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access icon free Finite-time robust fuzzy control for non-linear Markov jump systems under aperiodic sampling and actuator constraints

© The Institution of Engineering and Technology
Received 21/12/2016, Accepted 14/06/2017, Revised 13/04/2017, Published 15/06/2017

This study investigates the fuzzy control problem for a class of non-linear Markov jump systems with sampled-data inputs and actuator constraints over a finite-time interval. Takagi–Sugeno (T–S) fuzzy models are employed to approximate the non-linearity. The partly known transition probability matrix consisting of known, uncertain, and unknown elements is considered. The asynchronous errors of the membership functions induced by aperiodic sampling are taken care of to avoid conservative results. The objective is to procure a sampled-data fuzzy controller such that the resulting closed-loop system is finite-time bounded and a prescribed performance index is guaranteed simultaneously. By establishing a new piecewise Lyapunov–Krasovskii functional and utilising convex optimisation technique, a novel set of sufficient conditions for the existence of anticipated sampled-data controller are developed. Finally, two illustrative examples are presented to prove the effectiveness of the proposed approaches.

Inspec keywords: closed loop systems; nonlinear control systems; convex programming; robust control; performance index; sampling methods; sampled data systems; matrix algebra; fuzzy control; actuators; Markov processes; Lyapunov methods

Other keywords: finite-time interval; actuator constraints; sampled-data controller; performance index; Takagi-Sugeno models; convex optimisation technique; piecewise Lyapunov-Krasovskii functional; membership functions; aperiodic sampling; nonlinear Markov jump systems; asynchronous errors; T-S models; transition probability matrix; robust fuzzy control; closed-loop system

Subjects: Markov processes; Fuzzy control; Algebra; Actuating and final control devices; Discrete control systems; Optimisation techniques; Stability in control theory; Nonlinear control systems

References

    1. 1)
      • 5. Qiu, J., Gao, H., Ding, S.X.: ‘Recent advances on fuzzy-model-based nonlinear networked control systems: a survey’, IEEE Trans. Ind. Electron., 2016, 63, (2), pp. 1207–1217.
    2. 2)
      • 27. Liu, H., Zhou, G.: ‘Finite-time sampled-data control for switching T–S fuzzy systems’, Neurocomputing, 2015, 166, pp. 294–300.
    3. 3)
      • 28. Cheng, J., Park, J.H., Zhang, L., et al: ‘An asynchronous operation approach to event-triggered control for fuzzy markovian jump systems with general switching policies’, IEEE Trans. Fuzzy Syst., 2016, DOI: 10.1109/TFUZZ.2016.2633325.
    4. 4)
      • 23. Hetel, L., Fiter, C., Omran, H., et al: ‘Recent developments on the stability of systems with aperiodic sampling: an overview’, Automatica, 2017, 76, pp. 309–335.
    5. 5)
      • 11. Yin, Y., Shi, P., Liu, F., et al: ‘Fuzzy model-based robust H∞ filtering for a class of nonlinear nonhomogeneous Markov jump systems’, Analog Integr. Circuits Signal Process., 2013, 93, (9), pp. 2381–2391.
    6. 6)
      • 18. Cheng, J., Zhu, H., Zhong, S., et al: ‘Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals’, ISA Trans., 2013, 52, (6), pp. 768–774.
    7. 7)
      • 22. He, S., Xu, H.: ‘Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach’, Nonlinear Dyn., 2015, 80, (3), pp. 1159–1171.
    8. 8)
      • 21. Shen, H., Park, J.H., Wu, Z.G.: ‘Finite-time reliable L2−L∞/H∞ control for Takagi–Sugeno fuzzy systems with actuator faults’, IET Control Theory Appl., 2014, 8, (9), pp. 688–696.
    9. 9)
      • 32. Zou, L., Wang, Z., Gao, H., et al: ‘State estimation for discrete-time dynamical networks with time-varying delays and stochastic disturbances under the Round-Robin protocol’, IEEE Trans. Neural Netw. Learn. Syst., 2017, 28, (5), pp. 1139–1151, DOI: 10.1109/TNNLS.2016.25246212016.
    10. 10)
      • 19. He, S., Liu, F.: ‘Finite-time fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback’, IEEE Trans. Fuzzy Syst., 2012, 20, (4), pp. 605–614.
    11. 11)
      • 15. Shi, P., Zhang, Y., Agarwal, R.K.: ‘Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps’, Neurocomputing, 2015, 151, pp. 168–174.
    12. 12)
      • 13. Cheng, J., Park, J.H., Liu, Y., et al: ‘Finite-time H∞ fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions’, Fuzzy Sets Syst., 2017, 314, pp. 99–115.
    13. 13)
      • 26. Gao, H., Chen, T.: ‘Stabilization of nonlinear systems under variable sampling: a fuzzy control approach’, IEEE Trans. Fuzzy Syst., 2007, 15, (5), pp. 972–983.
    14. 14)
      • 29. Wang, M., Qiu, J., Chadli, M., et al: ‘A switched system approach to exponential stabilization of sampled-data T–S fuzzy systems with packet dropouts’, IEEE Trans. Cybern., 2016, 46, (12), pp. 3145–3156.
    15. 15)
      • 20. Wang, J., Li, F., Sun, Y., et al: ‘On asynchronous L2−L∞ filtering for networked fuzzy systems with Markov jump parameters over a finite-time interval’, IET Control Theory Appl., 2016, 10, (17), pp. 2175–2185.
    16. 16)
      • 6. Li, H., Yin, S., Pan, Y., et al: ‘Model reduction for interval type-2 Takagi–Sugeno fuzzy systems’, Automatica, 2015, 61, pp. 308–314.
    17. 17)
      • 33. Tanaka, K., Ikeda, T., Wang, H.O.: ‘Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities’, IEEE Trans. Fuzzy Syst., 1996, 4, (1), pp. 1–13.
    18. 18)
      • 25. Fridman, E.: ‘A refined input delay approach to sampled-data control’, Automatica, 2010, 46, (2), pp. 421–427.
    19. 19)
      • 31. Zeng, H.B., He, Y., Wu, M., et al: ‘New results on stability analysis for systems with discrete distributed delay’, Automatica, 2015, 60, pp. 189–192.
    20. 20)
      • 16. Luan, X., Liu, F., Shi, P.: ‘Finite-time filtering for non-linear stochastic systems with partially known transition jump rates’, IET Control Theory Appl., 2010, 4, (5), pp. 735–745.
    21. 21)
      • 4. Li, H., Gao, H., Shi, P., et al: ‘Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach’, Automatica, 2014, 50, (7), pp. 1825–1834.
    22. 22)
      • 8. Chadli, M., Karimi, H.R.: ‘Robust observer design for unknown inputs Takagi–Sugeno models’, IEEE Trans. Fuzzy Syst., 2013, 21, (1), pp. 158–164.
    23. 23)
      • 3. Shen, H., Park, J.H., Zhang, L., et al: ‘Robust extended dissipative control for sampled-data Markov jump systems’, Int. J. Control, 2014, 87, (8), pp. 1549–1564.
    24. 24)
      • 12. He, S., Liu, F.: ‘Filtering-based robust fault detection of fuzzy jumps systems’, Fuzzy Sets Syst., 2011, 185, pp. 95–110.
    25. 25)
      • 7. Qiu, J., Tian, H., Lu, Q., et al: ‘Nonsynchronized robust filtering design for continuous-time T–S fuzzy affine dynamic systems based on piecewise Lyapunov functions’, IEEE Trans. Cybern., 2013, 43, (6), pp. 1755–1766.
    26. 26)
      • 14. Amato, F., Ariola, M., Dorato, P.: ‘Finite-time control of linear systems subject to parametric uncertainties and disturbances’, Automatica, 2001, 37, (9), pp. 1459–1463.
    27. 27)
      • 17. Shen, H., Li, F., Wu, Z.G., et al: ‘Finite-time asynchronous H∞ filtering for discrete-time Markov jump systems over a lossy network’, Int. J. Robust Nonlinear Control, 2016, 26, (17), pp. 3831–3848.
    28. 28)
      • 9. Li, H., Wu, C., Shi, P., et al: ‘Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach’, IEEE Trans. Cybern., 2015, 45, (11), pp. 2378–2389.
    29. 29)
      • 10. Wang, J.W., Wu, H.N., Guo, L., et al: ‘Robust H∞ fuzzy control for uncertain nonlinear Markovian jump systems with time-varying delay’, Fuzzy Sets Syst., 2013, 212, pp. 41–61.
    30. 30)
      • 24. Zhang, D., Han, Q.L., Jia, X.: ‘Network-based output tracking control for T–S fuzzy systems using an event-triggered communication scheme’, Fuzzy Sets Syst., 2015, 273, pp. 26–48.
    31. 31)
      • 30. Feng, Z., Lam, J.: ‘Integral partitioning approach to robust stabilization for uncertain distributed tim-delay systems’, Int. J. Robust Nonlinear Control, 2012, 22, (6), pp. 676–689.
    32. 32)
      • 1. Shen, M., Ye, D.: ‘Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions’, Fuzzy Sets Syst., 2013, 217, pp. 80–95.
    33. 33)
      • 2. Zhang, L., Boukas, E.K.: ‘Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities’, Automatica, 2009, 45, (2), pp. 463–468.
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