Abstract and Applied Analysis

State Estimation for Wireless Network Control System with Stochastic Uncertainty and Time Delay Based on Sliding Mode Observer

Pengfei Guo, Jie Zhang, Hamid Reza Karimi, Yurong Liu, Ming Lyu, and Yuming Bo

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State estimation problem is considered for a kind of wireless network control system with stochastic uncertainty and time delay. A sliding mode observer is designed for the system under the situation that no missing measurement occurs and system uncertainty happens in a stochastic way. The observer designed for the system can guarantee the system states will be driven onto the sliding surface under control law, and the sliding motion of system states on sliding surface will be stable. By constructing proper Lyapunov-Krasovskii functional, sufficient conditions are acquired via linear matrix inequality. Finally, simulation result is employed to show the effectiveness of the proposed method.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 303840, 8 pages.

First available in Project Euclid: 6 October 2014

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Guo, Pengfei; Zhang, Jie; Karimi, Hamid Reza; Liu, Yurong; Lyu, Ming; Bo, Yuming. State Estimation for Wireless Network Control System with Stochastic Uncertainty and Time Delay Based on Sliding Mode Observer. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 303840, 8 pages. doi:10.1155/2014/303840. https://projecteuclid.org/euclid.aaa/1412605745

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  • J. Liang, Z. Wang, and X. Liu, “Distributed state estimation for uncertain Markov-type sensor networks with mode-dependent distributed delays,” International Journal of Robust and Nonlinear Control, vol. 22, no. 3, pp. 331–346, 2012.
  • L. Wu, P. Shi, and H. Gao, “State estimation and sliding-mode control of Markovian jump singular systems,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1213–1219, 2010.
  • O. Kosut, L. Jia, R. J. Thomas, and L. Tong, “Malicious data attacks on smart grid state estimation: attack strategies and countermeasures,” in Proceedings of the First IEEE International Conference on Smart Grid Communications (SmartGridComm '10), pp. 220–225, 2010.
  • B. Shen, Z. Wang, and X. Liu, “Bounded ${H}_{\infty }$ synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon,” IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 145–157, 2011.
  • H. R. Karimi and H. Gao, “New delay-dependent exponential ${H}_{\infty }$ synchronization for uncertain neural networks with mixed time delays,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 40, no. 1, pp. 173–185, 2010.
  • G. W. Irwin, J. Chen, A. McKernan, and W. G. Scanlon, “Co-design of predictive controllers for wireless network control,” IET Control Theory & Applications, vol. 4, no. 2, pp. 186–196, 2010.
  • H. R. Karimi and P. Maass, “Delay-range-dependent exponential ${H}_{\infty }$ synchronization of a class of delayed neural networks,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1125–1135, 2009.
  • D. Ding, Z. Wang, and B. Shen, “Recent advances on distributed filtering for stochastic systems over sensor networks,” International Journal of General Systems, vol. 43, no. 3-4, pp. 372–386, 2014.
  • H. R. Karimi, “Robust ${H}_{\infty }$ filter design for uncertain linear systems over network with network-induced delays and output quantization,” Modeling, Identification and Control, vol. 30, no. 1, pp. 27–37, 2009.
  • I. F. Akyildiz, X. Wang, and W. Wang, “Wireless mesh networks: a survey,” Computer Networks, vol. 47, no. 4, pp. 445–487, 2005.
  • D. Ding, Z. Wang, H. Dong, and H. Shu, “Distributed ${H}_{\infty }$ state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case,” Automatica, vol. 48, no. 8, pp. 1575–1585, 2012.
  • J. Kay and J. Frolik, “Quality of service analysis and control for wireless sensor networks,” in Proceedings of the IEEE International Conference on Mobile Ad-Hoc and Sensor Systems, pp. 359–368, October 2004.
  • H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Robust ${H}_{\infty }$ fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 4, pp. 712–725, 2010.
  • S. He and F. Liu, “Exponential passive filtering for a class of nonlinear jump systems,” Journal of Systems Engineering and Electronics, vol. 20, no. 4, pp. 829–837, 2009.
  • W. Ye, J. Heidemann, and D. Estrin, “Medium access control with coordinated adaptive sleeping for wireless sensor networks,” IEEE/ACM Transactions on Networking, vol. 12, no. 3, pp. 493–506, 2004.
  • S. He and F. Liu, “Observer-based finite-time control of time-delayed jump systems,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2327–2338, 2010.
  • H. R. Karimi, “A sliding mode approach to ${H}_{\infty }$ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 349, no. 4, pp. 1480–1496, 2012.
  • A. Micol, C. Martin, O. Dalverny, M. Mermet-Guyennet, and M. Karama, “Reliability of lead-free solder in power module with stochastic uncertainty,” Microelectronics Reliability, vol. 49, no. 6, pp. 631–641, 2009.
  • S. He, “Resilient ${L}_{2}-{L}_{\infty }$ filtering of uncertain markovian jumping systems within the finite-time interval,” Abstract and Applied Analysis, vol. 2013, Article ID 791296, 7 pages, 2013.
  • S. He and F. Liu, “Stochastic finite-time stabilization for uncertain jump systems via state feedback,” Journal of Dynamic Systems, Measurement, and Control, vol. 132, no. 3, Article ID 034504, 2010.
  • S. Peng, “Nonlinear expectations and stochastic calculus under uncertainty,” Microelectronics Reliability, 2010, http://arxiv.org/abs/1002.4546.
  • B. Shen, Z. Wang, H. Shu, and G. Wei, “${H}_{\infty }$ filtering for uncertain time-varying systems with multiple randomly occurred nonlinearities and successive packet dropouts,” International Journal of Robust and Nonlinear Control, vol. 21, no. 14, pp. 1693–1709, 2011.
  • H. R. Karimi, “Robust delay-dependent ${H}_{\infty }$ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching parameters,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 58, no. 8, pp. 1910–1923, 2011.
  • Z. G. Wu, P. Shi, H. Su, and J. Chu, “Asynchronous ${l}_{2}$-${l}_{\infty }$ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities,” Automatica, vol. 50, no. 1, pp. 180–186, 2014.
  • K. M. Hyde and H. R. Maier, “Distance-based and stochastic uncertainty analysis for multi-criteria decision analysis in excel using visual basic for applications,” Environmental Modelling and Software, vol. 21, no. 12, pp. 1695–1710, 2006.
  • Z. Wu, P. Shi, H. Su, and J. Chu, “Stochastic synchronization of markovian jump neural networks with time-varying delay using sampled data,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1796–1806, 2013.
  • S. He and F. Liu, “Robust stabilization of stochastic Markovian jumping systems via proportional-integral control,” Signal Processing, vol. 91, no. 11, pp. 2478–2486, 2011.
  • S. He and F. Liu, “Robust stabilization of stochastic markovian jumping systems via proportional-integral control,” Abstract and Applied Analysis, vol. 2012, Article ID 936375, 9 pages, 2012.
  • S. He and F. Liu, “Unbiased estimation of markov jump systems with distributed delays,” Signal Processing, vol. 100, pp. 85–92, 2014.
  • Z. Wang, Y. Liu, G. Wei, and X. Liu, “A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances,” Automatica, vol. 46, no. 3, pp. 543–548, 2010.
  • S. He and C. Liu, “Finite-time fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 605–614, 2012.
  • J. Sun, G. P. Liu, J. Chen, and D. Rees, “Improved delay-range-dependent stability criteria for linear systems with time-varying delays,” Automatica, vol. 46, no. 2, pp. 466–470, 2010.
  • P. Lin and Y. Jia, “Average consensus in networks of multi-agents with both switching topology and coupling time-delay,” Physica A: Statistical Mechanics and its Applications, vol. 387, no. 1, pp. 303–313, 2008.
  • Z. G. Wu, P. Shi, H. Su, and J. Chu, “Passivity analysis for discrete-time stochastic markovian jump neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 22, no. 10, pp. 1566–1575, 2011.
  • H. Shen, J. H. Park, L. Zhang, and Z. Wu, “Robust extended dissipative control for sampled-data markov jump systems,” International Journal of Control, pp. 1–16, 2013.
  • J. Qin, H. Gao, and W. X. Zheng, “Second-order consensus for multi-agent systems with switching topology and communication delay,” Systems & Control Letters, vol. 60, no. 6, pp. 390–397, 2011.
  • C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, no. 4, pp. 541–553, 2000.
  • W. Chen and S. Mehrdad, “Observer design for linear switched control systems,” in Proceedings of the American Control Conference, vol. 6, pp. 5796–5801, July 2004. \endinput