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Robust H 2/H ∞ global linearization filter design for nonlinear stochastic time-varying delay systems

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Abstract

One can design a robust H ∞ filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality (HJI), which is difficult to be solved. In this paper, the robust mixed H 2/H ∞ globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic Itô-type equation. Based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov–Krasovskii functional theory, and the robust H ∞ globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. For a given attenuation level, the H 2 globally linearized filtering problem with the worst case disturbance in the H ∞ filter case is known as the mixed H 2/H ∞ globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable. A simulation example is provided to illustrate the effectiveness of the proposed method.

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References

  1. Xu S Y, Lam J, Mao X R. Delay-dependent H ∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans Circuits Syst I, Reg Papers, 2007, 54: 2070–2077

    Article  MathSciNet  Google Scholar 

  2. Chen B S, Tsai C L, Chen Y F. Mixed H 2/H ∞ filtering design in multirate transmultiplexer system: LMI approach. IEEE Trans Signal Process, 2001, 49: 2693–2701

    Article  Google Scholar 

  3. Nagpal K M, Khargonekar P P. Filtering and smoothing in an H ∞ setting. IEEE Trans Autom Control, 1991, 36: 152–166

    Article  MathSciNet  MATH  Google Scholar 

  4. Xu S Y, Chen T. Reduced-order H ∞ filtering for stochastic system. IEEE Trans Signal Process, 2002, 50: 2998–3007

    Article  MathSciNet  Google Scholar 

  5. Chen G C, Shen Y. Robust H ∞ filter design for neutral stochastic uncertain systems with time-varying delay. J Math Anal Appl, 2009, 353: 196–204

    Article  MathSciNet  MATH  Google Scholar 

  6. Song B, Xu S Y, Xia J W, et al. Design of robust non-fragile H ∞ filters for uncertain neutral stochastic system with distributed delays. Asian J Control, 2010, 12: 39–45

    MathSciNet  Google Scholar 

  7. Wu H N, Luo B. Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H ∞ control. IEEE Trans Neural Netw Learn Syst, 2012, 23: 1884–1895

    Article  Google Scholar 

  8. Luo B, Wu H N. Computationally efficient simultaneous policy update algorithm for nonlinear H ∞ state feedback control with Galerkin’s method. Int J Robust Nonlin Control, 2013, 23: 991–1012

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu Y G, Zhang J F, Pan Z G. Design of satisfaction output feedback controls for stochastic nonlinear systems under quadratic tracking risk-sensitive index. Sci China Ser F-Inf Sci, 2003, 46: 126–144

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang W H, Feng G. Nonlinear stochastic H 2/H ∞ control with (x, u, v)-dependent noise: infinite horizon case. IEEE Trans Autom Control, 2008, 53: 1323–1328

    Article  MathSciNet  Google Scholar 

  11. Zhang W H, Chen B S, Tang H B, et al. Some remarks on general nonlinear stochastic H ∞ control with state, control, and disturbance-dependent noise. IEEE Trans Autom Control, 2014, 59: 237–242

    Article  MathSciNet  Google Scholar 

  12. Wu A G, Liu X N, Zhang Y. L 2-L ∞ filtering for nonlinear stochastic systems. Asian J of Control, 2012, 14: 1676–1682

    Article  MathSciNet  MATH  Google Scholar 

  13. Abbaszadeh M, Marquez H J. Nonlinear robust H ∞ filtering for a class of uncertain systems via convex optimization. J Control Theory Appl, 2012, 10: 152–158

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang W H, Chen B S, Tseng C S. Robust H ∞ filtering for nonlinear stochastic systems. IEEE Trans Signal Process, 2005, 53: 589–598

    Article  MathSciNet  Google Scholar 

  15. Chen B S, Chen W H, Wu H L. Robust H 2/H ∞ global linearization filter design for nonlinear stochastic systems. IEEE Trans Circuits Syst I, Reg Papers, 2009, 56: 1441–1454

    Article  MathSciNet  Google Scholar 

  16. Tseng C S. Robust fuzzy filter design for a class of nonlinear stochastic systems. IEEE Trans Fuzzy Syst, 2007, 15: 261–274

    Article  Google Scholar 

  17. Chen W H, Chen B S. Robust stabilization design for nonlinear stochastic system with Poisson noise via fuzzy interpolation method. Fuzzy Sets Syst, 2013, 217: 41–61

    Article  MathSciNet  MATH  Google Scholar 

  18. Calzolari A, Florchinger P, Nappo G. Nonlinear filtering for stochastic systems with fixed delay: approximation by a modified Milstein scheme. Comput Math Appl, 2011, 61: 2498–2509

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang W H, Feng G, Li Q H. Robust H ∞ filtering for general nonlinear stochastic state-delayed systems. Math Probl Eng, 2012, 2012: 231352(15)

  20. Yan H C, Zhang H, Shi H B, et al. Robust H ∞ filtering for uncertain nonlinear stochastic systems with mode-dependent time-delays and Markovian jump parameters. Circuits Syst Signal Process, 2011, 30: 303–321

    Article  MathSciNet  MATH  Google Scholar 

  21. Shen B, Wang Z D, Hung Y S. Distributed H ∞ filtering for polynomial nonlinear stochastic systems in sensor networks. IEEE Trans Ind Electron, 2011, 58: 1971–1979

    Article  Google Scholar 

  22. Li H P, Shi Y. Robust H ∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays. Automatica, 2012, 48: 159–166

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang Z D, Huang B. Robust H 2/H ∞ filtering for linear systems with error variance constraints. IEEE Trans Signal Process, 2000, 48: 2463–2467

    Article  MathSciNet  MATH  Google Scholar 

  24. Gao H J, Lam J, Xie L H, et al. New approach to mixed H 2/H ∞ filtering for polytopic discrete-time systems. IEEE Trans Signal Process, 2005, 53: 3183–3192

    Article  MathSciNet  Google Scholar 

  25. Qiu J Q, Feng G, Yang J. Improved delay-dependent H ∞ filtering design for discrete-time polytopic linear delay systems. IEEE Trans Circuits Syst II, Exp Briefs, 2008, 55: 178–182

    Article  Google Scholar 

  26. Velni J M, Grigoriadis K M. Rate-dependent mixed H 2/H ∞ filter design for parameter-dependent state delayed LPV systems. IEEE Trans Circuits Syst I, Reg Papers, 2008, 55: 2097–3105

    Article  MathSciNet  Google Scholar 

  27. Chen B S, Zhang W H, Chen Y Y. On the robust state estimation of nonlinear stochastic systems with state-dependent noise. In: Proceedings of the 2002 International Conference on Control and Automation, Xiamen, 2002. 2299–2304

    Google Scholar 

  28. Hinrichsen D, Pritchard A J. Stochastic H ∞. SIAM J Control Optim, 1998, 36: 1504–1538

    Article  MathSciNet  MATH  Google Scholar 

  29. Chen B S, Zhang W H. State feedback H ∞ control of nonlinear stochastic systems. SIAM J Control Optim, 2006, 44: 1973–1991

    Article  MathSciNet  MATH  Google Scholar 

  30. Chen P N, Qin H S, Wang Y, et al. Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control. Sci China Inf Sci, 2012, 55: 200–213

    Article  MathSciNet  MATH  Google Scholar 

  31. Yang R M, Wang Y Z. Stability for a class of nonlinear time-delay systems via Hamiltonian functional method. Sci China Inf Sci, 2012, 55: 1218–1228

    Article  MathSciNet  MATH  Google Scholar 

  32. Li C Y, Guo L. A dynamical inequality for the output of uncertain nonlinear systems. Sci China Inf Sci, 2013, 56: 012201

    MathSciNet  Google Scholar 

  33. Wang Y Z, Feng G. On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems. Sci China Inf Sci, 2013, 56: 108202

    MathSciNet  Google Scholar 

  34. Boyd S, Ghaoui L El, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994. 51–60

    Book  MATH  Google Scholar 

  35. Luo Q, Mao X R, Shen Y. Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations. Automatica, 2011, 47: 2075–2081

    Article  MathSciNet  MATH  Google Scholar 

  36. Mao X R. Stochastic Differential Equations and Applications. 2nd ed. Chichester: Horwood, 2007. 112–114

    Google Scholar 

  37. Berman N, Shaked U. H ∞ for nonlinear stochastic systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, 2003. 5025–5030

    Google Scholar 

  38. Gu K, Kharitonov V L, Chen J. Stability of Time-Delay Systems. Berlin: Springer, 2003. 316

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Weihua Mao

  2. College of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Weihua Mao & Feiqi Deng

  3. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China

    Anhua Wan

Authors
  1. Weihua Mao
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  2. Feiqi Deng
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  3. Anhua Wan
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Correspondence to Anhua Wan.

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Mao, W., Deng, F. & Wan, A. Robust H 2/H ∞ global linearization filter design for nonlinear stochastic time-varying delay systems. Sci. China Inf. Sci. 59, 32204 (2016). https://doi.org/10.1007/s11432-015-5386-7

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  • DOI: https://doi.org/10.1007/s11432-015-5386-7

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