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Saeed Jalali S M, Akbarzadeh Kalat A. Robust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance. JoC. 2021; 15 (1) :51-66
URL: http://joc.kntu.ac.ir/article-1-699-en.html
1- Shahrood University of Technology
Abstract:   (2376 Views)
This paper presents a robust ∞_H controller design, based on a generalized dynamic observer for uncertain singular systems in the presence of disturbance. The controller guarantees that the closed loop system be admissible. The main advantage of this method is that the uncertainty can be found in the system, the input and the output matrices. Also the generalized dynamic observer is used to estimate the states of system. This type of observer increases the steady state accuracy because of the integral term, and because of the dynamic term, it has a higher estimation speed than proportional-integral observers. First, the necessary conditions for existence a generalized dynamic robust observer are presented and some coefficients matrices of the observer are computed so that the estimation error asymptotically converges to zero. Then, the robust ∞_H controller is designed using state feedback in order to guarantee that the closed loop system is admissible. The existence conditions of the observer and the controller are given simultaneously using suitable Lyapunov function. Moreover, existing inequalities are transformed into linear matrix inequalities (LMI) using a set of algebraic relations, and by solving these LMIs, the coefficients of the observer and the controller are obtained. Finally, by presenting an algorithm, the computational method will be expressed in a systematic way, and a numerical example demonstrates the efficacy of the proposed method. 
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Type of Article: Research paper | Subject: Special
Received: 2019/08/4 | Accepted: 2020/06/5 | ePublished ahead of print: 2020/06/27 | Published: 2021/05/22

References
1. [1] G. R. Duan, Analysis and design of descriptor linear systems, Springer Science & Business Media, 2010. [DOI:10.1007/978-1-4419-6397-0_5]
2. [2[ M. Darouach and L. Boutat-Baddas, "Observers for a class of nonlinear singular systems," IEEE Transactions on Automatic Control, vol. 53, no. 11, pp. 2627-2633, 2008. [DOI:10.1109/TAC.2008.2007868]
3. [3[ I. Zamani, M. Shafiee and A. Ibeas, "Exponential stability of hybrid switched nonlinear singular systems with time-varying delay," Journal of the Franklin Institute, vol. 350, no. 1, pp. 171-193, 2013. [DOI:10.1016/j.jfranklin.2012.10.002]
4. [4] M. Darouach and M. Zasadzinski, "Data reconciliation in generalized linear dynamic systems," AICHE journal, vol. 37, no. 2, pp. 193-201, 1991. [DOI:10.1002/aic.690370205]
5. [5] J. Huang, W. Zhang, M. Shi, L. Chen and L. Yu, " H∞ observer design for singular one-sided Lur'e differential inclusion system," Journal of the Franklin Institute, vol. 354, no. 8, pp. 3305-3321, 2017 [DOI:10.1016/j.jfranklin.2017.02.030]
6. [6] F. L. Lewis, "A survey of linear singular systems," Circuits, Systems, and Signal Processing, vol. 5, no. 1, pp. 3-36, 1986. [DOI:10.1007/BF01600184]
7. [7] J. Dai, "Singular control systems," in Singular control systems, 1989, pp. 3-36. [DOI:10.1007/BFb0002475]
8. [8] C. Farhat and M. Geradin, "On the general solution by a direct method of a large‐scale singular system of linear equations: application to the analysis of floating structures," International Journal for Numerical Methods in Engineering, vol. 41, no. 4, pp. 675-696, 1998. https://doi.org/10.1002/(SICI)1097-0207(19980228)41:4<675::AID-NME305>3.0.CO;2-8 [DOI:10.1002/(SICI)1097-0207(19980228)41:43.0.CO;2-8]
9. [9] R. Shahnazi and Q. Zhao, "Adaptive fuzzy descriptor sliding mode observer‐based sensor fault estimation for uncertain nonlinear systems," Asian Journal of Control, vol. 18, no. 4, pp. 1478-1488, 2016. [DOI:10.1002/asjc.1249]
10. [10] J. M. Araújo, P. R. Barros and C. E. Dorea, "Design of observers with error limitation in discrete-time descriptor systems: A case study of a hydraulic tank system," IEEE Transactions on Control Systems Technology, vol. 20, no. 4, pp. 1041-1047, 2012. [DOI:10.1109/TCST.2011.2159719]
11. [11] D. G. Luenberger, "Observing state of linear system," IEEE Trans. Military Electron, Vols. MIL-8, no. 2, pp. 74-77, 1964. [DOI:10.1109/TME.1964.4323124]
12. [12] M. Darouach and M. Boutayed, "Design of observers for descriptor systems," IEEE transactions on Automatic Control, vol. 40, no. 7, pp. 1323-1327, 1995. [DOI:10.1109/9.400467]
13. [13] M. Hou and P. C. Muller, "Observer design for descriptor systems.," IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 164-169., 1999. [DOI:10.1109/9.739112]
14. [14] M. Darouach, "Observers and observer-based control for descriptor systems revisited," IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1367-1373, 2014. [DOI:10.1109/TAC.2013.2292720]
15. [15] M. Cao and F. Liao, "Design of a PD feedback controller for continuous-time descriptor systems," in Control and Decision Conference, 2014. [DOI:10.1109/CCDC.2014.6852248]
16. [16] Y. Han, Y. Kao and C. Gao, "Robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays via sliding mode approach," ISA Transactions, vol. 80, pp. 81-88, 2018. [DOI:10.1016/j.isatra.2018.05.023]
17. [17] M. Wang and T. Liang, "Adaptive Kalman filtering for sensor fault estimation and isolation of satellite attitude control based on descriptor systems," Transactions of the Institute of Measurement and Control, 2019. [DOI:10.1177/0142331218787605]
18. [18] M. Darouach, "H∞ unbiased filtering for linear descriptor systems via LMI," IEEE Transactions on Automatic Control, vol. 54, no. 8, pp. 1966-1972, 2009. [DOI:10.1109/TAC.2009.2023962]
19. [19] P. C. Muller and M. Hou, "On the observer design for descriptor systems," in Decision and Control, 1991., Proceedings of the 30th IEEE Conference on (pp. 1960-1961). IEEE., 1991.
20. [20] A. G. Wu and G. R. Duan, "Design of generalized PI observers for descriptor linear systems," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 12, pp. 2828-2837, 2006. [DOI:10.1109/TCSI.2006.885695]
21. [21] A. G. Wu and G. R. Duan, "Generalized PI observer design for linear systems," IMA Journal of Mathematical Control and Information, pp. 239-250, 2007. [DOI:10.1093/imamci/dnm021]
22. [22] D. Koenig, "Unknown input proportional multiple-integral observer design for linear descriptor systems," IEEE Transactions on Automatic control, pp. 212-217, 2005. [DOI:10.1109/TAC.2004.841889]
23. [23] G. C. Goodwin and R. H. Middleton, "The class of all stable unbiased state estimators," Systems & Control Letters, pp. 161-163, 1989. [DOI:10.1016/0167-6911(89)90033-9]
24. [24] H. J. Marquez, "A frequency domain approach to state estimation," Journal of the Franklin Institute, pp. 147-157, 2003. [DOI:10.1016/S0016-0032(03)00017-6]
25. [25] G. L. Osorio-Gordillo, M. Darouach, C. M. Astorga-Zaragoza and L. Boutat-Baddas, "New dynamical observers design for linear descriptor systems," IET Control Theory & Applications, vol. 10, no. 17, pp. 2223-2232, 2016. [DOI:10.1049/iet-cta.2016.0431]
26. [26] G. L. Osorio-Gordillo, M. Darouach, L. Boutat-Baddas and C. M. Astorga-Zaragoza, "On Dynamic Observers Design for Descriptor Systems," in New Trends in Observer-Based Control, 2019, pp. 3-45. [DOI:10.1016/B978-0-12-817038-0.00001-9]
27. [27] L. Boutat-Baddas, G. L. Osorio-Gordillo and M. Darouach, "H∞ dynamic observers for a class of nonlinear systems with unknown inputs," International Journal of Control, pp. 1-12, 2019. [DOI:10.1080/00207179.2019.1600031]
28. [28] G. L. Osorio-Gordillo, M. Darouach, L. Boutat-Baddas and C. M. Astorga-Zaragoza, "dynamical observer-based control for descriptor systems," IMA Journal of Mathematical Control and Information, vol. 35, no. 3, pp. 707-734, 2017. [DOI:10.1093/imamci/dnw072]
29. [29] S. P. Bhattacharyya, "Robust control under parametric uncertainty: An overview and recent results," Annual Reviews in Control, vol. 44, pp. 45-77, 2017. [DOI:10.1016/j.arcontrol.2017.05.001]
30. [30] M. S. Asadinia, T. Binazadeh and B. Safarinejadian, "A delay-range-dependent stabilization of uncertain singular time-delay systems with one-sided Lipschitz nonlinearities subject to input saturation," Journal of Vibration and Control, vol. 25, no. 4, pp. 868-881, 2019. [DOI:10.1177/1077546318802466]
31. [31] E. Arefinia, H. A. Talebi and A. Doustmohammadi, "A robust adaptive observer for a class of singular nonlinear uncertain systems," International Journal of Systems Science, vol. 48, no. 7, pp. 1404-1415, 2017. [DOI:10.1080/00207721.2016.1261198]
32. [32] Y. Ma, P. Yang, Y. Yan and Q. Zhang, " Robust observer-based passive control for uncertain singular time-delay systems subject to actuator saturation," ISA transactions, vol. 67, pp. 9-18, 2017. [DOI:10.1016/j.isatra.2016.12.004]
33. [33] E. K. Boukas and Z. K. Liu, "Robust H∞ filtering for polytopic uncertain time-delay systems with Markov jumps," Computers & Electrical Engineering, vol. 28, no. 3, pp. 171-193, 2002. [DOI:10.1016/S0045-7906(01)00058-1]
34. [34] M. S. Pasand, M. A. Sh and H. D. Taghirad, "Unknown input-proportional integral observer for singular systems: Application to fault detection," in Electrical Engineering (ICEE), 2010 18th Iranian Conference, 2010. [DOI:10.1109/ICCAS.2010.5670321]
35. [35] G. L. Osorio-Gordillo, M. Darouach and C. M. Astorga-Zaragoza, "H∞ dynamical observer design for linear descriptor systems," in American Control Conference (ACC), 2014. [DOI:10.1109/ACC.2014.6859212]
36. [36] M. Alma and M. Darouach, "Adaptive observers design for a class of linear descriptor systems," Automatica, vol. 50, no. 2, pp. 578-583, 2014. [DOI:10.1016/j.automatica.2013.11.036]
37. [37] N. F. Shamloo, A. A. Kalat and L. Chisci, "Indirect adaptive fuzzy control of nonlinear descriptor systems," European Journal of Control, 2019. [DOI:10.1007/s40815-019-00702-1]
38. [38] Y. Feng and M. Yagoubi, Robust Control of Linear Descriptor Systems, Springer, 2017. [DOI:10.1007/978-981-10-3677-4]
39. [39] Y. Uetake, "Adaptive observer for continuous descriptor systems," IEEE Transactions on automatic Control, vol. 39, no. 10, pp. 2095-2100, 1994. [DOI:10.1109/9.328803]
40. [40] M. Hou and P. C. Muller, "Design of observers for linear systems with unknown inputs," IEEE Transactions on automatic control, vol. 37, no. 6, pp. 871-875, 1992. [DOI:10.1109/9.256351]
41. [41] M. Darouach, M. Zasadzinski and M. Hayar, "Reduced-order observer design for descriptor systems with unknown inputs," IEEE transactions on automatic control, vol. 41, no. 7, pp. 1068-1072, 1996. [DOI:10.1109/9.508918]
42. [42] M. Darouach, M. Zasadzinski, A. B. Onana and S. Nowakowski, "Kalman filtering with unknown inputs via optimal state estimation of singular systems," International journal of systems science, vol. 26, no. 10, pp. 2015-2028, 1995. [DOI:10.1080/00207729508929152]
43. [43] X. Mao, N. Koroleva and A. Rodkina, "Robust stability of uncertain stochastic differential delay equations1," Systems & Control Letters, vol. 35, no. 5, pp. 325-336, 1998. [DOI:10.1016/S0167-6911(98)00080-2]
44. [44] E. L. Boukas, Control of singular systems with random abrupt changes, Springer Science & Business Media, 2008.
45. [45] M. K. Gupta, N. K. Tomar and S. Bhaumik, "On detectability and observer design for rectangular linear descriptor systems," International Journal of Dynamics and Control, vol. 4, no. 4, pp. 438-446, 2016. [DOI:10.1007/s40435-014-0146-x]
46. [46] H. Kimura, Chain-scattering approach to H∞ control, Springer Science & Business Media, 1996. [DOI:10.1007/978-1-4612-4080-8]
47. [47] M. Yuechao and Y. Yifang, "Observer-based H∞ guaranteed cost control for uncertain singular time-delay systems with input saturation," International Journal of Control, Automation and Systems, vol. 14, no. 5, pp. 1254-1261, 2016. [DOI:10.1007/s12555-014-0541-2]
48. [48] M. Yuechao and Y. Yifang , "Observer‐based H∞ control for uncertain singular time‐delay systems with actuator saturation," Optimal Control Applications and Methods, vol. 37, no. 5, pp. 867-884, 2016. [DOI:10.1002/oca.2197]
49. [49] B. Zheng and R. B. Bapat, "Generalized inverse A (2) T, S and a rank equation," Applied mathematics and computation, vol. 155, no. 2, pp. 407-415, 2004. [DOI:10.1016/S0096-3003(03)00786-0]
50. [50] D. C. Lay, Linear algebra and its applications, Greg Tobin, 2006.
51. [51] R. E. Skelton, T. Lwasaki and D. E. Griqoriadis, A unified algebraic approach to control design, CRC Press, 1997.
52. [52] J. Lan and R. J. Patton, "A new strategy for integration of fault estimation within fault-tolerant control," Automatica, vol. 69, pp. 48-59, 2016. [DOI:10.1016/j.automatica.2016.02.014]
53. [53] S. Xu and J. Lam, Robust control and filtering of singular systems, Vol. 332, Berlin: Springer, 2006.
54. [54] W. Xie, "An equivalent LMI representation of bounded real lemma for continuous-time systems," Journal of Inequalities and Applications, vol. 1, p. 672905, 2008. [DOI:10.1155/2008/672905]
55. [55] H. S. Wang, C. F. Yung and F. R. Chang, "Bounded real lemma and H∞ control for descriptor systems," IEE Proceedings-Control Theory and Applications, vol. 145, no. 3, pp. 316-322, 1998. [DOI:10.1049/ip-cta:19982048]
56. [56] S. Boed, L. EL Ghaoui, E. Feron and V. Balakrishnan, Linear matrix inequalities in system and control theory, vol. 15, Siam, 1994. [DOI:10.1137/1.9781611970777]
57. [57] M. Gerdin, Paramete estimation in linear descriptor systems, Linkoping University, Sweden, 2004.
58. [58] J. Löfberg, "YALMIP: A toolbox for modeling and optimization in MATLAB," in Proceedings of the CACSD Conference, 2004.

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