Robust filtering for a class of nonlinear stochastic systems with probability constraints

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• 作者：Lifeng Ma ; Zidong Wang ; Hak-Keung Lam ; Fuad E. Alsaadi…
• 刊名：Automation and Remote Control
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：77
• 期：1
• 页码：37-54
• 全文大小：571 KB
• 参考文献：1.Jamshidi, M., Seraji, H., and Kim, Y.T., Decentralized Control of Nonlinear Robot Manipulators, Robotics, 1987, vol. 3, nos. 3–4, pp. 361–370.CrossRef
  2.Rudolph, J., Flatness-based Control by Quasi-static Feedback Illustrated on a Cascade of Two Chemical Reactors, Int. J. Control, 2000, vol. 73, no. 2, pp. 115–131.CrossRef MathSciNet MATH
  3.Petersen, I.R., Robust Output Feedback Guaranteed Cost Control on Nonlinear Stochastic Systems via an IQC Approach, IEEE Trans. Automat. Control, 2009, vol. 54, no. 6, pp. 1299–1304.CrossRef MathSciNet
  4.Bashkirtseva, I., Attainability Analysis in the Stochastic Sensitivity Control, Int. J. Control, 2015, vol. 88, no. 2, pp. 276–284.CrossRef MathSciNet
  5.Shulgin, B., Neiman, A., and Anishchenko, V., Mean Switching Frequency Locking in Stochastic Bistable Systems Drivers by a Periodic Force, Phys. Rev. Lett., 1995, vol. 75, no. 23, pp. 4157–4160.CrossRef
  6.Grigorenko, A., Nikitin, S., and Roschepkin, G., Stochastic Resonance at Higher Harmonics in Monostable Systems, Phys. Rev. Lett., 1997, vol. 56, no. 5, pp. 4907–4910.
  7.Kushner, H.J., Numerical Algorithms for Optimal Controls for Nonlinear Stochastic Systems with Delays, IEEE Trans. Automat. Control, 2010, vol. 55, no. 9, pp. 2170–2176.CrossRef MathSciNet
  8.Khoo, S., Yin, J., Man, Z., and Yu, X., Finite-time Stabilization of Stochastic Nonlinear Systems in Strict-feedback Form, Automatica, 2013, vol. 49, no. 5, pp. 1403–1410.CrossRef MathSciNet
  9.Chen, Y. and Hoo, K.A., Stability Analysis for Closed-loop Management of a Reservoir Based on Identification of Reduced-order Nonlinear Model, Syst. Sci. Control Eng.: Open Access J., 2013, vol. 1, no. 1, pp. 12–19.CrossRef
  10.Wei, G., Wang, Z., and Shen, B., Probability-dependent Gain-scheduled Control for Discrete Stochastic Delayed Systems with Randomly Occurring Nonlinearities, Int. J. Robust Nonlin. Control, 2013, vol. 23, no. 7, pp. 815–826.CrossRef MathSciNet MATH
  11.Shaked, U. and de Souza, C.E., Robust Minimum Variance Filtering, IEEE Trans. Signal Process., 1995, vol. 43, no. 11, pp. 2474–2483.CrossRef
  12.Van Veen, B.D., van Drongelen, W., Yuchtman, M., and Suzuki, A., Localization of Brain Electrical Activity via Linearly Constrained Minimum Variance Spatial Filtering, IEEE Trans. Biomed. Eng., 1997, vol. 44, no. 9, pp. 867–880.CrossRef
  13.Wang, Z. and Fang, J., Robust H ∞ Filter Design with Variance Constraints and Parabolic Pole Assignment, IEEE Signal Process. Lett., Vol. 13, No. 3, 2006, pp. 137–140.CrossRef
  14.Hotz, A. and Skelton, R.E., A Covariance Control Theory, Int. J. Control, 1987, vol. 46, no. 1, pp. 13–32.CrossRef MathSciNet MATH
  15.Ding, D., Wang, Z., Shen, B., and Dong, H., Envelope-constrained H ∞ Filtering with Fading Measurements and Randomly Occurring Nonlinearities: The Finite Horizon Case, Automatica, 2015, vol. 55, pp. 37–45.CrossRef MathSciNet
  16.Ding, D., Wang, Z., Lam, J., and Shen, B., Finite-Horizon H ∞ Control for Discrete Time-varying Systems with Randomly Occurring Nonlinearities and Fading Measurements, IEEE Trans. Automat. Control, 2003 (in press, DOI: 10.1109/TAC.2014.2380671).
  17.Hung, Y. and Fuwen, Y., Robust H ∞ Filtering with Error Variance Constraints for Discrete Timevarying Systems with Uncertainty, Automatica, 2003, vol. 39, pp. 1185–1194.CrossRef MATH
  18.Wang, Z., Yang, F., and Liu, X., Robust Filtering for Systems with Stochastic Non-linearities and Deterministic Uncertainties, Proc. IMechE Part I: J. Systems and Control Engineering, 2006, vol. 220, pp. 171–182.
  19.Kalman, R. and Bucy, R., A New Approach to Linear Filtering and Prediction Problems, ASME J. Basic Eng., 1960, vol. 82, pp. 34–45.
  20.Bernstein, D. and Haddad, W., Steady-state Kalman Filtering with an H ∞ Error Bound, Syst. Control Lett., 1989, vol. 12, no. 1, pp. 9–16.CrossRef MathSciNet MATH
  21.Rotstein, H., Sznaier, M., and Idan, M., Mixed H 2/H ∞ Filtering Theory and an Aerospace Application, Int. J. Robust Nonlin. Control, 1996, vol. 6, pp. 347–366.CrossRef MathSciNet MATH
  22.Hu, J., Wang, Z., Gao, H., and Stergioulas, L.K., Extended Kalman Filtering with Stochastic Nonlinearities and Multiple Missing Measurements, Automatica, 2012, vol. 48, no. 9, pp. 2007–2015.CrossRef MathSciNet MATH
  23.Gao, H., Lam, J., and Wang, C., Induced l2 and Generalized H ∞ Filtering for Systems with Repeated Scalar Nonlinearities, IEEE Trans. Signal Process., 2005, vol. 53, no. 11, pp. 4215–4226.CrossRef MathSciNet
  24.Gao, H., Lam, J., and Wang, C., New Approach to Mixed H 2/H ∞ Filtering for Polytopic Discrete-time Systems, IEEE Trans. Signal Process., 2005, vol. 53, no. 8, pp. 3183–3192.CrossRef MathSciNet
  25.Gao, H., Lam, J., and Wang, C., Robust H ∞ Filtering for Discrete Stochastic Time-delay Systems with Nonlinear Disturbances, Nonlin. Dynam. Syst. Theory, 2004, vol. 4, no. 3, pp. 285–301.MathSciNet MATH
  26.Gao, H., Lam, J., and Wang, C., A Delay-dependent Approach to Robust H ∞ Filtering for Uncertain Discrete-time State-delayed Systems, IEEE Trans. Signal Process., 2004, vol. 52, no. 6, pp. 1631–1640.CrossRef MathSciNet
  27.Gershon, E., Shaked, U., and Yaesh, I., H ∞ Control and Filtering of Discrete-time Stochastic Systems with Multiplicative Noise, Automatica, 2001, vol. 37, pp. 409–417.CrossRef MathSciNet MATH
  28.Wang, F. and Balakrishnan, V., Robust Kalman Filters for Linear Time-varying Systems with Stochastic Parametric Uncertainties, IEEE Trans. Signal Process., 2002, vol. 50, pp. 803–813.CrossRef MathSciNet
  29.Kassam, S.A. and Poor, H.V., Robust Techniques for Signal Processing: A Survey, Proc. IEEE, 1985, vol. 73, no. 3, pp. 433–481.CrossRef MATH
  30.Rao, C.V., Rawlings, J.B., and Mayne, D.Q., Constrained State Estimation for Nonlinear Discrete-time systems: stability and Moving Horizon Approximations, IEEE Trans. Automat. Control, 2003, vol. 48, pp. 246–258.CrossRef MathSciNet
  31.Alessandri, A., Baglietto, M., and Battistelli, G., A Minimax Receding-horizon Estimator for Uncertain Discrete-time Linear Systems, Proc. Am. Control Conf., 2004, pp. 205–210.
  32.Rotea, M. and Lana, C., State Estimation with Probability Constraints, Int. J. Control, 2008, vol. 81, no. 6, pp. 920–930.CrossRef MathSciNet MATH
  33.Kogan, M.M., Optimal Estimation and Filtration under Unknown Covariances of Random Factors, Autom. Remote Control, 2014, vol. 75, no. 11, pp. 1964–1981.CrossRef MathSciNet
  34.Dong, H., Wang, Z., Lam, J., and Gao, H., Distributed Filtering in Sensor Networks with Randomly Occurring Saturations and Successive Packet Dropouts, Int. J. Robust Nonlin. Control, 2014, vol. 24, no. 12, pp. 1743–1759.CrossRef MathSciNet MATH
  35.Ma, J., Bo, Y., Zhou, Y., and Guo, Z., Error Variance-constrained H ∞ Filtering for a Class of Nonlinear Stochastic Systems with Degraded Measurements: The Finite Horizon Case, Int. J. Syst. Sci., 2012, vol. 43, no. 12, pp. 2361–2372.CrossRef MathSciNet MATH
  36.Ding, D., Wang, Z., Shen, B., and Dong, H., Envelope-constrained H ∞ Filtering with Fading Measurements and Randomly Occurring Nonlinearities: The Finite-horizon Case, Automatica, 2015, vol. 55, pp. 37–45.CrossRef MathSciNet
  37.Shen, B., Wang, Z., Shu, H., and Wei, G., H ∞ Filtering for Uncertain Time-varying Systems with Multiple Randomly Occurred Nonlinearities and Successive Packet Dropouts, Int. J. Robust Nonlin. Control, 2011, vol. 21, no. 14, pp. 1693–1709.CrossRef MathSciNet MATH
  38.Luo, Y., Wei, G., Liu, Y., and Ding, X., Reliable H ∞ State Estimation for 2-D Discrete Systems with Infinite Distributed Delays and Incomplete Observations, Int. J. General Syst., 2015, vol. 44, no. 2, pp. 155–168.CrossRef MathSciNet MATH
  39.Yaz, Y. and Yaz, E., On LMI Formulations of Some Problems Arising in Nonlinear Stochastic System Analysis, IEEE Trans. Automat. Control, 1999, vol. 44, no. 4, pp. 813–816.CrossRef MathSciNet MATH
  
• 作者单位：Lifeng Ma (1)
  Zidong Wang (2) (3)
  Hak-Keung Lam (4)
  Fuad E. Alsaadi (3)
  Xiaohui Liu (2)
  
  1. School of Automation, Nanjing Univerity of Science and Technology, Nanjing, China
  2. Brunel University London, Uxbridge, Middlesex, UK
  3. King Abdulaziz University, Jeddah, Saudi Arabia
  4. King’s College London, Strand Campus, London, UK
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Systems Theory and Control
  Automation and Robotics
  Mechanical Engineering
  Computer-Aided Engineering and Design
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1608-3032

文摘

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method. Original Russian Text © Lifeng Ma, Zidong Wang, Hak-Keung Lam, Fuad E. Alsaadi, Xiaohui Liu, 2016, published in Avtomatika i Telemekhanika, 2016, No. 1, pp. 50–71.This paper was recommended for publication by O.A. Stepanov, a member of the Editorial Board