This study addresses the Problem of composite hierarchical anti-disturbance control [disturbance-observer-based controllers (DOBC) and ℋ_∞ control] for Markovian jump singular systems with non-linearity and two types of disturbances (the first is generated by an exogenous system and the latter is norm-bounded). The authors’ attention is focused on the design of a disturbance observer to estimate the first disturbance, and then on constructing a composite hierarchical control scheme such that the solution to the composite system is unique and exists, the composite system can be guaranteed to be stochastically admissible, and different types of disturbances can be attenuated and rejected simultaneously. By constructing a proper stochastic Lyapunov–Krasovskii functional, sufficient conditions for the existence of the desired DOBCs are established. Finally, a numerical eEEExample is provided to show the effectiveness of the proposed approaches.

References

1. 1)
  - J. Lam , Z. Shu , S. Xu , E.K. Boukas . Robust H∞ control of descriptor discrete-time Markovian jump systems. Int. J. Control , 3 , 374 - 385
2. 2)
  - G. Lu , D.W.C. Ho . Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation. IEEE Trans. Autom. Control , 5 , 818 - 823
3. 3)
  - 7. Nikiforov, V.O.: ‘Nonlinear servocompensation of unknown external disturbances’, Automatica, 2001, 37, pp. 1647–1653 (doi: 10.1016/S0005-1098(01)00117-0).
4. 4)
  - L.X. Zhang , E.K. Boukas . Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica , 463 - 468
5. 5)
  - 19. Wu, L., Su, X., Shi, P.: ‘Output feedback control of Markovian jump repeated scalar nonlinear systems’, IEEE Trans. Automat. Control, 2014, 59, (1), pp. 199–204 (doi: 10.1109/TAC.2013.2267353).
6. 6)
  - W.-H. Chen . Disturbance observer based control for nonlinear systems. IEEE/ASME Trans. Mechatronics , 4 , 706 - 710
7. 7)
  - 36. Li, F., Wang, X., Shi, P.: ‘Robust quantized H∞ control for network control systems with Markovian jumps and time delays’, Int. J. Innov. Comput. Inf. Control, 2013, 9, (12), pp. 4889–4902.
8. 8)
  - 27. Uezato, E., Ikeda, M.: ‘Stict LMI conditions for stability, robust stabilization and ℋ∞ control of descriptor systems’. Proc. 38th IEEE Conf. on Desicion and Control, Phoenix, Arizona, USA, December 1999, pp. 4092–4097.
9. 9)
  - 22. Boukas, E.K.: ‘Control of singular systems with random abrupt changes’ (SpringerBerlin, 2008).
10. 10)
  - X. Chen , C.Y. Su , T. Fukuda . A nonlinear disturbance observer for multivariable systems and its application to magnetic bearing systems. IEEE Trans. Control Syst. Technol. , 569 - 577
11. 11)
  - 30. Xu, S., Lam, J.: ‘Robust control and filtering of singular systems’ (Springer, Berlin, 2006).
12. 12)
  - S. Xu , P.V. Dooren , R. Stefan , J. Lam . Robust stability and stabilization of discrete-time singular systems with state delay and parameter uncertainty. IEEE Trans. Autom. Control , 7 , 1122 - 1128
13. 13)
  - J. Huang , Z. Chen . A general framework for tackling the output regulation problem. IEEE Trans. Autom. Control , 2203 - 2218
14. 14)
  - 16. Boukas, E.K.: ‘Stochastic switching systems: analysis and design’ (Birkhauser, Boston, 2005).
15. 15)
  - 28. Dai, L.: ‘Singular control systems’ (Springer, Berlin, 1989).
16. 16)
  - 8. She, J., Ohyama, Y., Nakano, M.: ‘A new approach to the estimation and rejection of disturbances in servo systems’, IEEE Trans. Control Syst. Technol., 2005, 13, (3), pp. 378–385 (doi: 10.1109/TCST.2004.841650).
17. 17)
  - 6. Marino, R., Santosuosso, G.L.: ‘Global compensation of unknown sinusoidal disturbances for a class of nonlinear nonminimum phase systems’, IEEE Trans. Autom. Control, 2005, 50, (11), pp. 1816–1822 (doi: 10.1109/TAC.2005.858647).
18. 18)
  - L.X. Zhang . H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems. Automatica , 2570 - 2576
19. 19)
  - Y. Niu , D.W.C. Ho , X. Wang . Sliding mode control for Itô stochastic systems with Markovian switching. Automatica , 1784 - 1790
20. 20)
  - 12. Guo, L., Wen, X.: ‘Hierarchical anti-disturbance adaptive control for non-linear systems with composite disturbances and applications to missile systems’, Trans. Inst. Meas. Control, 2011, 33, (8), pp. 942–956 (doi: 10.1177/0142331210361555).
21. 21)
  - Y. Xia , J. Zhang , E.K. Boukas . Control for discrete singular hybrid systems. Automatica , 2635 - 2641
22. 22)
  - 14. Yao, X., Guo, L.: ‘Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer’, Automatica, 2013, 49, (8), pp. 2538–2545 (doi: 10.1016/j.automatica.2013.05.002).
23. 23)
  - 17. Wu, L.G., Su, X.J., Shi, P.: ‘Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems’, Automatica, 2012, 48, (8), pp. 1929–1933 (doi: 10.1016/j.automatica.2012.05.064).
24. 24)
  - Y. Xia , E.-K. Boukas , P. Shi , J. Zhang . Stability and stabilization of continuous-time singular hybrid systems. Automatica , 6 , 1504 - 1509
25. 25)
  - 11. Iwasaki, M., Shibata, T., Matsui, N.: ‘Disturbance-observer-based nonlinear friction compensation in the table drive systems’, IEEE/ASME Trans. Mechatronics, 1999, 4, (1), pp. 3–8 (doi: 10.1109/3516.752078).
26. 26)
  - 17. Costa, O.L.V., Fragoso, M.D., Marques, R.P.: ‘Discrete-time Markov jump linear systems’ (Springer, Berlin, 2005).
27. 27)
  - 10. Jiang, J., Chen, Q., Yao, B., Guo, J.: ‘Desired compensation adaptive robust control of mobile satellite communication system with disturbance and model uncertainties’, Int. J. Innov. Comput. Inf. Control, 2013, 9, (1), pp. 153–164.
28. 28)
  - Z.-J. Yang , H. Tsubakihara , S. Kanae , K. Wada , C.-Y. Su . A novel robust nonlinear motion controller with disturbance observer. IEEE Trans. Control Syst. Technol. , 1 , 137 - 147
29. 29)
  - S. Ma , C. Zhang . Robust stability and H∞ control for uncertain discrete Markovian jump singular systems with mode-dependent time-delay. Int. J. Robust Nonlinear Control , 9 , 965 - 985
30. 30)
  - Z. Fei , H. Gao , P. Shi . New results on stabilization of Markovian jump systems with time delay. Automatica , 10 , 2300 - 2306
31. 31)
  - L. Zhang , E. Boukas , J. Lam . Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Trans. Automat. Control , 10 , 2458 - 2464
32. 32)
  - L. Guo , W.-H. Chen . Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int. J. Robust Nonlinear Control , 3 , 109 - 125
33. 33)
  - W.-H. Chen . Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. J. Guid. Control Dyn. , 1 , 161 - 166
34. 34)
  - L.G. Wu , P. Shi , H.J. Gao . State estimation and sliding-mode control of Markovian jump singular systems. IEEE Trans. Autom. Control , 5 , 1213 - 1219
35. 35)
  - 7. Zhang, L., Gao, H., Kaynak, O.: ‘Network-induced constraints in networked control systems—a survey’, IEEE Trans. Ind. Inf., 2013, 9, (1), pp. 403–416 (doi: 10.1109/TII.2012.2219540).
36. 36)
  - 9. Gao, X., Teo, K.L., Duan, G.: ‘An optimal control approach to robust control of nonlinear spacecraft rendezvous system with θ − D technique’, Int. J. Innov. Comput. Inf. Control, 2013, 9, (5), pp. 2099–2110.
37. 37)
  - 15. Wei, X., Zhang, H., Guo, L.: ‘Composite disturbance-observer-based control and variable structure control for non-linear systems with disturbances’, Trans. Inst. Meas. Control, 2009, 31, (5), pp. 401–423 (doi: 10.1177/0142331208099282).

Disturbance-observer-based control & ℋ_∞ control for non-linear Markovian jump singular systems with multiple disturbances

References

Related content

Disturbance-observer-based control & ℋ∞ control for non-linear Markovian jump singular systems with multiple disturbances

References

Related content

Disturbance-observer-based control & ℋ_∞ control for non-linear Markovian jump singular systems with multiple disturbances