Non-fragile observers design for nonlinear systems with unknown Lipschitz constant

Zhou, Fan ; Shen, Yanjun ; Wu, Zebin

Kybernetika, Tome 60 (2024) no. 4, pp. 475-491

Abstract (VO)

In this paper, the problem of globally asymptotically stable non-fragile observer design is investigated for nonlinear systems with unknown Lipschitz constant. Firstly, a definition of globally asymptotically stable non-fragile observer is given for nonlinear systems. Then, an observer function of output is derived by an output filter, and a dynamic high-gain is constructed to deal with unknown Lipschitz constant. Even the observer gains contain diverse large disturbances, the observer errors are proven to converge to the origin based on Lyapunov stability theorem and a matrix inequality. Finally, an experimental simulation is provided to confirm the validity of the proposed method.

Détail

DOI : 10.14736/kyb-2024-4-0475

Classification : 93C10
Keywords: non-fragile; observer; high gain; unknown Lipschitz constant; output filter

Bibliographie

[1] Al-Saggaf, U., Bettayeb, M., Djennoune, S.: Fixed-time synchronization of memristor chaotic systems via a new extended high-gain observer. European J. Control 63 (2022), 1, 164-174. | DOI | MR

[2] Andreu, C., Ramon, C.: Addressing the relative degree restriction in nonlinear adaptive observers: A high-gain observer approach. J. Franklin Inst. 359 (2022), 8, 3857-3882. | DOI | MR

[3] Astolfi, D., Zaccarian, L., Jungers, M.: On the use of low-pass filters in high-gain observers. Systems Control Lett. 148 (2021), 104856. | DOI | MR

[4] Chen, M., Chen, C.: Robust nonlinear observer for Lipschitz nonlinear systems subject to disturbances. IEEE Trans. Automat. Control 52 (2007), 12, 2365-2369. | DOI | MR

[5] Chen, H., Li, Y.: Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities. Proc. Amer. Math. Soc. 135 (2007), 12, 1-7. | DOI | MR

[6] Chen, C., Qian, C., Sun, Z., Liang, Y.: Global output feedback stabilization of a class of nonlinear systems with unknown measurement sensitivity. IEEE Trans. Automat. Control 63 (2018), 7, 2212-2217. | DOI | MR

[7] Chen, W., Sun, H., Lu, X.: A variable gain impulsive observer for Lipschitz nonlinear systems with measurement noises. J. Franklin inst. 350 (2022), 18, 11186-11207. | DOI | MR

[8] Chowdhury, D., Al-Nadawi, Y. K., Tan, X.: Dynamic inversion-based hysteresis compensation using extended high-gain observer. Automatica 135 (2022), 109977. | DOI | MR

[9] Duan, G.: High-order system approaches: III. observability and observer design. ACTA Automat. Sinica 46 (2020), 9, 1885-1895.

[10] Dutta, L., Das, D.: Nonlinear disturbance observer based multiple‐model adaptive explicit model predictive control for nonlinear MIMO system. Int. J. Robust Nonlinear Control 33 (2023), 11, 5934-5955. | DOI | MR

[11] Guo, X., Yang, G.: Non-fragile H$\infty$ filter design for delta operator formulated systems with circular region pole constraints: an LMI optimization approach. ACTA Automatica Sinica 35 (2009), 9, 1209-1215. | DOI | MR

[12] Hua, C., Guan, X.: Synchronization of chaotic systems based on PI observer design. Physics Lett. A 334 (2005), 5-6, 382-389. | DOI

[13] Huang, J., Han, Z.: Adaptive non-fragile observer design for the uncertain Lur'e differential inclusion system. Appl. Math. Modell. 37 (2013), 1-2, 72-81. | DOI | MR

[14] Jeong, C. S., Yaz, E. E., Yaz, Y. I.: Resilient design of discrete-time observers with general criteria using LMIs. Math. Computer Modell. 42 (2005), 9-10, 931-938. | DOI | MR

[15] Zhang, H. Jian. H., Wang, Y., Liu, X.: Adaptive state disturbance observer design for nonlinear system with unknown lipschitz constant. Chinese Automation Congress 2015, pp. 880-885.

[16] Koo, M., Choi, H.: State feedback regulation of high-order feedforward nonlinear systems with delays in the state and input under measurement sensitivity. Int. J. Systems Sci. 52 (2021), 10, 2034-2047. | DOI | MR

[17] Lakshmanan, S., Joo, Y.: Decentralized observer-based integral sliding mode control design of large-scale interconnected systems and its application to doubly fed induction generator-based wind farm model. Int. J. Robust Nonlinear Control 33 (2023), 10, 5758-5774. | DOI | MR

[18] Li, G., Xu, D., Zhou, abd S.: A parameter-modulated method for chaotic digital communication based on state observers. ATAC Physica Sinica 53 (2004), 3, 706-709. DOI  | MR

[19] Li, W., Yao, X., Krstic, M.: Adaptive-gain observer-based stabilization of stochastic strict-feedback systems with sensor uncertainty. Automatica 120 (2020), 109112. | DOI | MR

[20] Lin, Z.: Co-design of linear low-and-high gain feedback and high gain observer for suppression of effects of peaking on semi-global stabilization. Automatica 137 (2022), 110124. | DOI | MR

[21] Lin, L., Shen, Y.: Adaptive anti-measurement-disturbance stabilization for a class of nonlinear systems via output feedback. J. Control Theory Appl. 2021. | DOI

[22] Liu, Y., Fei, S.: Chaos synchronization between the Sprott-B and Sprott-C with linear coupling. ATAC Physica Sinica 53 (2006), 3, 1035-1039.

[23] Liu, C., Liao, K., Qian, K., Li, Y., Ding, Q.: The robust sliding mode observer design for nonlinear system with measurement noise and multiple faults. Systems Engrg. Electron. (2022).

[24] Marino, R., Tomei, P.: Nonlinear Control Design: Geometric, Adaptive and Robust. Prentice Hall, Hertfordshire 1995. | Zbl

[25] Perruquetti, W., Floquet, T., Moulay, E.: Finite-time observers: application to secure communication. IEEE Trans. Automat. Control 53 (2008), 1, 356-360. | DOI | MR

[26] Shen, Y., Xia, X.: Semi-global finite-time observers for nonlinear systems. Automatica 44 (2008), 12, 3152-3156. | DOI | MR | Zbl

[27] Thau, F. E.: Observing the state of nonlinear dynamic systems. Int. J. Control 17 (1973), 3, 471-479. | DOI

[28] Xiang, Z., Wang, R., Jiang, B.: Nonfragile observer for discrete-time switched nonlinear systems with time delay. Circuits Systems Signal Process. 30 (2011), 1, 73-87. | DOI | MR

[29] Yang, G., Wang, J.: Robust nonfragile kalman filtering for uncertain linear systems with estimator gain uncertainty. IEEE Trans. Automat. Control 46 (2001), 2, 343-348. | DOI | MR

[30] Zheng, Q., Xu, S., Zhang, Z.: Nonfragile H-infinity observer design for uncertain nonlinear switched systems with quantization. Appl. Math. Comput. 386 (2020), 125435. | DOI | MR