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Volume 4 Issue 3
Jul.  2017

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Xinxin Fu, Yu Kang and Pengfei Li, "Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models," IEEE/CAA J. Autom. Sinica, vol. 4, no. 3, pp. 507-511, July 2017. doi: 10.1109/JAS.2017.7510559
Citation: Xinxin Fu, Yu Kang and Pengfei Li, "Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models," IEEE/CAA J. Autom. Sinica, vol. 4, no. 3, pp. 507-511, July 2017. doi: 10.1109/JAS.2017.7510559

Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models

doi: 10.1109/JAS.2017.7510559
Funds:

the National High Technology Research and Development Program of China (863 Program) 2014AA06A503

the National Natural Science Foundation of China 61422307

the National Natural Science Foundation of China 61673361

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  • In this paper, we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems. Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods, and it preserves important structures of the nonlinear systems. Also, the form of Euler-Maruyama model is simple and easy to be calculated. The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems, and may be useful to many practical control applications, such as tracking control in mechanical systems. And the effectiveness of the approach is demonstrated by a simulation example.

     

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  • [1]
    E. Yaz and A. Azemi, "Observer design for discrete and continuous non-linear stochastic systems, " Int. J. Syst. Sci. , vol. 24, no. 12, pp. 2289-2302, Dec. 1993. doi: 10.1080/00207729308949629
    [2]
    A. Barbata, M. Zasadzinski, H. Souley Ali, and H. Messaoud, "Exponential observer for a class of one-sided lipschitz stochastic nonlinear systems, " IEEE Trans. Automat. Control, vol. 60, no. 1, pp. 259-264, Jan. 2015. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=6818378&punumber%3D9
    [3]
    A. P. Dani, S. J. Chung, and S. Hutchinson, "Observer design for stochastic nonlinear systems via contraction-based incremental stability, " IEEE Trans. Automat. Control, vol. 60, no. 3, pp. 700-714, Mar. 2015. http://ieeexplore.ieee.org/document/6899639/
    [4]
    B. J. Driessen, "Observer/controller with global practical stability for tracking in robots without velocity measurement, " Asian J. Control, vol. 17, no. 5, pp. 1898-1913, Sep. 2015 doi: 10.1002/asjc.1049/full?scrollTo=references
    [5]
    B. Xian, M. S. de Queiroz, D. M. Dawson, and M. L. McIntyre, "A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems, " Automatica, vol. 40, no. 4, pp. 695-700, Apr. 2004. http://www.sciencedirect.com/science/article/pii/S0005109803003960
    [6]
    G. Ellis, Observers in Control Systems:A Practical Guide. Boston, USA:Academic Press, 2002.
    [7]
    M. Arcak and D. Nesić, "A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation, " Automatica, vol. 40, no. 11, pp. 1931-1938, Nov. 2004. http://www.sciencedirect.com/science/article/pii/S000510980400175X
    [8]
    H. Y. Jin, B. Q. Yin, Q. Ling, and Y. Kang, "Sampled-data observer design for nonlinear autonomous systems, " in Proc. Chinese Control and Decision Conf. . Guilin, China, 2009, pp. 1516-1520. http://dl.acm.org/citation.cfm?id=2258202
    [9]
    H. Katayama and H. Aoki, "Straight-line trajectory tracking control for sampled-data underactuated ships, " IEEE Trans. Control Syst. Technol. , vol. 22, no. 4, pp. 1638-1645, Jul. 2014. http://netra.math.ttu.edu/ip/pbs/p_mot_bio.html
    [10]
    H. Beikzadeh and H. J. Marquez, "Multirate observers for nonlinear sampled-data systems using input-to-state stability and discretetime approximation, " IEEE Trans. Automat. Control, vol. 59, no. 9, pp. 2469-2474, Sep. 2014. http://ieeexplore.ieee.org/document/6730927/
    [11]
    D. Nesic and D. S. Laila, "A note on input-to-state stabilization for nonlinear sampled-data systems, " IEEE Trans. Automat. Control, vol. 47, no. 7, pp. 1153-1158, Jul. 2002. http://ieeexplore.ieee.org/document/1017562/
    [12]
    L. Grüne and D. Nesic, "Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models, " SIAM J. Control Optimiz., vol. 42, no. 1, pp. 98-122, 2003. doi: 10.1137/S036301290240258X
    [13]
    É. Gyurkovics and A. M. Elaiw, "Stabilization of sampled-data non-linear systems by receding horizon control via discrete-time approximations, " Automatica, vol. 40, no. 12, pp. 2017-2028, Dec. 2004. https://www.semanticscholar.org/paper/Stabilization-of-sampled-data-nonlinear-systems-by-Gyurkovics-Elaiw/0f04d91b9618bc84a1cb87146b610e79a7e4630b/figure/29
    [14]
    D. Nesić and L. Grüne, "A receding horizon control approach to sampled-data implementation of continuous-time controllers, " Syst. Control Lett. , vol. 55, no. 8, pp. 660-672, Aug. 2006. http://www.sciencedirect.com/science/article/pii/S0167691106000399
    [15]
    O. Techakesari, J. J. Ford, and D. Nesić, "Practical stability of approximating discrete-time filters with respect to model mismatch, " Automatica, vol. 48, no. 11, pp. 2965-2970, Nov. 2012.
    [16]
    D. J. Higham, X. R. Mao, and A. M. Stuart, "Exponential mean-square stability of numerical solutions to stochastic differential equations, " LMS J. Comput. Math. , vol. 6, pp. 297-313, Jan. 2003. https://wenku.baidu.com/view/89f98bd7360cba1aa811da8e.html
    [17]
    D. J. Higham, "An algorithmic introduction to numerical simulation of stochastic differential equations, " SIAM Rev. , vol. 43, no. 3, pp. 525-546, Sep. 2001. doi: 10.1137/S0036144500378302
    [18]
    X. R. Mao, "Numerical solutions of stochastic functional differential equations, " LMS J. Comput. Math. , vol. 6, pp. 141-161, Jan. 2003. http://www.sciencedirect.com/science/article/pii/S0377042702007501
    [19]
    X. R. Mao, "Exponential stability of equidistant Euler-Maruyama approximations of stochastic differential delay equations, " J. Comput. Appl. Math. , vol. 200, no. 1, pp. 297-316, Mar. 2007. http://www.sciencedirect.com/science/article/pii/S0377042706000173
    [20]
    X. R. Mao, "Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations, " J. Comput. Appl. Math. , vol. 296, pp. 362-375, Apr. 2016. http://www.sciencedirect.com/science/article/pii/S0377042715004884
    [21]
    X. R. Mao, C. G. Yuan, and G. Yin, "Approximations of EulerMaruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions, " J. Comput. Appl. Math. , vol. 205, no. 2, pp. 936-948, Aug. 2007. http://www.sciencedirect.com/science/article/pii/S0377042706004146
    [22]
    X. R. Mao and L. Szpruch, "Strong convergence rates for backward Euler-Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients, " Stochastics, vol. 85, no. 1, pp. 144-171, Feb. 2013. doi: 10.1080/17442508.2011.651213
    [23]
    M. Milošević, "Almost sure exponential stability of solutions to highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama approximation, " Math. Comp. Modell. , vol. 57, no. 3-4, pp. 887-899, Feb. 2013. http://www.sciencedirect.com/science/article/pii/S0895717712002555
    [24]
    H. L. Ngo and D. Taguchi, "Strong convergence for the EulerMaruyama approximation of stochastic differential equations with discontinuous coefficients, " Mathematics, 2016. https://www.researchgate.net/publication/301880520_Strong_convergence_for_the_Euler-Maruyama_approximation_of_stochastic_differential_equations_with_discontinuous_coefficients
    [25]
    Z. J. Wu, M. Y. Cui, and P. Shi, "Backstepping control in vector form for stochastic Hamiltonian systems, " SIAM J. Control Optimiz. , vol. 50, no. 2, pp. 925-942, Apr. 2012. doi: 10.1137/100817905
    [26]
    H. Zhang, Y. Q. Xia, and Z. J. Wu, "Noise-to-state stability of random switched systems and its applications, " IEEE Trans. Automat. Control, vol. 61, no. 6, pp. 1607-1612, Jun. 2016. https://www.semanticscholar.org/paper/Noise-to-State-Stability-of-Random-Switched-Zhang-Xia/616d8ae45464e96e36ab19febfb378a881bc6c1d
    [27]
    S. M. Yang and S. J. Ke, "Performance evaluation of a velocity observer for accurate velocity estimation of servo motor drives, " IEEE Trans. Ind. Appl. , vol. 36, no. 1, pp. 98-104, Jan. -Feb. 2000. http://www.doc88.com/p-738474686733.html
    [28]
    W. S. Chen and X. B. Li, "Observer-based consensus of second-order multi-agent system with fixed and stochastically switching topology via sampled data, " Int. J. Robust Nonlinear Control, vol. 24, no. 3, pp. 567-584, Feb. 2014. doi: 10.1002/rnc.2906/abstract
    [29]
    Y. L. Cheng and D. M. Xie, "Distributed observer design for bounded tracking control of leader-follower multi-agent systems in a sampleddata setting, " Int. J. Control, vol. 87, no. 1, pp. 41-51, Jan. 2014. doi: 10.1080/00207179.2013.820353
    [30]
    L. Xie and P. P. Khargonekar, "Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems, " Automatica, vol. 48, no. 7, pp. 1423-1431, Jul. 2012.
    [31]
    H. C. Yan, Z. Z. Su, H. Zhang, and F. W. Yang, "Observer-based H control for discrete-time stochastic systems with quantisation and random communication delays, " IET Control Theory Appl. , vol. 7, no. 3, pp. 372-379, Feb. 2013.

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