2008.
T. L. Molloy, J. M. Kennedy, and J. J. Ford, “Minimax robust quickest change detection with exponential delay penalties,” IEEE Control Systems Letters, vol. 1, no. 2, pp. 280–285, 2017.
H. Habibullah, H. R. Pota, and I. R. Petersen, “A novel application of minimax LQG control technique for highspeed spiral imaging,” Asian Journal of Control, vol. 20, no. 4, pp. 1400–1412, 2017.
L. S. Aragone, J. Gianatti, P. A. Lotito, and L. A. Parente, “An approximation scheme for uncertain minimax optimal control problems,” Set-Valued and Variational Analysis, vol. 2, pp. 1–24, 2017.
S. Zhuk, A. Polyakov, and O. Nakonechnyi, “Note on minimax sliding mode control design for linear systems,” IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3395–3400, 2017.
A. K. Hassan, A. S. Mohamed, M. M. Maghrabi, and N. H. Rafat, “Optimal design of one-dimensional photonic crystal filters using minimax optimization approach,” Applied Optics, vol. 54, no. 6, pp. 1399–409, 2015.
X. Yuan and Y. Jing, “Research for AQM based on minimax method,” Neural Computing & Applications, vol. 25, no. 7–8, pp. 1755–1760, 2014.
M. Sheikhan, R. Shahnazi, and E. Hemmati, “Adaptive active queue management controller for TCP communication networks using PSO-RBF models,” Neural Computing & Applications, vol. 22, no. 5, pp. 933–945, 2013.
W. Dong, G. Y. Gu, X. Zhu, and H. Ding, “A high-performance flight control approach for quadrotors using a modified active disturbance rejection technique,” Robotics & Autonomous Systems, vol. 83, pp. 177–187, 2016.
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Recommended by Associate Editor Ding Zhai under the direction of Editor Guang-Hong Yang. This work is supported by the National Natural Science Foundation of China under Grant 61773108.
Zan-Hua Li received her B.S. degree in mathematics from Northeast Normal University, China, in 2002, and her M.S. degrees in Northeastern University in 2006. She is currently pursuing a Ph.D. degree in Northeastern University, she is with School of Science, Shenyang Ligong University. Her research interests include nonlinear control, adaptive control, control problems of network systems.
Yang Liu received the B.S. and M.S. degrees in University of Science and Technology Liaoning, China, in 2012 and 2015, respectively. He is currently pursuing a Ph.D. degree in Northeastern University. From 2016 to 2018, he is a Visiting Scholar with the Department of Electrical Engineering, Lakehead University, Thunder Bay, ON, Canada. His current research interests include finite time control for nonlinear systems, control problems in modern communication network systems, prescribed performance control, robust control.
Yuan-Wei Jing received his M.S. and Ph.D. degrees in automatic control from Northeastern University, China, in 1984 and 1988, respectively. From 1998 to 1999, he was a Senior Visiting Scholar with the Computer Science Telecommunication Program of University Missouri, Kansas City. He is currently with the College of Information Science and Engineering, Northeastern University. His current research interests include complex control systems and control problems in modern communication network systems.
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Li, ZH., Liu, Y. & Jing, YW. Active Queue Management Algorithm for TCP Networks with Integral Backstepping and Minimax. Int. J. Control Autom. Syst. 17, 1059–1066 (2019). https://doi.org/10.1007/s12555-018-0447-5
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DOI: https://doi.org/10.1007/s12555-018-0447-5