Browse > Article
http://dx.doi.org/10.12989/ose.2022.12.2.159

Adaptive backstepping control with grey theory for offshore platforms  

Hung, C.C. (Department of Mechanical Engineering, National Taiwan University)
Nguyen, T. (Ha Tinh University, Dai Nai Campus)
Publication Information
Ocean Systems Engineering / v.12, no.2, 2022 , pp. 159-172 More about this Journal
Abstract
To ensure stable performance, adaptive regulators with new theories are designed for steel-covered offshore platforms to withstand anomalous wave loads. This model shows how to control the vibration of the ocean panel as a solution using new results from Lyapunov's stability criteria, an evolutionary bat algorithm that simplifies computational complexity and utilities. Used to reduce the storage space required for the method. The results show that the proposed operator can effectively compensate for random delays. The results show that the proposed controller can effectively compensate for delays and random anomalies. The improved prediction method means that the vibration of the offshore structure can be significantly reduced. While maintaining the required controllability within the ideal narrow range.
Keywords
evolved control systems; offshore platforms; predictive control; time delays;
Citations & Related Records
Times Cited By KSCI : 18  (Citation Analysis)
연도 인용수 순위
1 Tsai P.W. (2014), "A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method", Appl. Soft Comput., 25, 461-472. https://doi.org/10.1016/j.asoc.2014.08.045.   DOI
2 Zhang, H., Wu, F., Huang, X. and Ban, X. (2017), "Experiments on mixing and dissipation in internal solitary waves over two triangular obstacles", Environ. Fluid Mech., 8(2008), 199-214. https://doi.org/10.1007/s10652-008-9055-x.   DOI
3 Zhang, H., Wu, F., Ban, X. and Huang, X. (2017), "Localized mixing due to an interfacial solitary wave breaking on seabed topography in different ridge heights", J. Offshore Mech. Arct. Eng. T. ASME, 129 (2007), 245-250. https://doi.org/10.1115/1.2426991.   DOI
4 Terroa, M.J., Mahmoudb, M.S. and Abdel-Rohmanc M. (1999), "Multi-loop feedback control of offshore steel jacket platforms", Comput. Struct., 70(2), 185-202. https://doi.org/10.1016/S0045-7949(98)00152-7.   DOI
5 Liu, K.F., Chen, C. and Cheng, M. (2009), "Modeling and control for nonlinear structural systems via a NN-based approach", Exp. Syst. Appl., 36, 4765-4772. https://doi.org/10.1016/j.eswa.2008.06.062.   DOI
6 Chiang, W., Yeh, K., Chen, C. and Chen, C. (2007), "Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method", Appl. Math. Comput., 205, 568-577. https://doi.org/10.1016/j.amc.2008.05.104.   DOI
7 Meng, Y.Z., Wang, R., Fu, Q. and Chen, T. (2022), "Composite components damage tracking and dynamic structural behaviour with AI algorithm", Steel Compos. Struct., 42(2) 151-159. https://doi.org/10.12989/scs.2022.42.2.151.   DOI
8 Lin, M.L. and Chen, C.W. (2010), "Application of fuzzy models for the monitoring of ecologically sensitive ecosystems in a dynamic semiarid landscape from satellite imagery", Eng. Comput., 27, 5-19.   DOI
9 Lin, J., Shen, C., Chen, C. and Cheng, M. (2010), "Stability analysis of an oceanic structure using the Lyapunov method", Eng. Comput., 27, 186-204. https://doi.org/10.1108/02644401011022364.   DOI
10 Lin, M., Chen, C., Wang, Q., Cao, Y., Shih, J., Lee, Y., Chen, C. and Wang, S. (2009), "Fuzzy model-based assessment and monitoring of desertification using MODIS satellite imagery", Eng. Comput., 26, 745-760.   DOI
11 Liu, K.F., Chen, C., Shen, C., Chen, C. and Cheng, M. (2009), "A stability criterion for time-delay tension leg platform systems subjected to external force", China Ocean Eng., 23, 49-57.
12 Meng, Y.Z., Wang, R., Fu, Q. and Chen, T. (2022), "Dynamic intelligent control of composite buildings by using M-TMD and evolutionary algorithm", Steel Compos. Struct., 42(5), 591-598. https://doi.org/10.12989/scs.2022.42.5.591.   DOI
13 Liu, K.F., Yeh, K. and Chen, C. (2009), "Adaptive fuzzy sliding mode control for seismically excited bridges with lead rubber bearing isolation", Int. J. Uncertain. Fuzziness Knowl. Based Syst., 17, 705-727. https://doi.org/10.1142/S0218488509006224.   DOI
14 Liu, K.F., Yeh, K. and Chen, C. (2009), "The stability of an oceanic structure with T-S fuzzy models", Math. Comput. Simul., 80, 402-426. https://doi.org/10.1016/j.matcom.2009.08.001.   DOI
15 Meng, Y.Z., Wang, R., Fu, Q. and Chen, T. (2022), "NN model-based evolved control by DGM model for practical nonlinear systems", Exp. Syst. Appl., https://doi.org/10.1016/j.eswa.2021.115873.   DOI
16 Reyes, C., Hilaire, T., Paul, S. and Mecklenbrauker, C.F. (2010), "Evaluation of the root mean square error performance of the PAST-consensus algorithm", Proceedings of the 2010 International ITG Workshop on Smart Antennas (WSA), https://doi.org/10.1109/WSA.2010.5456452.   DOI
17 Hsiao, F., Chen, C. and Tsai, K. (2005), "Stability conditions of fuzzy systems and its application to structural and mechanical systems", Adv. Eng. Softw., 37(2006), 624-629. https://doi.org/10.1016/j.advengsoft.2005.12.002.   DOI
18 Zhang, H., Wu, F., Ban, X. and Huang, X. (2017), "Diagnosing and revising logistic regression models", Eng. Comput., 25(2008), 121-139. https://doi.org/10.1108/02644400810855940.   DOI
19 Tim, C. and Chen, C. (2020), "Intelligent fuzzy algorithm for nonlinear discrete-time systems", T. Inst. Measurement Control, 42(7), 1358-1374. https://doi.org/10.1177/0142331219891383.   DOI
20 Hasan, S.D., Islam, N. and Moin, K. (2010), "A review of fixed offshore platforms under earthquake forces", Struct. Eng. Mech., 35(4), 479-491. https://doi.org/10.12989/sem.2010.35.4.479.   DOI
21 Hsiao, F., Chen, C., Liang, Y., Xu, S. and Chiang, W. (2005), "T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays", IEEE T. Circuits Syst. I Regul. Pap., 52-I, 1883-1893. https://doi.org/10.1109/TCSI.2005.852492.   DOI
22 Hsiao, F., Chen, C., Wu, Y. and Chiang, W. (2005), "Fuzzy controllers for nonlinear interconnected tmd systems with external force", J. Chinese Inst. Engineers, 28(1), 175-181.   DOI
23 Wu, C. (2010), "Modeling and fuzzy PDC control and its application to an oscillatory TLP structure", Math. Probl. Eng., An Open Access J., https://doi.org/10.1155/2010/120403.   DOI
24 Yuan, C.C. and Hsu, J.R. (2009), "A stability criterion for time-delay tension leg platform systems subjected to external force", China Ocean Eng., 23, 49-57.
25 Chen, C.Y.J., Kuo, D., Hsieh, C. and Chen, T. (2020), "System simulation and synchronization for optimal evolutionary design of nonlinear controlled systems", Smart Struct. Syst., 26(6), 797-807. https://doi.org/10.12989/sss.2020.26.6.797.   DOI
26 Wu, C., Weiling, C., Ken, Y., Zhenyuan, C. and Liteh, L. (2002), "A stability criterion of time-delay fuzzy systems", J. Mar. Sci. Technol., 10, 33-35.
27 Yuan C.C., Cheng, M.H. andHsu, J.R. (2011), "Laboratory experiments on waveform inversion of an internal solitary wave over a slope-shelf", Environ. Fluid Mech., 11, 353-384.   DOI
28 Yuan C.C., Hsu, J.R. and Chen, C. (2005), "Fuzzy logic derivation of neural network models with time delays in subsystems", Int. J. Artif. Intell. Tools, 14, 967-974.   DOI
29 Yuan, C.C. and Hsu, J.R. (2006), "Numerical model of an internal solitary wave evolution on impermeable variable seabed in a stratified two-layer fluid system", China Ocean Eng., 20, 303-313.   DOI
30 Hsiao, F., Chiang, W. and Chen, C. (2004), "Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems", Math. Comput. Simul., 66, 523-537. https://doi.org/10.1016/j.matcom.2004.04.001.   DOI
31 Tim, C. and Chen, C.Y.J. (2019), "Meteorological tidal predictions in the Mekong estuary using an evolved ANN time series", Mar. Technol. Soc. J., 53(6), 27-34. https://doi.org/10.4031/MTSJ.53.6.3.   DOI
32 Tim, C., Morozov, S.N. and Chen, C.Y.J. (2019), "Hazard data analysis for underwater vehicles by submarine casualties", Mar. Technol. Soc. J., 53(6), 21-26. https://doi.org/10.4031/MTSJ.53.6.2.   DOI
33 Wang, R., Meng, Y.Z., Fu, Q. and Chen, T. (2022), "Grey FNN control and robustness design for practical nonlinear systems", J. Eng. Res., https://doi.org/10.36909/jer.11273.   DOI
34 Yuan, C.C., Yang, Y., Chen, C., Chen, L. and Chen, T. (2010), "Linking the balanced scorecard (BSC) to business management performance: A preliminary concept of fit theory for navigation science and management", Int. J. Phys. Sci., 5, 1296-1305.
35 Chen, P.C., Chen, C., Chiang, W. and Lo, D.C. (2011), "GA-based decoupled adaptive FSMC for nonlinear systems by a singular perturbation scheme", Neural Comput. Appl., 20(4), 517-526.   DOI
36 Yuan C.C. (2007), "An experimental study of stratified mixing caused by internal solitary waves in a twolayered fluid system over variable seabed topography", Ocean Eng., 34, 1995-2008.   DOI
37 Zhen, C., Wang, R., Meng, Y.Z., Fu, Q. and Chen, T. (2021), "Grey signal predictor and evolved control for practical nonlinear mechanical systems", J. Grey Syst., 33(1), 156-170.
38 Yuan, C.C., Hsu, J.R., Chen, H., Kuo, C. and Cheng, M. (2007), "Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes", Ocean Eng., 34, 157-170.   DOI
39 Yuan, C.C., Hsu, J.R., Cheng, M., Chen, H. and Kuo, C. (2007), "An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes", Ocean Eng., 34, 171-184.   DOI
40 Zandi, Y., Shariati, M., Marto, A., Wei, X., Karaca, Z., Dao, D., Toghroli, A., Hashemi, M.H., Sedghi, Y., Wakil, K. and Khorami, M. (2018), "Computational investigation of the comparative analysis of cylindrical barns subjected to earthquake", Steel Compos. Struct., 28(4), 439-447. https://doi.org/10.12989/scs.2018.28.4.439.   DOI
41 Zhang, Y. (2015), "A fuzzy residual strength based fatigue life prediction method", Struct. Eng. Mech., 56(2), 201-221. https://doi.org/10.12989/sem.2015.56.2.201.   DOI
42 Zhen, C., Wang, R., Meng, Y.Z., Fu, Q. and Chen, T. (2021), "Active TMD systematic design of fuzzy control and the application in high-rise buildings", Earthq. Struct., 21(6), 577-585. https://doi.org/10.12989/eas.2021.21.6.577.   DOI
43 Chen, C.W. (2014), "A criterion of robustness intelligent nonlinear control for multiple time-delay systems based on fuzzy Lyapunov methods", Nonlin. Dyn., 76(1), 23-31. https://doi.org/10.1007/s11071-013-0869-9.   DOI
44 Alexantion, P.S., Mandell, J.F., Scott, M.E. and Maccagnano, J.Z. (2011), "Stability analysis and robustness design of nonlinear systems: An NN-based approach", Appl. Soft Comput., 11, 2735-2742. https://doi.org/10.1016/j.asoc.2010.11.004.   DOI
45 Cairns, D.S., Mandell, J.F., Scott, M.E. and Alexantion, X.Y. (2018), "Dynamic intelligent control of composite buildings by using M-TMD and evolutionary algorithm", Smart Struct. Syst., 29(5), 1-11. https://doi.org/10.12989/sss.2022.29.5.001.   DOI
46 Chen, C., Chen, P. and Chiang, W. (2011), "Stabilization of adaptive neural network controllers for nonlinear structural systems using a singular perturbation approach", J. Vib. Control, 17, 1241-1252. https://doi.org/10.1177/1077546309352827.   DOI
47 Chen, P.C., Chen, C. and Chiang, W. (2008), "GA-based fuzzy sliding mode controller for nonlinear systems", Math. Probl. Eng., An Open Access Journal, https://doi.org/10.1155/2008/325859.   DOI
48 Wu, C. (2007), "A novel delay-dependent criterion for time-delay T-S fuzzy systems using fuzzy Lyapunov method", Int. J. Artif. Intell. Tools., 16, 545-552.   DOI
49 Zhou, X., Lin, Y. and Gu, M. (2015), "Optimization of multiple tuned mass dampers for large-span roof structures subjected to wind loads", Wind Struct., 20(3), 363-388. https://doi.org/10.12989/was.2015.20.3.363.   DOI
50 Zhang, H., Ban, X., Wu, F. and Huang, X. (2017), "Analysis of experimental data on internal waves with statistical method", Eng. Comput., 24(2007), 116-150. https://doi.org/.1108/02644400710729536.
51 Zhang, H., Wu, F., Ban, X. and Huang, X. (2017), "Assessment of the major hazard potential of interfacial solitary waves moving over a trapezoidal obstacle on a horizontal plateau", Nat. Hazards, 62(2012), 841-852. https://doi.org/10.1007/s11069-012-0107-7.   DOI
52 Zhang, H., Wu, F., Ban, X. and Huang, X. (2017), "Potential hazards and dynamical analysis of interfacial solitary wave interactions", Nat. Hazards, 65(2012), 255-278. https://doi.org/10.1007/s11069-012-0360-9.   DOI
53 Zhang, H., Wu, F., Ban, X. and Huang, X. (2017), "Using discriminant analysis to determine the breaking criterion for an ISW propagating over a ridge", Environ. Fluid Mech., 10(2010), 577-586. https://doi.org/10.1007/s10652-010-9172-1.   DOI
54 Tim, C., Lohnash, M., Owens, E. and Chen, C. (2020), "PDC Intelligent control-based theory for structure system dynamics", Smart Struct. Syst., 25(4), 401-408. https://doi.org/10.12989/sss.2020.25.4.401.   DOI
55 Chen, P.C., Chen, C. and Chiang, W. (2009), "GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems", Exp. Syst. with Appl., 36, 5872-5879.   DOI
56 Zhang, H., Wu, F., Ban, X. and Huang, X. (2017), "Statistical and dynamical analyses of propagation mechanisms of solitary internal waves in a two-layer stratification", J. Mar. Sci. Technol., 16(2011), 100-114. https://doi.org/10.1007/s00773-010-0112-z.   DOI
57 Tim, C. and Cheng, C. (2019), "Modelling and verification of an automatic controller for a water treatment mixing tank", Desalination and Water Treatment, 159, 318-326. https://doi.org/10.5004/dwt.2019.24143.   DOI
58 Tim, C., Dkuo, N.J. and Chen, C. (2020), "A composite control for UAV systems with time delays", Aircraft Eng. Aerosp. Technol., 92(7), 949-954. https://doi.org/10.1108/AEAT-11-2019-0219.   DOI
59 Tim, C., Hung, C.C., Huang, Y.C., Chen, J.C., Rahman, S. and Islam Mozumder, T. (2021), "Grey signal predictor and fuzzy controls for active vehicle suspension systems via Lyapunov theory", Int. J. Comput. Commun. Control, 16(3), 3991-2021. https://doi.org/10.15837/ijccc.2021.3.3991.   DOI
60 Tim, C., Kapron, N. and Chen, J.C. (2020), "Using evolving ANN-based algorithm models for accurate meteorological forecasting applications in Vietnam", Math. Probl. Eng., 8179652, https://doi.org/10.1155/2020/8179652.   DOI
61 Tsai, P.W., Pan, J.S., Liao, B.Y., Tsai, M.J. and Istanda, V. (2012), "Bat algorithm inspired algorithm for solving numerical optimization problems", Appl. Mech. Mater., 148, 134-137. https://doi.org/10.4028/www.scientific.net/AMM.148-149.134.   DOI
62 Chiang, W.L. (2002), "A new approach to stability analysis for nonlinear time-delay systems", Int. J. Fuzzy Syst., 4(2), 735-738.
63 Chen, T., Yang, H.P. and Chen, C. (2008), "A mathematical tool for inference in logistic regression with small-sized data sets: A practical application on ISW-Ridge relationships", Math. Probl. Eng., Open Access Journal, https://doi.org/10.1155/2008/186372.   DOI
64 Chiang, W.L., et al. (2001), "Application and robust H control of PDC fuzzy controller for nonlinear systems with external disturbance", J. Mar. Sci. Technol., 9(2), 84-90.
65 Tsai, P.W., Alsaedi, A., Hayat, T. and Chen, C.W. (2016), "A novel control algorithm for interaction between surface waves and a permeable floating structure", China Ocean Eng., 30(2), 161-176. https://doi.org/10.1007/s13344-016-0009-7.   DOI
66 Tsai, P.W., Hayat, T., Ahmad, B. and Chen, C.W. (2015), "Structural system simulation and control via NN based fuzzy model", Struct. Eng. Mech., 56(3), 385-407. https://doi.org/10.12989/sem.2015.56.3.385.   DOI
67 Tsai, P.W., Tseng, C.P., Hsu, W. and Chiang, W. (2012), "A novel strategy to determine insurance and risk control plan for natural disaster risk management", Nat, Hazards, 64, 1391-1403. https://doi.org/10.1007/s11069-012-0305-3.   DOI
68 Cairns, D.S., Scott, M.E. and Maccagnano, J.Z. (2011), "Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method", Neural Comput. Appl., 20, 527-534. https://doi.org/10.1007/s00521-011-0576-8.   DOI
69 Chen, C.W. (2014), "Interconnected TS fuzzy technique for nonlinear time-delay structural systems", Nonlinear Dynam., 76(1), 13-22. https://doi.org/10.1007/s11071-013-0841-8.   DOI
70 Chen, P.C., Chen, C. and Chiang, W. (2009), "A novel stability condition and its application to GA-based fuzzy control for nonlinear systems with uncertainty", J. Marine Sci. Technol., 17, 293-299.
71 Chen, T. and Chen, C. (2010), "Application of data mining to the spatial heterogeneity of foreclosed mortgages", Exp. Syst. with Appl., 37, 993-997.   DOI
72 Hsiao, F., Chiang, W., Xu, S. and Wu, S. (2003), "Application and fuzzy H∞ control via T-S fuzzy models for nonlinear time-delay systems", Int. J. Artif. Intell. Tools, 12(2), 117-137.   DOI
73 Hsiao, F., Hwang, J., Chen, C. and Tsai, Z. (2005), "Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control", IEEE T. Fuzzy Syst., 13(2005), 152-163. https://doi.org/10.1109/TFUZZ.2004.836067.   DOI
74 Khurram, S. and Cheng, C. (2019), "Prediction and control of buildings with sensor actuators of fuzzy EB algorithm", Earthq. Struct., 17(3), 307-315. https://doi.org/10.12989/eas.2019.17.3.307.   DOI
75 Chiang, W., Chen, C. and Hsiao, F. (2004), "Stability analysis of nonlinear interconnected systems via T-S fuzzy models", Int. J. Comput. Intell. Appl., 4, 41-55.   DOI
76 Chiang, W., Chen, C., Lin, C., Tsai, C., Chen, C. and Yeh, K. (2007), "A novel delay-dependent criterion for time-delay T-S fuzzy systems using fuzzy Lyapunov method", Int. J. Artif. Intell. Tools, 16, 545-552. https://doi.org/10.1142/S0218213007003400.   DOI
77 Hsiao, F., Chiang, W., Chen, C., Xu, S. and Wu, S. (2005), "Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance", Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, 13(3), 281-295.   DOI
78 Hsiao, F., Chiang, W., Xu, S. and Wu, S. (2005), "Fuzzy control for nonlinear systems via neural-network-based approach", Int. J. Comput. Method. Eng. Sci. Mech., 6, 145-152   DOI
79 Chiang, W., Tsai, C., Chen, C. and Wang, M. (2007), "Fuzzy Lyapunov method for stability conditions of nonlinear systems", Int. J. Artif. Intell. Tools, 15, 163-172. https://doi.org/10.1142/S0218213006002618.   DOI
80 Hsieh, T., Wang, M., Chen, C., Chen, C., Yu, S., Yang, H.P. and Chen, T. (2006), "A new viewpoint of S-curve regression model and its application to construction management", Int. J. Artif. Intell. Tools, 15, 131-142.   DOI
81 Hung, C.C., Tim, C. and Abu, A.A. (2019), "Optimal fuzzy design of Chua's circuit system". Int. J. Innov. Comput. Inform. Control, 15(6), 2355-2366. https://doi.org/ 10.24507/ijicic.15.06.2355.   DOI
82 Tim, C. and Chen, J.C. (2019), "Decentralized fuzzy C-Means robust algorithm for continuous systems", Aircraft Eng. Aerosp. Technol., 92(2), 222-228. https://doi.org/10.1108/AEAT-04-2019-0082.   DOI
83 Chiang, W., Chen, C. and Wu, D. (2007), "Modeling, H∞ control and stability analysis for structural systems using Takagi-Sugeno fuzzy model", J. Vib. Control, 13, 1519-1534. https://doi.org/10.1177/1077546307073690.   DOI
84 Lin, J., Chen, C. and Lee, W. (2010), "Modeling and fuzzy PDC control and its application to an oscillatory TLP structure", Math. Probl. Eng., 1-13. https://doi.org/10.1155/2010/120403.   DOI
85 Goldberg, D.E. (1989), Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley, MA. https://doi.org/10.1023/A:1022602019183.   DOI
86 Tim, C., Huang, Y., Hung, C.C., Frias, S., Muhammad, J.A. and Chen, C. (2021), "Smart structural stability and NN based intelligent control for nonlinear systems", Smart Struct. Syst., 27(6), 917-926. https://doi.org/10.12989/sss.2021.27.6.917.   DOI
87 Tim, C., Kuo, D., Huiwi, M., Gong-yo, T. and Chen, J. (2021), "Evolved predictive vibration control for offshore platforms based on the Lyapunov stability criterion", Ship. Offshore Struct., 16(7), 700-713. https://doi.org/10.1080/17445302.2020.1776548.   DOI
88 Lin, J., Chen, C., Shen, C. and Cheng, M. (2010), "Application of fuzzy-model-based control to nonlinear structural systems with time delay: an LMI method", J. Vib. Control, 16, 1651-1672. https://doi.org/10.1177/1077546309104185.   DOI
89 Lin, C., Wang, J.F., Chen, C., Chen, C. and Yen, C.V. (2009), "Improving the generalization performance of RBF neural networks using a linear regression technique", Exp. Syst. with Appl., 36, 12049- 12053.   DOI
90 Lin, J., Chen, C., Lee, W. and Chen, C. (2010), "Fuzzy control for an oceanic structure: A case study in time-delay TLP system", J. Vib. Control, 16, 147-160. https://doi.org/10.1177/1077546309339424.   DOI
91 Tim, C. and Chen, C. (2021), "Evolved auxiliary controller with applications to aerospace", Aircraft Eng. Aerosp. Technol., 93(4), 529-543. https://doi.org/10.1108/AEAT-12-2019-0233.   DOI
92 Wang, R., Meng, Y.Z., Fu, Q. and Chen, T. (2022), "Stochastic intelligent GA-NN controller design for active TMD shear building", Struct. Eng. Mech., 81(1), 51-57. https://doi.org/10.12989/sem.2022.81.1.051.   DOI
93 Wang, R., Meng, Y.Z., Fu, Q. and Chen, T. (2022), "Systematic fuzzy Navier-Stokes equations for aerospace vehicles", Aircraft Eng. Aerosp. Technol., 94(3), 351-359. https://doi.org/10.1108/AEAT-06-2020-0109.   DOI
94 Wu, C. (2006), "Fuzzy Lyapunov method for stability conditions of nonlinear systems", Int. J. Artif. Intell. Tools, 15, 163-171.   DOI
95 Wu, C. (2007), "Modeling, control and stability analysis for structural systems using Takagi Sugeno fuzzy model", J. Vib. Control, 13, 1519-1534.   DOI
96 Sakthivel, R., Santra, S., Mathiyalagan, K. and Anthoni, S.M. (2014), "Anthoni, robust reliable sampled-data control for offshore steel jacket platforms with nonlinear perturbations", Nonlinear Dynam., 78, 1109-1123. https://doi.org/10.1093/imamci/dnv046.   DOI