access icon free Robust state and fault estimation for non-linear stochastic systems with unknown disturbances: a multi-step delayed solution

© The Institution of Engineering and Technology
Received 19/04/2018, Accepted 08/08/2019, Revised 24/06/2019, Published 09/08/2019

A study on the simultaneous state and fault estimation for non-linear discrete-time stochastic systems subjected to unknown disturbances is presented. The augmented system approach, system reformation using the state-dependent coefficient (SDC) factorisation, and unknown input filtering method are integrated to simultaneously estimate the state of the system and actuator and/or sensor faults. To achieve this aim, the non-linear system with faults and unknown disturbances is first transformed into an equivalent augmented system by using delayed measurements and the SDC factorisation. Next, within the SDC factorised linear-like augmented system and inspired by the robust two-stage Kalman filter, a novel multi-step estimator named as the robust simultaneous state and fault estimator is proposed to yield a robust state and fault estimation with a multi-step delay. Moreover, a novel real-time state estimator is designed based on the proposed hybrid fault reconstruction model in order to address the inherent time-delay problem. A comparison of the performance of the proposed filters with those of existing methods from the literature is demonstrated using a non-linear two-link manipulator system with friction forces acting simultaneously at each joint.

Inspec keywords: fault diagnosis; Kalman filters; nonlinear control systems; discrete time systems; filtering theory; friction; state estimation; stochastic systems; manipulators; linear systems; robust control; delays

Other keywords: unknown disturbances; system reformation; augmented system approach; multistep estimator; inherent time-delay problem; SDC factorisation; nonlinear two-link manipulator system; actuator; real-time state estimator; fault estimation; state-dependent coefficient factorisation; multistep delay; nonlinear discrete-time stochastic systems; robust simultaneous state; equivalent augmented system; hybrid fault reconstruction model; unknown input filtering method; nonlinear system; robust state; fault estimator; nonlinear stochastic systems

Subjects: Nonlinear control systems; Time-varying control systems; Simulation, modelling and identification; Interpolation and function approximation (numerical analysis); Tribology (mechanical engineering); Distributed parameter control systems; Discrete control systems; Robot and manipulator mechanics; Manipulators; Linear control systems; Control system analysis and synthesis methods; Stability in control theory

References

    1. 1)
      • 42. Xiao, M., Zhang, Y., Wang, Z., et al: ‘Augmented robust three-stage extended Kalman filter for mars entry-phase autonomous navigation’, Int. J. Syst. Sci., 2018, 49, (1), pp. 27–42.
    2. 2)
      • 50. Li, H., Shi, Y.: ‘Robust H∞ filtering for nonlinear stochastic systems with uncertainties and markov delays’, Automatica, 2012, 48, (1), pp. 159–166.
    3. 3)
      • 41. Ben Hmida, F., Khémiri, K., Ragot, J., et al: ‘Unbiased minimum-variance filter for state and fault estimation of linear time-varying systems with unknown disturbances’, Math. Probl. Eng., 2010, 2010, Article ID 345586, 17 pages.
    4. 4)
      • 35. Ben Hmida, F., Khémiri, K., Ragot, J., et al: ‘Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs’, J. Franklin Inst., 2012, 349, (7), pp. 2369–2388.
    5. 5)
      • 10. Xiao, Q., Wu, Y., Fu, H., et al: ‘Two-stage robust extended Kalman filter in autonomous navigation for the powered descent phase of mars edl’, IET Signal Process., 2015, 9, (3), pp. 277–287.
    6. 6)
      • 17. Torben, K., John, L.: ‘A new continuous discrete unscented Kalman filter’, IEEE Trans. Autom. Control, 2018, 46, (5), pp. 2198–2205.
    7. 7)
      • 55. Hsieh, C.-S.: ‘Robust two-stage Kalman filters for systems with unknown inputs’, IEEE Trans. Autom. Control, 2000, 45, (12), pp. 2374–2378.
    8. 8)
      • 2. Gao, Z., Liu, X.: ‘Integrated fault estimation and fault-tolerant control for stochastic systems with brownian motions’, Int. J. Robust Nonlinear Control, 2018, 28, (6), pp. 1915–1941.
    9. 9)
      • 38. Gao, Y., Liu, J., Sun, G., et al: ‘Fault deviation estimation and integral sliding mode control design for lipschitz nonlinear systems’, Syst. Control Lett., 2019, 123, pp. 8–15.
    10. 10)
      • 37. Liu, X., Gao, Z.: ‘Robust finite-time fault estimation for stochastic nonlinear systems with brownian motions’, J. Franklin Inst., 2017, 354, (6), pp. 2500–2523.
    11. 11)
      • 16. Maybeck, P.S.: ‘Stochastic models, estimation, and control’, vol. 3 (Academic Press, New York, 1982).
    12. 12)
      • 44. Xiao, M., Zhang, Y., Fu, H., et al: ‘Nonlinear unbiased minimum-variance filter for mars entry autonomous navigation under large uncertainties and unknown measurement bias’, ISA Trans., 2018, 76, pp. 97–109.
    13. 13)
      • 3. Chen, L., Zhao, Y., Fu, S.: , et al ‘Fault estimation observer design for descriptor switched systems with actuator and sensor failures’, IEEE Trans. Circuits Syst., 2018, 66, (2), pp. 810–819.
    14. 14)
      • 1. Chen, X., Sun, R., Wang, F.: , et al ‘Two-stage unscented Kalman filter algorithm for fault estimation in spacecraft attitude control system’, IET Control Theory Applic., 2018, 12, (13), pp. 1781–1791.
    15. 15)
      • 31. Hsieh, C.-S.: ‘Multi-step delayed input and state estimation: a system reformation approach’. 4th Int. Conf. on Information Science and Control Engineering (ICISCE), Changsha, China, 2017, pp. 1551–1555.
    16. 16)
      • 13. Mohammadi, H., Yao, H., Khademi, G., et al: ‘Extended Kalman filtering for state estimation of a hill muscle model’, IET Control Theory Applic., 2017, 12, (3), pp. 384–394.
    17. 17)
      • 6. Zhang, M.-H.: ‘Quantitative analysis on financial markets’ (World Scientific Publishing Co. Pte. Ltd., Singapore, 2015).
    18. 18)
      • 27. Hsieh, C.-S.: ‘Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs’, Automatica, 2009, 45, (9), pp. 2149–2153.
    19. 19)
      • 18. NøRgaard, M., Poulsen, N.-K., Ravn, O.: ‘New developments in state estimation for nonlinear systems’, Automatica, 2000, 36, (11), pp. 1627–1638.
    20. 20)
      • 23. Xu, J., Jing, Y., Dimirovski-Georgi, M., et al: ‘Two-stage unscented Kalman filter for nonlinear systems in the presence of unknown random bias’. 2008 American Control Conf., Seattle, USA, 2008, pp. 3530–3535.
    21. 21)
      • 59. Patton, R., Chen, L., Klinkhieo, S.: ‘An LPV pole-placement approach to friction compensation as an FTC problem’, Int. J. Appl. Math. Comput. Sci., 2012, 22, (1), pp. 149–160.
    22. 22)
      • 11. Dixon, W.-E., Walker, I.-D., Dawson, D-M., et al: ‘Fault detection for robot manipulators with parametric uncertainty: a prediction-error-based approach’, IEEE Trans. Robot. Autom., 2000, 16, (6), pp. 689–699.
    23. 23)
      • 54. Wang, J., Hu, L., Chen, F., et al: ‘Multiple-step fault estimation for interval type-II TS fuzzy system of hypersonic vehicle with time-varying elevator faults’, Int. J. Adv. Robot. Syst., 2017, 14, (2), pp. 1–11.
    24. 24)
      • 56. Hsieh, C.-S.: ‘State estimation for descriptor systems via the unknown input filtering method’, Automatica, 2013, 49, (5), pp. 1281–1286.
    25. 25)
      • 19. Quine, B-M.: ‘A derivative-free implementation of the extended Kalman filter’, Automatica, 2006, 42, (11), pp. 1927–1934.
    26. 26)
      • 30. Chavan, R.A., Fitch, K., Palanthandalam, M.H.J.: ‘Recursive input reconstruction with a delay’. American Control Conf. (ACC), Portland, USA, 2014, pp. 628–633.
    27. 27)
      • 14. Chen, B., Hu, G.: ‘Nonlinear state estimation under bounded noises’, Automatica, 2018, 98, pp. 159–168.
    28. 28)
      • 24. Kim, K.-H., Lee, J.-G., Park, C.-G.: ‘Adaptive two-stage extended Kalman filter for a fault-tolerant ins-gps loosely coupled system’, IEEE Trans. Aerosp. Electron. Syst., 2009, 45, (1), pp. 125–137.
    29. 29)
      • 26. Hsieh, C.-S.: ‘A unified framework for state estimation of nonlinear stochastic systems with unknown inputs’. 9th Asian Control Conf. (ASCC), Istanbul, Turkey, 2013, pp. 1–6.
    30. 30)
      • 15. Julier, S., Uhlmann, J., Durrant-Whyte, H.F.: ‘A new method for the nonlinear transformation of means and covariances in filters and estimators’, IEEE Trans. Autom. Control, 2000, 45, (3), pp. 477–482.
    31. 31)
      • 48. Wang, Z., Ho, D.-W.C., Liu, X.: ‘Variance-constrained filtering for uncertain stochastic systems with missing measurements’, IEEE Trans. Autom. Control, 2003, 48, (7), pp. 1254–1258.
    32. 32)
      • 53. Huang, S.J., Yang, G.H.: ‘Fault tolerant controller design for TS fuzzy systems with time-varying delay and actuator faults: a k-step fault-estimation approach’, IEEE Trans. Fuzzy Syst., 2014, 22, (6), pp. 1526–1540.
    33. 33)
      • 21. Julier, S.-J., Uhlmann, J.-K.: ‘Unscented filtering and nonlinear estimation’, Proc. IEEE, 2004, 92, (3), pp. 401–422.
    34. 34)
      • 5. Bessaoudi, T., Ben Hmida, F.: ‘Recursive five-step filter for state and fault estimation of linear descriptor stochastic systems with unknown disturbances’, J. Circuits Syst. Comput., 2017, 27, (6), pp. 1850083-1–1850083–24.
    35. 35)
      • 49. Liu, M., Cao, X., Shi, P.: ‘Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults’, IEEE Trans. Fuzzy Syst., 2013, 21, (5), pp. 789–799.
    36. 36)
      • 7. Swan, G.W.: ‘Optimal control applications in biomedical engineering a survey’, Opt. Control Appl. Methods, 1981, 2, (4), pp. 311–334.
    37. 37)
      • 58. Hsieh, C.-S., Majidi, M.-A.: ‘Implementation issues of unbiased minimum-variance state estimation for systems with unknown inputs’. Int. Automatic Control Conf. (CACS), Kaohsiung, Taiwan, 2014, pp. 323–328.
    38. 38)
      • 36. Laghrouche, S., Liu, J., Shakil Ahmed, F., et al: ‘Adaptive second-order sliding mode observer-based fault reconstruction for pem fuel cell air-feed system’, IEEE Trans. Control Syst. Technol., 2015, 23, (3), pp. 1098–1109.
    39. 39)
      • 33. Hsieh, C.-S.: ‘Unbiased minimum-variance input and state estimation for systems with unknown inputs: a system reformation approach’, Automatica, 2017, 84, pp. 236–240.
    40. 40)
      • 43. Bessaoudi, T., Ben Hmida, F., Hsieh, C.-S.: ‘Robust state and fault estimation for nonlinear stochastic systems with unknown disturbances’. 4th Int. Conf. on Information Science and Control Engineering (ICISCE), Changsha, China, 2017, pp. 1699–1704.
    41. 41)
      • 29. Yong, S.-Z., Zhu, M., Frazzoli, E.: ‘A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems’, Automatica, 2016, 63, pp. 321–329.
    42. 42)
      • 12. Yin, S., Yang, H., Kaynak, O.: ‘Sliding mode observer-based ftc for markovian jump systems with actuator and sensor faults’, IEEE Trans. Autom. Control, 2017, 62, (7), pp. 3551–3558.
    43. 43)
      • 40. Fu, H., Yang, Y., Xiao, Q., et al: ‘Autonomous navigation method based on unbiased minimum-variance estimation during mars entry’, Adv. Space Res., 2015, 55, (5), pp. 1512–1528.
    44. 44)
      • 9. Zhou, Q., Shi, P., Xu, S., et al: ‘Observer-based adaptive neural network control for nonlinear stochastic systems with time delay’, IEEE Trans. Neural Netw. Learn. Syst., 2013, 24, (1), pp. 71–80.
    45. 45)
      • 52. Zhou, D.-H., Frank, P.-M.: ‘Strong tracking filtering of nonlinear time-varying stochastic systems with coloured noise: application to parameter estimation and empirical robustness analysis’, Int. J. Control, 1996, 65, (2), pp. 295–307.
    46. 46)
      • 45. Yang, R., Zheng, W.X.: ‘H∞ filtering for discrete-time 2-D switched systems: an extended average dwell time approach’, Automatica, 2018, 98, pp. 302–313.
    47. 47)
      • 57. Hsieh, C.-S.: ‘State estimation for nonlinear systems with unknown inputs using SDC factorization’. TENCON 2015-2015 IEEE Region 10 Conf., Macau, China, 2015, pp. 1–6.
    48. 48)
      • 22. Zhang, L., Meilei, L., Nium, Z., et al: ‘Two-stage cubature Kalman filter for nonlinear system with random bias’. Int. Conf. on Multisensor Fusion and Information Integration for Intelligent Systems (MFI), Beijing, China, 2014.
    49. 49)
      • 51. Bessaoudi, T., Ben Hmida, F., Hsieh, C.-S.: ‘Robust state and fault estimation for linear descriptor and nonlinear stochastic systems with disturbances’, in Boubaker, O., Zhu, Q., Mohamoud, M., et al (Eds.): ‘New trends in observer-based control' (Elsevier, London, 2019), pp. 357–405.
    50. 50)
      • 39. Bessaoudi, T., Marouen, H., Ben Hmida, F.: ‘Unbiased minimum variance state and fault estimation for nonlinear stochastic systems with unknown disturbances’. 16th Int. Conf. on Sciences and Techniques of Automatic Control and Computer Engineering (STA), Monastir, Tunisia, 2015, pp. 291–295.
    51. 51)
      • 28. Yong, S.-Z., Zhu, M., Frazzoli, E.: ‘Simultaneous input and state estimation with a delay’. 54th Annual Conf. on Decision and Control (CDC), Osaka, Japan, 2015, pp. 468–475.
    52. 52)
      • 4. Bessaoudi, T., Ben Hmida, F., Hsieh, C.-S.: ‘Robust state and fault estimation for linear descriptor stochastic systems with disturbances: a dc motor application’, IET Control Theory Applic., 2017, 11, (5), pp. 601–610.
    53. 53)
      • 46. Zhang, Y., Wang, Z., Zou, L., et al: ‘Event-based finite-time filtering for multirate systems with fading measurements’, IEEE Trans. Aerosp. Electron. Syst., 2017, 53, (3), pp. 1431–1441.
    54. 54)
      • 8. Lin, Z., Lin, Y., Zhang, W.: ‘A unified design for state and output feedback H∞ control of nonlinear stochastic markovian jump systems with state and disturbance-dependent noise’, Automatica, 2009, 45, (12), pp. 2955–2962.
    55. 55)
      • 32. Hsieh, C.-S.: ‘Multi-step delayed input and state estimation: a system augmentation approach’. Int. Symp. on Computer Science and Intelligent Controls, Budapest, Hungary, 2017, pp. 63–68.
    56. 56)
      • 25. Hsieh, C.-S.: ‘State estimation for nonlinear systems with unknown inputs’. 7th IEEE Conf. on Industrial Electronics and Applications (ICIEA), Singapore, 2012, pp. 1533–1538.
    57. 57)
      • 20. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman filters’, IEEE Trans. Autom. Control, 2009, 54, (6), pp. 1254–1269.
    58. 58)
      • 47. Savkin, A., Peterson, I.-R., Ugronovskii, V.A.: ‘Robust control design using H-infinity methods’ (Springer-Verlag, London, 2000).
    59. 59)
      • 34. Zhang, Y., Wang, Z., Ma, L.: ‘Variance-constrained state estimation for networked multi-rate systems with measurement quantization and probabilistic sensor failures’, Int. J. Robust Nonlinear Control, 2016, 26, (16), pp. 3507–3523.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2018.5213
Loading

Related content

content/journals/10.1049/iet-cta.2018.5213
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading