ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Robust H∞ fault-tolerant control for stochastic Markov jump time-delay systems with actuator faults and application; pp. 102–110

Full article in PDF format | 10.3176/proc.2021.1.10

Authors
Fu Xingjian, Pang Xinrui

Abstract

This paper investigates the robust H∞ fault-tolerant controller design under actuator failure for a class of the stochastic Markov jump time-delay systems with parameter uncertainties. The existence condition of the state feedback robust H∞ fault-tolerant controller with actuator failure is presented. The robust H∞ fault-tolerant control algorithm is derived in the form of linear matrix inequality via the Lyapunov stability theory. The proposed control does not need to estimate the boundary value of an actuator fault, nor does it depend on fault detection and diagnostic devices. By solving the linear matrix inequality, a robust fault-tolerant controller, which makes the closed-loop system asymptotically stable and whose H∞ performance is restricted by a given bound, is designed such that its structure is comparably simpler and does not require a large number of calculations. The designed controller is applied to a UAV illustrative example. The numerical results and computer simulation demonstrate the effectiveness of the proposed fault-tolerant control.


References

1. Bristol, E. On a new measure of interaction for multivariable process control. IEEE Trans. Automat. Contr., 1966, 11(1), 133–134. 
https://doi.org/10.1109/TAC.1966.1098266

2. Rosenbrock, H. H. State-Space and Multivariable Theory. John Wiley & Sons, New York, NY, USA, 1970. 

3. Dimirovski, G. M., Barnett, S., Kleftouris, D. N., and Gough, N. E. An input-output package for MIMO non-linear control systems. IFAC Proceedings Volumes, 1979, 12(3), 265–273.
https://doi.org/10.1016/S1474-6670(17)65813-0

4. Niederlinski A. A. Heuristic approach to the design of linear multivariable interacting control systems. Automatica, 1971, 7(6), 691–701. 
https://doi.org/10.1016/0005-1098(71)90007-0

5. Pichai, V., Sezer, M. E., and Šiljak, D. D. Vulnerability of dynamic systems. Int. J. Control, 1981, 34(6), 1049–1060. 
https://doi.org/10.1080/0020717810 8922581

6. Šiljak, D. D. On pure structure of dynamic systems. Nonlinear Anal. Theory Methods Appl., 1977, 1(4),397–413. 
https://doi.org/10.1016/S0362-546X(97)90006-7

7. Šiljak, D. D. Reliable control using multiple control systems. Int. J. Control, 1980, 31(2), 303–329. 
https://doi.org/10.1080/ 00207178008961043

8. Jiang J. and Yu, X. Fault-tolerant control systems: a comparative study between active and passive approaches. Annu. Rev. Control, 2012, 36(1), 60–72. 
https://doi.org/10.10 16/j.arcontrol.2012.03.005

9. Lan, J. and Patton, R. J. A new strategy for integration of fault estimation within fault-tolerant control. Automatica, 2016, 69, 48–59. 
https://doi.org/10.1016/j.automatica.2016.02.014

10. Tšukrejev, P., Kruuser, K., and Karjust, K. Production monitoring system development for manufacturing processes of photovoltaic modules. Proc. Estonian Acad. Sci., 2019, 68(4), 401–406. 
https://doi.org/10.3176/proc.2019.4.09

11. Liu, Y., Yang, G.-H., and Li, X.-J. Fault-tolerant control for uncertain linear systems via adaptive and LMI approaches. Int. J. Syst. Sci., 2017, 48(2), 347–356. 
https://doi.org/10.1080/00207721.2016.1181225

12. Lanzon, A., Freddi, A., and Longhi, S. Flight control of a quadrotor vehicle subsequent to a rotor failure. J. Guid. Control  Dyn., 2014, 37(2), 580–591. 
https://doi.org/10.2514/1.59869

13. He, Y. and Liu, T. Time delay integral backstepping based fault tolerant control of quadrotor aircraft. Systems Engineering and Electronics, 2015, 37(10), 2341–2346. 
https://doi.org/10.3969/j.issn.1001506X.2015.10.23

14. Zhou,,C., Yang,,G., Su, J., and Sun, G. The control strategy for dual three-phase PMSM based on normal decoupling transformation under fault condition due to open phases. Transactions of China Electrotechnical Society, 2017, 32(3), 86–96. 

15. Li, X. and Zhu, F. Fault-tolerant control for Markovian jump systems with general uncertain transition rates against simultaneous actuator and sensor faults. Int. J. Robust Nonlinear Control, 2017, 27(18), 4245–4274. 
https://doi.org/10.1002/rnc.3791

16. Tao, H., Liu, Y., and Yang, H. Robust iterative learning fault tolerant control for actuator fault output time-delay double rate sampling system. Journal of Nanjing University of Science and Technology, 2018, 42(4), 430–438. 
https://doi.org/10.14177/j.cnki.32-1397n.2018.42.04.007

17. Mathiyalagan, K., Anbuvithya, R., Sakthivel, R.,Park, J. H., and Prakash, P. Reliable stabilization for memristor-based recurrent neural networks with time-varying delays. Neurocomputing, 2015, 153, 140–147. 
https://doi.org/10.1016/j.neucom.2014.11.043

18. Limin, W., Jisheng, Y., Jingxian, Y.-U., Li, B., and Gao, F. Iterative learning fault-tolerant control for batch processes based on T-S fuzzy model. Journal of Chemical Industry and Engineering, 2017, 68(3), 1081–1089. 
https://doi.org/10.11949/j.issn.0438-1157.20161608

19. Ma, W., Xu, X., and Zhu, H. Networked non-fragile H∞ control for Lipschitz nonlinear system with quantization and packet dropout in both feedback and forward channels. J. Comput. Inf. Technol., 2017, 25(3), 181–190. 
https://doi.org/10.20532/cit.2017.1003404

20. Wang, L., Sun, L., Yu, J., Zhang, R., and Gao, F. Robust iterative learning fault-tolerant control for multiphase batch processes with uncertainties. Ind. Eng. Chem. Res., 2017, 56, 10099–10109. 
https://doi.org/10.1021/acs.iecr.7b00525

21. Tong, S., Huo, B., and Li, Y. Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans. Fuzzy Syst., 2014, 22(1), 1–15. 
https://doi.org/10.1109/TFUZZ.201 3.2241770

22. Mahmoud, M. S. and Khalid, H. M. Model prediction-based approach to fault-tolerant control with applications. IMA J. Math. Control Inf., 2014, 31(2), 217–244. 
https://doi.org/10.1093/imamci/dnt007

23. Kwon, N. K., Park, I. S., and Park, P. G. H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Appl. Math. Comput., 2017, 295, 126–135. 
https://doi.org/10.1016/j.amc.2016.09.004

24. Zhou, Q., Yao, D., Wang J., and Wu, C. Robust control of uncertain semi-Markovian jump systems using sliding mode control method. Appl. Math. Comput., 2016, 286, 72–87. 
https://doi.org/10.1016/j.amc.2016.03.013

25. Zhang, Y., Shi, Y., and Shi, P. Robust and non-fragile finite-time H control for uncertain Markovian jump nonlinear systems. Appl. Math. Comput., 2016, 279, 125138. 
https://doi.org/10.1016/j.amc.2016.01.012

26. Moon, J. and Başar, T. Robust mean field games for coupled Markov jump linear systems. Int. J. Control, 2016, 89(7), 1367–1381. 
https://doi.org/10.1080/00207179.2015.1129560

27. Zhang, D., Jing, Y., Zhang, Q., and Dimirovski, G. M. Stabilization of singular T-S fuzzy Markovian jump systems with mode-dependent derivative-term coefficient via sliding mode control. Appl. Math. Comput., 2020, 364, 1–19. 
https://doi.org/10.1016/j.amc.2019.124643

28. Li, Q., Dimirovski, G. M., Fu, J., and Wang, J. Switching strategy in tracking constant references for linear time-varying-delay systems with actuator failures. Int. J. Control, 2019, 92(8), 1870–1882. 
https://doi.org/10.1080/00207179.2017.1415464

29. Li, L., Zhao, J., and Dimirovski, G. M. Observer-based reliable exponential stabilization and H control for switched systems with faulty actuators: an average dwell time approach. Nonlinear Analysis: Hybrid Systems, 2011, 5(3), 479–491. 
https://doi.org/10.1016/j.nahs.2010.10.006

30. Liu, J. C., Zhang, J. Robust H-infinity control for Markovian jump systems with time-varying time-delay in input and state. Control Theory and Applications, 2010, 27(6), 809–814. 

31. Liu J., Zhang J., Zhou L., and Tu, G. The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications. Appl. Math. Comput., 2018, 320, 251–263. 
https://doi.org/10.1016/j.amc.2017.09.032

32. Jiang, B., Gao, C., and Xie, J. Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations. Appl. Math. Comput., 2015, 271, 187–200. 
https://doi.org/10.1016/j.amc.2015.08.118

33. Li, X.-H., Zhu, F.-L. Simultaneous estimation of actuator and sensor faults for uncertain time-delayed Markovian jump systems. ACTA AUTOMATICA SINICA. 2017, 43(1), 72–82. 
https://doi.org/10.16383/j.aas.2017.c150389


Back to Issue