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Keywords:
Takagi–Sugeno model; descriptor system; fault tolerant control; linear matrix inequality; Lyapunov method; unknown input observer
Summary:
This paper proposes a fault tolerant control scheme for nonlinear systems in descriptor form. The approach is based on the design of an unknown input observer in order to estimate the missing state variables as well as actuator faults, such design is carried out once a proper estimation error system is obtained via a recent factorization method; then, the estimated signals are employed in the control law in order to drive the states asymptotically to the origin despite actuator faults. The designing conditions are given in terms of linear matrix inequalities. Numerical as well as physical systems are used to illustrate the advantages of the proposal.
References:
[1] Aouaouda, S., Bouarar, T., Bouhali, O.: Fault tolerant tracking control using unmeasurable premise variables for vehicle dynamics subject to time varying faults. J. Franklin Inst. 351 (2014), 9, 4514-4537. DOI  | MR 3248448
[2] Bedioui, N., Houimli, R., Besbes, M.: Simultaneous sensor and actuator fault estimation for continuous-time polytopic LPV system. Int. J. Systems Sci. 50 (2019), 6, 1290-1302. DOI  | MR 3952805
[3] Bernal, M., Sala, A., Lendek, Z., Guerra, T. M.: Analysis and synthesis of nonlinear control systems. Springer, 2022.
[4] Bessa, I., Puig, V., Palhares, R. M.: {TS} fuzzy reconfiguration blocks for fault tolerant control of nonlinear systems. J. Franklin Inst. 357 (2020), 8, 4592-4623. DOI  | MR 4096222
[5] Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M., Schröder, J.: Diagnosis and Fault-tolerant Control, volume 2. Springer, 2006. MR 3495879
[6] Boyd, S., Ghaoui, L. E., Feron, E., Belakrishnan, V.: Linear Matrix Inequalities in System and Control Theory, volume 15. SIAM: Studies In Applied Mathematics, Philadelphia 1994. MR 1284712
[7] Chen, L., Edwards, Ch., Alwi, H., Sato, M., Nateghi, S., Shtessel, Y.: Sliding mode observers for robust fault estimation in linear parameter varying systems. Int. J. Robust Nonlinear Control 33 (2023), 15, 9084-9108. DOI  | MR 4645844
[8] Edwards, C., Spurgeon, S. K., Patton, R. J.: Sliding mode observers for fault detection and isolation. Automatica 36 (2000), 4, 541-553. DOI  | MR 1828900
[9] Estrada-Manzo, V., Lendek, Zs, Guerra, T. M.: Unknown input estimation for nonlinear descriptor systems via LMIs and Takagi-Sugeno models. In: 2015 54th IEEE Conference on Decision and Control (CDC), IEEE, 2015, pp. 6349-6354. MR 3310825
[10] Estrada-Manzo, V., Lendek, Z., Guerra, T. M., Pudlo, P.: Controller design for discrete-time descriptor models: a systematic LMI approach. IEEE Trans. Fuzzy Systems 23 (2015), 5, 1608-1621. DOI  | MR 3310825
[11] Farhat, A., Koenig, D.: PI robust fault detection observer for a class of uncertain switched systems using LMIs. In: 9th IFAC Symposium on Fault Detection, Supervision andSafety for Technical, Paris 2015, pp. 125-130.
[12] Ltd, Feedback instruments, Sussex, East, K., U.: Digital Pendulum Control Experiments 33-936S, 2015.
[13] Frank, P. M.: Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results. Automatica 26 (1990), 3, :459-474. DOI 
[14] Gahinet, P., Nemirovski, A., Laub, A. J., Chilali, M.: LMI Control Toolbox. Math Works, Natick 1995.
[15] Gao, Z., Cecati, C., Ding, S. X.: A survey of fault diagnosis and fault-tolerant techniques – part I: Fault diagnosis with model-based and signal-based approaches. IEEE Trans. Industr. Electron. 62 (2015), 6, 3757-3767. DOI 10.1109/TIE.2015.2417501
[16] Guerra, T.-M., Bernal, M., Kruszewski, A., Afroun, M.: A way to improve results for the stabilization of continuous-time fuzzy descriptor models. In: 46th IEEE Conference on Decision and Control, IEEE 2007, pp. 5960-5964. MR 2394401
[17] Guerra, T.-M., Estrada-Manzo, V., Lendek, Zs.: Observer design for Takagi-Sugeno descriptor models: An LMI approach. Automatica 52 (2015), 154-159. DOI  | MR 3310825
[18] Guerra, T. M., Márquez, R., Kruszewski, A., Bernal, M.: $H_\infty$ LMI-based observer design for nonlinear systems via Takagi-Sugeno models with unmeasured premise variables. IEEE Trans. Fuzzy Systems 26 (2018), 3, 1498-1509. DOI 
[19] Guzman, J, López-Estrada, F.-R., Estrada-Manzo, V., Valencia-Palomo, G.: Actuator fault estimation based on a proportional-integral observer with nonquadratic Lyapunov functions. Int. J. Systems Sci. 52 (2021), 9, 1938-1951. DOI  | MR 4280762
[20] Ichalal, D., Mammar, S.: On unknown input observers for LPV systems. IEEE Trans. Indust. Electron. 62 (2015), 9, 5870-5880. DOI 
[21] Ichalal, D., Marx, B., Ragot, J., Maquin, D.: New fault tolerant control strategies for nonlinear Takagi-Sugeno systems. Int. J. Appl. Math. Computer Sci. 22 (2012), 1, 197-210. DOI 10.2478/v10006-012-0015-8 | MR 2953662
[22] Ichalal, D., Marx, B., Ragot, J., Maquin, D.: Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables. In: 17th Mediterranean Conference on Control and Automation 2009, pp. 353-358.
[23] Ichalal, D., Marx, B., Ragot, J., Maquin, D.: Fault detection, isolation and estimation for Takagi-Sugeno nonlinear systems. J. Franklin Inst. 351 (2014), 7, 3651-3676. DOI  | MR 3214936
[24] Isermann, R.: Fault-diagnosis Applications: Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault-Tolerant Systems. Springer Science and Business Media, 2011. MR 3186363
[25] Jiang, B., Zhang, K., Shi, P.: Integrated fault estimation and accommodation design for discrete-time {Takagi-Sugeno} fuzzy systems with actuator faults. IEEE Trans. Fuzzy Syst. 19 (2010), 2, 291-304. DOI 
[26] Jiang, G. P., Wang, S. P., Song, W. Z.: Design of observer with integrators for linear systems with unknown input disturbances. Electronics Lett. 36 (2000), 13, 1168-1169. DOI  | MR 1675763
[27] Khalil, H. K., Praly, L.: High-gain observers in nonlinear feedback control. Int. J. Robust Nonlinear Control 24 (2014), 6, 993-1015. DOI  | MR 3181173
[28] Koenig, D.: Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation. IEEE Trans. Automat. control 50 (2005), 2, 212-217. DOI  | MR 2116426
[29] Lendek, Z., Guerra, T. M., Babuška, R.: On non-PDC local observers for TS fuzzy systems. In: IEEE International Conference on Fuzzy Systems (FUZZ), 2010, pp. 1-7.
[30] Lendek, Z., Guerra, T. M, Babuška, R., De-Schutter, B.: Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models. Springer-Verlag, Netherlands 2010.
[31] Li, X., Zhu, F., Chakrabarty, A., Zak, S. H.: Nonfragile fault-tolerant fuzzy observer-based controller design for nonlinear systems. IEEE Trans. Fuzzy Systems 24 (2016), 6, 1679-1689. DOI 
[32] Li, Y., Sun, K., Tong, S.: Observer-based adaptive fuzzy fault-tolerant optimal control for SISO nonlinear systems. IEEE Trans. Cybernet. 49 (2018), 2, 649-661. DOI 
[33] Liu, Z., Liu, J., He, W.: Robust adaptive fault tolerant control for a linear cascaded ode-beam system. Automatica 98 (2018), 42-50. DOI  | MR 3866918
[34] López-Estrada, F. R., Astorga-Zaragoza, C. M., Theilliol, D., Ponsart, J. Ch., Valencia-Palomo, G., Torres, L.: Observer synthesis for a class of Takagi-Sugeno descriptor system with unmeasurable premise variable. application to fault diagnosis. Int. J. Systems Sci. 48 (2017), 16, 3419-3430. DOI  | MR 3732973
[35] López-Estrada, F. R., Santos-Estudillo, O., Valencia-Palomo, G., Gómez-Peñate, S., Hernandez-Gutiérrez, C.: Robust qLPV tracking fault-tolerant control of a 3 DOF mechanical crane. Math. Comput. Appl. 25 (2020), 3, 48. MR 4179272
[36] Marx, B., Ichalal, D., Ragot, J., Maquin, D., Mammar, S.: Unknown input observer for LPV systems. Automatica 100 (2019), 67-74. DOI  | MR 3880693
[37] Marx, B., Koenig, D., Ragot, J.: Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis. IET Control Theory Appl. 1 (2007), 5, 1487-1495. DOI  | MR 2350837
[38] Oh, S., Khalil, H. K.: Nonlinear output-feedback tracking using high-gain observer and variable structure control. Automatica 33 (1997), 10, 1845-1856. DOI  | MR 1481844
[39] Ohtake, H., Tanaka, K., Wang, H. O.: Fuzzy modeling via sector nonlinearity concept. In: Proc. Joint 9th IFSA World Congress and 20th NAFIPS International Conference 1 (2001), pp. 127-132.
[40] Orjuela, R., Ichalal, D., Marx, B., Maquin, D., Ragot, J.: Polytopic models for observer and fault-tolerant control designs. In: New Trends in Observer-Based Control, Elsevier 2019, pp. 295-335.
[41] Orjuela, R., Marx, B., Ragot, J., Maquin, D.: On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy. IET Control Theory Appl. 3 (2009), 7, 877-890. DOI  | MR 2537968
[42] Pertew, A. M., Marquez, H. J., Zhao, Q.: LMI-based sensor fault diagnosis for nonlinear Lipschitz systems. Automatica 43 (2007), 8, 1464-1469. DOI  | MR 2320532
[43] Quintana, D., Estrada-Manzo, V., Bernal, M.: An exact handling of the gradient for overcoming persistent problems in nonlinear observer design via convex optimization techniques. Fuzzy Sets Systems 416 (2021), :125-140. DOI  | MR 4258759
[44] Quintana, D., Estrada-Manzo, V., Bernal, M.: Fault detection and isolation via a novel convex optimization scheme. IEEE Latin America Trans. 17 (2019), 07, 1096-1101. DOI 
[45] Rodrigues, M., Hamdi, H., Braiek, N. B., Theilliol, D.: Observer-based fault tolerant control design for a class of LPV descriptor systems. J. Franklin Inst. 351 (2014), 6, 3104-3125. DOI  | MR 3201022
[46] Rotondo, D., Witczak, M., Puig, V., Nejjari, F., Pazera, M.: Robust unknown input observer for state and fault estimation in discrete-time Takagi-Sugeno systems. Int. J. Systems Sci. 47 (2016), 14, 3409-3424. DOI  | MR 3486707
[47] Sami, M., Patton, R. J.: Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults. Int. J. Control Automat. Systems 11 (2013), 6, 1149-1161. DOI 
[48] Scherer, C.: Linear Matrix Inequalities in Control Theory. Delf University, Delf 2004.
[49] Tan, Ch. P., Edwards, Ch.: Sliding mode observers for detection and reconstruction of sensor faults. Automatica 38 (2002), 10, 1815-1821. DOI  | MR 2134023
[50] Tanaka, H., Sugie, T.: General framework and BMI formulae for simultaneous design of structure and control systems. In: Proc. 36th Conference on Decision and Control (CDC), San Diego 1997, pp. 773-778.
[51] Tanaka, K., Wang, H. O.: Fuzzy Control Systems Design and Analysis: A linear matrix inequality approach. John Wiley and Sons, New York 2001.
[52] Tuan, H. D., Apkarian, P., Narikiyo, T., Yamamoto, Y.: Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Trans. Fuzzy Systems 9 (2001), 2, 324-332. DOI 
[53] Wang, J. L., Yang, G. H., Liu, J.: An LMI approach to $H_{}$ index and mixed $H_{}$/$H_{\infty}$ fault detection observer design. Automatica 43 (2007), 9, 1656-1665. DOI 10.1016/j.automatica.2007.02.019 | MR 2327079
[54] Wen, S., Chen, M. Z. Q., Zeng, Z., Huang, T., Li, Ch.: Adaptive neural-fuzzy sliding-mode fault-tolerant control for uncertain nonlinear systems. IEEE Trans. Systems Man Cybernet.: Systems 47 (2017), 8, 2268-2278. DOI 
[55] Xie, X., Yue, D., Ma, T, Zhu, X.: Further studies on control synthesis of discrete-time TS fuzzy systems via augmented multi-indexed matrix approach. IEEE Trans. Cybernet. 44 (2014), 12, 2784-2791. DOI 
[56] Xiong, Y., Saif, M.: Unknown disturbance inputs estimation based on a state functional observer design. Automatica 39 (2003), 8, 1389-1398. DOI  | MR 2141683
[57] Zemouche, A., Boutayeb, M.: On LMI conditions to design observers for Lipschitz nonlinear systems. Automatica 49 (2013), 2, 585-591. DOI  | MR 3004728
[58] Zemouche, A., Zhang, F., Mazenc, F., Rajamani, R.: High-gain nonlinear observer with lower tuning parameter. IEEE Trans. Automat. Control 64 (2018), 8, 3194-3209. DOI  | MR 3992861
[59] Zhang, X., Polycarpou, M. M., Parisini, T.: A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems. IEEE Trans. Automat. Control 47 (2002), 4, 576-593. DOI  | MR 1893516
[60] Y.Zhang, Jiang, J.: Bibliographical review on reconfigurable fault-tolerant control systems. Ann. Rev. Control 32 (2008), 2, 229-252. DOI 
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