access icon free Data-driven sliding mode tracking control for unknown Markovian jump non-linear systems

This study aims to investigate the sliding mode control (SMC) problem for non-linear Markovian jump systems (MJSs) in which the transition probability could only be partly obtained and the system models and orders are unknown. Firstly, a mode-dependent data-driven sliding surface is established and by using the high-order SMC strategy, a data-based SMC law is proposed to guarantee the reachability of the SMC system. With the linear matrix inequalities technique, the tracking error of the closed-loop non-linear MJS is demonstrated to be asymptotically stochastically stable. Furthermore, a simulation experiment is carried out to prove the effectiveness of this method.

Inspec keywords: variable structure systems; asymptotic stability; reachability analysis; closed loop systems; nonlinear control systems; probability; stochastic systems; linear matrix inequalities; error analysis

Other keywords: high-order SMC strategy; unknown Markovian jump nonlinear systems; SMC system reachability; closed-loop nonlinear MJS error tracking; linear matrix inequalities; mode-dependent data-driven sliding surface; asymptotic stochastically stability; data-driven sliding mode tracking control; data-based SMC law

Subjects: Other topics in statistics; Combinatorial mathematics; Stability in control theory; Error analysis in numerical methods; Linear algebra (numerical analysis); Time-varying control systems; Nonlinear control systems; Multivariable control systems

References

    1. 1)
      • 31. Shi, P., Xia, Y., Liu, G., et al.: ‘On designing of sliding-mode control for stochastic jump systems’, IEEE Trans. Autom. Control, 2006, 51, (1), pp. 97103.
    2. 2)
      • 22. Weng, Y., Gao, X.: ‘Data-driven robust output tracking control for gas collector pressure system of coke ovens’, IEEE Trans. Ind. Electron., 2017, 64, (5), pp. 41874198.
    3. 3)
      • 34. Zhang, H., Wang, J., Shi, Y.: ‘Robust H sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities’, Syst. Control Lett., 2013, 62, (12), pp. 11141124.
    4. 4)
      • 2. Liu, J., Vazquez, S., Wu, L., et al.: ‘Extended state observer-based sliding-mode control for three-phase power converters’, IEEE Trans. Ind. Electron., 2017, 64, (1), pp. 2231.
    5. 5)
      • 7. Xia, Y., Fu, M., Yang, H., et al.: ‘Robust sliding-mode control for uncertain time-delay systems based on delta operator’, IEEE Trans. Ind. Electron., 2009, 56, (9), pp. 36463655.
    6. 6)
      • 10. Lin, C.: ‘Nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks’, IEEE Trans. Fuzzy Syst., 2006, 14, (6), pp. 849859.
    7. 7)
      • 21. Weng, Y., Gao, X.: ‘Adaptive sliding mode decoupling control with data-driven sliding surface for unknown MIMO nonlinear discrete systems’, Circuit Syst. Signal Process., 2017, 36, (3), pp. 969997.
    8. 8)
      • 13. Yan, M., Shi, Y.: ‘Robust discrete-time sliding mode control for uncertain systems with time-varying state delay’, IET Control Theory Appl., 2008, 2, (8), pp. 662674.
    9. 9)
      • 15. Xia, Y., Liu, G., Shi, P., et al.: ‘Sliding mode control of uncertain linear discrete time systems with input delay’, IET Control Theory Appl., 2007, 1, (4), pp. 11691175.
    10. 10)
      • 9. Liu, D., Yi, J., Zhao, D., et al.: ‘Adaptive sliding mode fuzzy control for a two-dimensional overhead crane’, IEEE/ASME Trans. Mechatronics, 2005, 15, (5), pp. 505522.
    11. 11)
      • 4. Song, J., Niu, Y., Zou, Y.: ‘Finite-time sliding mode control synthesis under explicit output constraint’, Automatica, 2016, 65, pp. 111114.
    12. 12)
      • 42. Zhang, W., Tang, Y., Miao, Q., et al.: ‘Synchronization of stochastic dynamical networks under impulsive control with time delays’, IEEE Trans. Neural Netw., 2014, 25, (10), pp. 17581768.
    13. 13)
      • 16. Khandekar, A., Malwatkar, G., Patre, B.: ‘Discrete sliding mode control for robust tracking of higher order delay time systems with experimental application’, ISA Trans., 2013, 52, (1), pp. 3644.
    14. 14)
      • 28. Sworder, D., Rogers, R.: ‘An LQ-solution to a control problem associated with a solar thermal central receiver’, IEEE Trans. Autom. Control, 1983, 28, (10), pp. 971978.
    15. 15)
      • 20. Hou, Z., Wang, Z.: ‘From model-based control to data-driven control: survey, classification and perspective’, Inf. Sci., 2013, 235, pp. 335.
    16. 16)
      • 39. Shen, Q., Zhang, T.: ‘Novel design of adaptive neural network controller for a class of nonaffine nonlinear systems’, Commun. Nonlinear. Sci., 2012, 17, (3), pp. 11071116.
    17. 17)
      • 33. Li, H., Shi, P., Yao, D., et al.: ‘Observer-based adaptive sliding mode control for nonlinear Markovian jump systems’, Automatica, 2016, 64, pp. 133142.
    18. 18)
      • 35. Dong, H., Wang, Z., Gao, H.: ‘Distributed H filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks’, IEEE Trans. Ind. Electron., 2013, 60, (10), pp. 46654672.
    19. 19)
      • 23. Li, F., Wu, L., Shi, P., et al.: ‘State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties’, Automatica, 2015, 51, pp. 385393.
    20. 20)
      • 41. Bu, X., Hou, Z., Yu, F., et al.: ‘Model free adaptive control with disturbance observer’, Control. Eng. Appl. Inf., 2012, 14, (4), pp. 4249.
    21. 21)
      • 18. Mihoub, M., Nouri, A.S., Abdennour, R.: ‘Multimodel discrete second order sliding mode control: stability analysis and real time application on a chemical reactor’, in Bartoszewicz, A (Ed.): ‘Sliding mode control’ (Intech Open Access Press, 2011, 1st edn.), pp. 473490.
    22. 22)
      • 40. Utkin, V., Poznyak, A.: ‘Adaptive sliding mode control with application to super-twist algorithm: equivalent control method’, Automatica, 2013, 49, (1), pp. 3947.
    23. 23)
      • 14. Goyal, V., Deolia, V.K., Sharma, T.: ‘Neural network based sliding mode control for uncertain discrete-time nonlinear systems with time-varying delay’, Int. J. Comput. Intell. Res., 2016, 12, (2), pp. 125138.
    24. 24)
      • 8. Wu, L., Gao, H.: ‘Sliding mode control of two-dimensional systems in Roesser model’, IET Control Theory Appl., 2008, 2, (4), pp. 352364.
    25. 25)
      • 6. Song, J., Niu, Y., Zou, Y.: ‘Finite-time stabilization via sliding mode control’, IEEE Trans. Autom. Control, 2017, 62, (3), pp. 14781483.
    26. 26)
      • 12. Young, K., Utkin, V., Ozguner, U.: ‘A control engineer's guide to sliding mode control’, IEEE Trans. Control Syst. Technol., 1999, 7, (3), pp. 328342.
    27. 27)
      • 26. Kang, Y., Li, Z., Dong, Y., et al.: ‘Markovian-based fault-tolerant control for wheeled mobile manipulators’, IEEE Trans. Control Syst. Technol., 2012, 20, (1), pp. 266276.
    28. 28)
      • 25. Liu, M., Ho, D., Niu, Y.: ‘Stabilization of Markovian jump linear system over networks with random communication delay’, Automatica, 2009, 45, (2), pp. 416421.
    29. 29)
      • 11. Liu, J., Wu, C., Wang, Z., et al.: ‘Reliable filter design for sensor networks in the type-2 fuzzy framework’, IEEE Trans. Ind. Inf., 2017, 13, (4), pp. 17421752.
    30. 30)
      • 37. Hou, Z., Jin, S.: ‘Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems’, IEEE Trans. Neural Netw., 2011, 22, (12), pp. 21732188.
    31. 31)
      • 19. Mihoub, M., Nouri, A.S., Ben Abdennour, R.: ‘The multimodel approach for a numerical second order sliding mode control of highly non stationary systems’. Proc. American Control Conf., Washington, USA, June 2008, pp. 47214726.
    32. 32)
      • 29. Li, X., Bar-Shalom, Y.: ‘Design of an interacting multiple model algorithm for air traffic control tracking’, IEEE Trans. Control Syst. Technol., 1993, 1, (3), pp. 186194.
    33. 33)
      • 32. Wu, L., Shi, P., Gao, H.: ‘State estimation and sliding-mode control of Markovian jump singular systems’, IEEE Trans. Autom. Control, 2010, 55, (5), pp. 12131219.
    34. 34)
      • 24. Mao, Z., Jiang, B., Shi, P.: ‘H fault detection filter design for networked control systems modelled by discrete Markovian jump systems’, IET Control Theory Appl., 2007, 1, (5), pp. 13361343.
    35. 35)
      • 5. Niu, Y., Ho, D.: ‘Design of sliding mode control subject to packet losses’, IEEE Trans. Autom. Control, 2010, 55, (11), pp. 26232628.
    36. 36)
      • 38. Hou, Z., Jin, S.: ‘A novel data-driven control approach for a class of discrete-time nonlinear systems’, IEEE Trans. Control Syst. Technol., 2011, 19, (6), pp. 15491558.
    37. 37)
      • 27. Li, Z., Xia, Y., Sun, F.: ‘Adaptive fuzzy control for multilateral cooperative teleoperation of multiple robotic manipulators under random network-induced delays’, IEEE Trans. Fuzzy Syst., 2014, 22, (2), pp. 437450.
    38. 38)
      • 17. Mihoub, M., Nouri, A., Ben Abdennour, R.: ‘Real-time application of discrete second order sliding mode control to a chemical reactor’, Control Eng. Pract., 2009, 17, (9), pp. 10891095.
    39. 39)
      • 1. Wu, L., Zheng, W.: ‘Passivity-based sliding mode control of uncertain singular time-delay systems’, Automatica, 2009, 45, (9), pp. 21202127.
    40. 40)
      • 36. Zhang, L., Boukas, E.: ‘Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities’, Automatica, 2009, 45, (2), pp. 463468.
    41. 41)
      • 3. Liu, J., Luo, W., Yang, X., et al.: ‘Robust model-based fault diagnosis for PEM fuel cell air-feed system’, IEEE Trans. Ind. Electron., 2016, 63, (5), pp. 32613270.
    42. 42)
      • 30. Chen, B., Niu, Y., Zou, Y.: ‘Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation’, Automatica, 2013, 49, (6), pp. 17481754.
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