Improved Mode-Dependent State-Feedback Stabilization of Discrete-Time Networked Control Systems with Markovian Communication Delays
(*) Corresponding author
The modeling issues in dynamical systems in many processes, networked control systems (NCS) are very complex. The models may contain subsystems with different parameters, which arise when using a network in an NCS such as time delay, limited bandwidth, and so on. Controlling these types of multiple time delay system is challenging, due to mathematical complexity. This paper considers the design of a stabilizing state-feedback controller for a networked control system with random communication delays. Sensor-to-controller (S-C) and controller-to-actuator delays are modeled by two independent Markov chains. Network-induced random delays are modeled as a Markov chain, and the resulting closed-loop system is transformed into a Markovian jump linear system (MJLS). The focus is on the design of a controller that fully incorporates the effect of the C-A delay. The resulting closed-loop system is described by a new discrete-time Markovian jump linear system with Markov delays model. Then, by applying a type of stochastic Lyapunov functional, sufficient conditions on the stochastic stabilizability and the existence of controller are derived in terms of coupled linear matrix inequalities (LMIs). The efficacy of the proposed method is shown through illustrative examples. Simulation results demonstrate the applicability and the effectiveness of the obtained theoretical results.
Copyright © 2019 The Authors - Published by Praise Worthy Prize under the CC BY-NC-ND license.
J. Nilsson, Real-time control systems with delays, PhD dissertation, Dept. Auto. Control, Lund Institute of Technology Sweden, 1998.
Y. Tipsuwan, M. Y. Chow, Control methodologies in networked control systems, Control Engineering Practice 11 (10) , pp. 1099–1111, 2003.
T. C. Yang, Networked control systems: a brief survey, IET Control Theory and Applications 153 (4),pp. 403-412, 2006.
J. P. Hespanha, P. Naghshtabrizi, Y. Xu, A survey of recent results in networked control systems, Proceedings of the IEEE 95 (1), pp. 138–172, 2007.
K. Y. You, L. H. Xie, Survey of recent progress in networked control systems, Acta Automatica Scinica 39 (2),pp. 101-117, 2013.
W. Zheng, H. Wang, Z. Zhang, P. Yin, Dynamic output feedback control for nonlinear uncertain systems with multiple time-varying delays Automation, Control and Intelligent Systems, pp. 8-99, 19, Vol. 6(1), 2018.
L. X. Zhang, H. J. Gao, O. Kaynak, Network-induced constraints in networked control systems—a survey, IEEE Transactions on Industrial Informatics 9 (1), pp. 403–416, 2013.
G.C. Walsh, H. Ye, Scheduling of networked control systems, IEEE Control Systems Magazine 21(1), pp 57-65, 2001.
D. Zhang, P. Shi, Q.G.Wang, L. Yu, Analysis and synthesis of networked control systems: A survey of recent advances and challenges, ISA Transactions, 66, pp. 376–392, 2017.
Muhammed, S., Venkata Mahesh, P., Mathew, A., Sunil Kumar, T., Model Approximation and Controller Synthesis for H∞ Robust Control of Multiple Time Delay Transfer Functions, (2016) International Review of Automatic Control (IREACO), 9 (1), pp. 1-10.
E. K. Boukas, P. Shi, M. Karan, C. Y. Kaya, Linear discrete-time systems with Markovian jumpsand mode-dependent time-delays: Stability and stabilizability, Mathematical Problems in Engineering 8 (2), pp. 123-133, 2002.
Mohsen Bahreini, Jafar Zarei, Robust finite-time stabilization for networked control systems via static output-feedback control:
Markovian jump systems approach, Circuits Systems and Signal Processing, Vol. 37, N. 4,pp.1523-1541, 2018.
Kang Y., Zhao YB., Zhao P. Networked control system: A Markovian jump system approach. Stability Analysis of Markovian jump Systems pp 131-147. Springer, Singapore. 2018.
L. Zhang, E. K. Boukas, J. Lam, Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities, IEEE Transactions on AutomaticControl, 53 (10), pp. 2458-2464, 2008.
M. Liu, D. W. C. Ho, Y. Niu, Stabilization of Markovian jump linear system over networks withrandom communication delay, Automatica, 45, pp. 416-421, 2009.
R. Krtolica, U. Ozguner, H. Chan, H. Goktas, J. Winkelman, M. Liubakka, Stability of linear feedback systems with random communication delays, International Journal of Control, 59 (4), pp. 925–953, 1994.
J. Nilsson, B. Bernhardsson, B. Wittenmark, Stochastic analysis and control of real-time systemswith random time delays, Automatica, 34 (1),pp. 57–64, 1998.
L. Xiao, A. Hassibi, J. P. How, Control with random communication delays via a discrete-time jump linear system approach, Proc. American Control Conference 3, pp.2199–2204, 2000.
H. Lin, G. Zhai, P. J. Antsaklis, Robust stability and disturbance attenuation analysis of a class of networked control systems, Proc. 42nd IEEE Conf. Decision and Control, pp. 1182–1187, 2003.
L. Zhang, Y. Shi, T. Chen, B. Huang, A new method for stabilization of networked control systems with random delays, IEEE Transactions on Automatic Control 50 (8), pp. 1177-1181, 2005.
Y. Shi, B. Yu, Output feedback stabilization of networked control systems with random delaysmodeled by markov chains, IEEE Transactions on Automatic Control, 54 (7), pp. 1668-1673, 2009.
J. Wu, T. Chen, Design of networked control systems with packet dropouts, IEEE Transactions on Automatic Control, 52 (7),pp. 1314-1319, 2007.
Q. Li, X. BuGong, L. ShanBin, H2/H∞ control of networked control systems with random time delays, Science China Information Sciences, 54 (12), pp. 2615-2630, 2011.
L. Qiu, Q. Luo, F. Gong, S. Li, B. Xu, Stability and stabilization of networked control systems withrandom time delays and packet dropouts, Journal of the Franklin Institute, 350 (7),pp. 1886-1907, 2013.
M. S. Mahmoud, G. D. Khan, Robust mixed H2/H∞ control of networked control systems with random delays and partially known transition matrix, Journal of the Franklin Institute, 351 (12),pp. 5548-5564, 2014.
Y. Shi, B. Yu, Robust mixed H2/H∞ control of systems with random delays in both forward and backward communication links, Automatica, 47, pp.754-760, 2011.
H. Zhang, J. Wang, Robust two-mode-dependent controller design for networked control systems with random delays modelled by Markov chains, International Journal of Control, 88 (12),pp. 2499-2509, 2015.
H. Zhang, Y. Shi, J. Wang, Observer-based tracking controller design for networked predictivecontrol systems with uncertain Markov delays, International Journal of Control, 86 (10),pp.1824-1836, 2015.
J. Zhang, C. Peng, M. R. Fei, Y. C. Tian, Output feedback control of networked control systemswith a stochastic communication protocol, Journal of Franklin Institute, 354 (9), pp. 3838-3853, 2017.
M. S. Mahmoud, N. B. Almutairi, Feedback fuzzy control for quantized networked systems wit random delays, Applied mathematics and computation, 200, pp. 80-97, 2016.
A. Elahi, A. Alfi, Finite-time H∞ control of uncertain networked control systems with randomly varying communication delays, ISA Transactions, 69, pp. 65-88, 2017.
Quanser Consulting Inc., IP-02 Self-Erecting, Linear Motion Inverted Pendulum, Markham Ontario Canada, 1996.
Hasanien, H., Muyeen, S., Benbouzid, M., Optimal Control of a One-Area LFC System Including Time Delay Using Shuffled Frog Leaping Algorithm, (2017) International Journal on Energy Conversion (IRECON), 5 (5), pp. 130-134.
Herrera, J., Rios, M., A Robust Control for Damping Electromechanical Oscillations Modelling Additive Uncertainties in Power Systems, (2016) International Review of Electrical Engineering (IREE), 11 (5), pp. 467-476.
- There are currently no refbacks.
Please send any question about this web site to firstname.lastname@example.org
Copyright © 2005-2023 Praise Worthy Prize