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http://dx.doi.org/10.12989/sss.2022.29.5.693

LDI NN auxiliary modeling and control design for nonlinear systems  

Chen, Z.Y. (School of Science, Guangdong University of Petrochemical Technology)
Wang, Ruei-Yuan (School of Science, Guangdong University of Petrochemical Technology)
Jiang, Rong (School of Science, Guangdong University of Petrochemical Technology)
Chen, Timothy (Division of Engineering and Applied Science, California Institute of Technology)
Publication Information
Smart Structures and Systems / v.29, no.5, 2022 , pp. 693-703 More about this Journal
Abstract
This study investigates an effective approach to stabilize nonlinear systems. To ensure the asymptotic nonlinear stability in nonlinear discrete-time systems, the present study presents controller for an EBA (Evolved Bat Algorithm) NN (fuzzy neural network) in the algorithm. In fuzzy evolved NN modeling, the auxiliary circuit with high frequency LDI (linear differential inclusions) and NN model representation is developed for the nonlinear arbitrary dynamics. An example is utilized to demonstrate the system more robust compared with traditional control systems.
Keywords
artificial intelligence; fuzzy theory; intelligent algorithm; LDI; NN controller;
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1 Adeli, H. and Jiang, X. (2006), "Dynamic fuzzy wavelet neural network model for structural system identification", J. Struct. Eng., 132(1), 102-111. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:1(102).   DOI
2 Adeli, H. and Kim, H. (2004), "Wavelet-hybrid feedback-least mean square algorithm for robust control of structures", J. Struct. Eng., 130(2), 128-137. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:1(128).   DOI
3 Bedirhanoglu, I. (2014), "A practical neuro-fuzzy model for estimating modulus of elasticity of concrete", Struct. Eng. Mech., 51(2), 249-265. https://doi.org/10.12989/sem.2014.51.2.249.   DOI
4 Cao, B., Zhao, J., Liu, X., Arabas, J., Tanveer, M., Singh, A.K. and Lv, Z. (2022), "Multiobjective evolution of the explainable fuzzy rough neural network with gene expression programming", IEEE Trans. Fuzzy Syst., 1-1. https://doi.org/10.1109/TFUZZ.2022.3141761.   DOI
5 Chen, C.W. (2005), "Stability conditions of fuzzy systems and its application to structural and mechanical systems", Adv. Eng. Softw., 37, 624-629. https://doi.org/10.1016/j.advengsoft.2005.12.002.   DOI
6 Chen, C.W. (2007), "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
7 Chen, C.W. (2011b), "Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method", Neur. Comput. Appl., 20, 527-534. https://doi.org/10.1007/s00521-011-0576-8.   DOI
8 Chen, C.W. (2014b), "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
9 Connor, J.J. (2003), Introduction to Structural Motion Control, Prentice-Hall, Upper Saddle River, NJ, USA.
10 Fossen, T.I. (1994), Guidance and Control of Ocean Vehicles, John Wiley and Sons, 448-451.
11 Ghamkhar, M., Hussain, M., Khadimallah, M.A., Ayed, H., Naz, M.Y and Tounsi, A. (2022), "Design of intelligent estimation of composite fluid-filled shell for three layered active control structure", Comput. Concrete, 29(2), 117-126. https://doi.org/10.12989/cac.2022.29.2.117.   DOI
12 Kim, H. and Adeli, H. (2004), "Hybrid feedback-least mean square algorithm for structural control", J. Struct. Eng., 130(2), 120-127. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:1(120).   DOI
13 Steinberg, A.M. and Kadushin, I. (1973), "Stabilization of nonlinear systems with dither control", J. Math. Anal. Appl., 43, 273-284. https://doi.org/10.1016/0022-247X(73)90275-8.   DOI
14 Hsiao, F.H., Hwang, J.D., Chen, C.W. and Tsai, Z.R. (2005b), "Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control", IEEE Trans. Fuzzy Syst., 13, 152-163. https://doi.org/10.1109/TFUZZ.2004.836067.   DOI
15 Chen, C.W., Lin, C.L., Tsai, C.H., Chen, C.Y. and Yeh, K. (2007b), "A novel delay-dependent criterion for time-delay TS fuzzy systems using fuzzy Lyapunov method", Int. J. Artif. Intell. Tool., 16, 545-552. https://doi.org/10.1142/S0218213007003400.   DOI
16 Chen, C.W., Shen, C.W., Chen, C.Y. and Cheng, M.J. (2011a), "Stability analysis of an oceanic structure using the Lyapunov method", Eng. Comput., 27, 186-204. https://doi.org/10.1108/02644401011022364.   DOI
17 Chen, C.W., Tseng, C.P., Hsu, W.K. and Chiang, W.L. (2012), "A novel strategy to determine the insurance and risk control plan for natural disaster risk management", Nat. Hazard., 64, 1391-1403. https://doi.org/10.1007/s11069-012-0305-3.   DOI
18 Kalman, R.E. (1963), "New methods in Wiener filtering theory", Eds. J.L. Bogdanoff and F. Kozin, Proceedings of the First Symposium on Engineering Applications of Random Function Theory and Probability, John Wiley & Sons, New York.
19 Kayabekir, A.E., Bekdas, G., Nigdeli, S.M. and Geem, Z.W. (2020), "Optimum design of PID controlled active tuned mass damper via modified harmony search", Appl. Sci., 10(8), 2976. https://doi.org/10.3390/app10082976.   DOI
20 Kmet, S. (2004), "Non-linear rheology of tension structural element under single and variable loading history part I. Theoretical derivations", Struct. Eng. Mech., 18(5), 565-589. https://doi.org/10.12989/sem.2004.18.5.565.   DOI
21 Levant, A. (1998), "Robust exact differentiation via sliding mode technique", Automatica, 34(3), 379-384. https://doi.org/10.1016/S0005-1098(97)00209-4.   DOI
22 Li, M., Chen, S., Shen, Y., Liu, G., Tsang, I.W. and Zhang, Y. (2022), "Online multi-agent forecasting with interpretable collaborative graph neural networks", IEEE Trans. Neur. Network. Learn. Syst., 1-15. https://doi.org/10.1109/TNNLS.2022.3152251.   DOI
23 Tanaka, K., Ikeda, T. and Wang, H.O. (1996), "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H/sup/spl infin//control theory, and linear matrix inequalities", IEEE Tran. Fuzzy Syst., 4(1), 1-13 https://doi.org/10.1109/91.481840.   DOI
24 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
25 Ulusoy, S., Bekdas, G. and Nigdeli, S.M. (2020), "Active structural control via metaheuristic algorithms considering soil-structure interaction", Struct Eng. Mech., 75(2), 175-191. https://doi.org/10.12989/sem.2020.75.2.175.   DOI
26 Li, Y., Du, L. and Wei, D. (2022), "Multiscale CNN based on component analysis for SAR ATR", IEEE Trans. Geosci. Remote Sens., 60, 1-12. https://doi.org/10.1109/TGRS.2021.3100137.   DOI
27 Liu, X., Zhao, J., Li, J., Cao, B. and Lv, Z. (2022), "Federated neural architecture search for medical data security", IEEE Trans. Indus. Inform., 1-1. https://doi.org/10.1109/TII.2022.3144016.   DOI
28 Hsiao, F.H., Chen, C.W., Liang, Y.W., Xu, S.D. and Chiang, W.L. (2005a), "TS fuzzy controllers for nonlinear interconnected systems with multiple time delays", IEEE Trans. Circuit. Syst. I Regul. Pap., 52(9), 1883-1893. https://doi.org/10.1109/TCSI.2005.852492.   DOI
29 Ulusoy, S., Nigdeli, S.M. and Bekdas, G. (2021), "Novel metaheuristic-based tuning of PID controllers for seismic structures and verification of robustness", J. Build. Eng., 33, 101647. https://doi.org/10.1016/j.jobe.2020.101647.   DOI
30 Gauthier, D.J., Sukow, D.W., Concannon, H.M. and Socolar, J.E. (1994), "Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization", Phys. Rev. E, 50, 2343-2346. https://doi.org/10.1103/PhysRevE.50.2343.   DOI
31 Shariatmadar, H. and Razavi, H.M. (2014), "Seismic control response of structures using an ATMD with fuzzy logic controller and PSO method", Struct. Eng. Mech., 51(4), 547-564. https://doi.org/10.12989/sem.2014.51.4.547.   DOI
32 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
33 Chen, C.W., Yeh, K. and Liu, K.F.R. (2009a), "Adaptive fuzzy sliding mode control for seismically excited bridges with lead rubber bearing isolation", Int. J. Uncertain. Fuzz. Knowl. Bas. Syst., 17, 705-727. https://doi.org/10.1142/S0218488509006224.   DOI
34 Chen, C.W., Yeh, K., Chiang, W.L., Chen, C.Y. and Wu, D.J. (2007a), "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
35 Chen, C.Y., Lin, J.W., Lee, W.I. and Chen, C.W. (2009c), "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
36 Yeh, K., Chen, C.Y. and Chen, C.W. (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
37 Hung, C.C., Chen, T., Abi Astolfi, A., Rao, S.R., Young, H.T., Wutim, C. and Chen, C.Y.J. (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
38 Kapitaniak, T., Kocarev, L.J. and Chua, L.O. (1993), "Controlling chaos without feedback and control signals", Int. J. Bifurcation Chaos, 3, 459-468. https://doi.org/10.1142/S0218127493000362.   DOI
39 Jiang, X. and Adeli, H. (2005), "Dynamic wavelet neural network for nonlinear identification of highrise buildings", Comput.- Aided Civil Infrastr. Eng., 20(5), 316-330. https://doi.org/10.1111/j.1467-8667.2005.00399.x.   DOI
40 Wang, S., Guo, H., Zhang, S., Barton, D. and Brooks, P. (2022), "Analysis and prediction of double-carriage train wheel wear based on SIMPACK and neural networks", Adv. Mech. Eng., 14(3), 16878132221078491. https://doi.org/10.1177/16878132221078491.   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 Zheng, W., Cheng, J., Wu, X., Sun, R., Wang, X. and Sun, X. (2022), "Domain knowledge-based security bug reports prediction", Knowledge-Bas. Syst., 241, 108293. https://doi.org/10.1016/j.knosys.2022.108293.   DOI
43 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
44 Londhe, P.S., Santhakumar, M., Patre, B.M. and Waghmare, L.M. (2017), "Task space control of an autonomous underwater vehicle manipulator system by robust single-input fuzzy logic control scheme", IEEE J. Oceanic Eng., 42(1), 13-28. https://doi.org/10.1109/JOE.2016.2548820.   DOI
45 Lu, J., Wang, Y., Zhai, X. and Zhou, H. (2022), "Impact response of a novel flat steel-concrete-corrugated steel panel", Steel Compos. Struct., 42(2), 277-288. https://doi.org/10.12989/scs.2022.42.2.277.   DOI
46 Lu, L.T., Chiang, W.L. and Tang, J.P. (1998), "LQG/LTR control methodology in active structure control", J. Eng. Mech., 124(4), 446-454. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(446).   DOI
47 Ozdemir, M.T., Kobya, V., Yayli, M.O. and Mardani-Aghabaglou, A. (2021), "Vibration analysis of steel fiber reinforced self-compacting concrete beam on elastic foundation", Comput. Concrete, 27(2), 85-97. https://doi.org/10.12989/cac.2021.27.2.085.   DOI
48 Meng, Q., Lai, X., Yan, Z., Su, C. and Wu, M. (2021), "Motion planning and adaptive neural tracking control of an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint", IEEE Trans. Neur. Network. Learn Syst., 1-15. https://doi.org/10.1109/TNNLS.2021.3054611.   DOI
49 Meng, Q., Ma, Q. and Zhou, G. (2022), "Adaptive output feedback control for stochastic uncertain nonlinear time-delay systems", IEEE Trans. Circuit Syst. II, Exp. Brief., 1-1. https://doi.org/10.1109/TCSII.2022.3152523.   DOI
50 Moore, B.C. (1981), "Principal component analysis in linear systems: controllability, observability, and model reduction", IEEE Trans. Automat. Control, 26(1), 17-32. https://doi.org/10.1109/TAC.1981.1102568.   DOI
51 Son, L., Bur, M., Rusli, M. and Adriyan, A. (2016), "Design of double dynamic vibration absorbers for reduction of two DOF vibration system", Struct. Eng. Mech., 57(1), 161-178. https://doi.org/10.12989/sem.2016.57.1.161.   DOI
52 Stein, G. and Athans, M. (1987), "The LQG/LTR procedure for multivariable feedback control design", IEEE Trans. Automat. Control, 32(2), 05-114. https://doi.org/10.1109/TAC.1987.1104550.   DOI
53 Taherifar, R., Zareei, S.A., Bidgoli, M.R. and Kolahchi, R. (2020), "Seismic analysis in pad concrete foundation reinforced by nanoparticles covered by smart layer utilizing plate higher order theory", Steel Compos. Struct., 37(1), 99-115. https://doi.org/10.12989/scs.2020.37.1.099.   DOI
54 Wang, H.O. and Abed, E.H. (1995), "Bifurcation control of a chaotic system", Automatica, 31, 1213-1226. https://doi.org/10.1016/0005-1098(94)00146-A.   DOI
55 Chen, C.W. (2011a), "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
56 Maciejowski, J.M. (1989), Multivariable Feedback Design, Addition-Wesley Publishing Co., Chapter 5, 222-264.
57 Mazloom, M., Tajar, S.F. and Mahboubi, F. (2020), "Long-term quality control of self-compacting semi-lightweight concrete using short-term compressive strength and combinatorial artificial neural networks", Comput. Concrete, 25(5), 401-409. https://doi.org/10.12989/cac.2020.25.5.401.   DOI
58 Lv, Z., Chen, D., Feng, H., Wei, W. and Lv, H. (2022), "Artificial intelligence in underwater digital twins sensor networks", ACM Trans. Sensor Network., 18(3), 1-27. https://doi.org/10.1145/3519301.   DOI
59 Wang, H.O., Tanaka, K. and Griffin, M.F. (1996), "An approach to fuzzy control of nonlinear systems: stability and design issues", IEEE Trans. Fuzzy Syst., 4, 14-23. https://doi.org/10.1109/91.481841.   DOI
60 Wu, Z., Cao, J., Wang, Y., Wang, Y., Zhang, L. and Wu, J. (2020), "hPSD: A hybrid PU-learning-based spammer detection model for product reviews", IEEE Trans. Cybernet., 50(4), 1595-1606. https://doi.org/10.1109/TCYB.2018.2877161.   DOI
61 Zames, G. and Shneydor, N. (1976), "Dither in nonlinear systems", IEEE Trans. Automat. Control, 21, 660-667. https://doi.org/10.1109/TAC.1976.1101357.   DOI
62 Zames, G. and Shneydor, N. (1977), "Structural stabilization on quenching by dither in nonlinear systems", IEEE Trans. Automat. Contr., 22, 353-361. https://doi.org/10.1109/TAC.1977.1101504.   DOI
63 Zhao, C., Zhu, Y., Du, Y., Liao, F. and Chan, C. (2022), "A novel direct trajectory planning approach based on generative adversarial networks and rapidly-exploring random tree", EEE Trans. Intel. Transp. Syst., 1-12. https://doi.org/10.1109/TITS.2022.3164391.   DOI
64 Yang, J.N., Wu, J.C., Samali, B. and Agrawal, A.K. (1998), "A Benchmark Problem for Response Control of Wind-Excited Tall Buildings", Proceedings of the 2nd world Conference on Structural Control, Vol. 2, 1407-1416.
65 Chen, C.W., Chen, P.C. and Chiang, W.L. (2011b), "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
66 Zheng, C., An, Y., Wang, Z., Wu, H., Qin, X., Eynard, B. and Zhang, Y. (2022), "Hybrid offline programming method for robotic welding systems", Robot. Comput.-Integr. Manuf., 73, 102238. https://doi.org/10.1016/j.rcim.2021.102238.   DOI
67 Zheng, W., Xun, Y., Wu, X., Deng, Z., Chen, X. and Sui, Y. (2021), "A comparative study of class rebalancing methods for security bug report classification", IEEE Trans. Reliab., 70(4), 1-13. https://doi.org/10.1109/TR.2021.3118026.   DOI
68 Zhong, C., Li, H., Zhou, Y., Lv, Y., Chen, J. and Li, Y. (2022), "Virtual synchronous generator of PV generation without energy storage for frequency support in autonomous microgrid", Int. J. Elec. Pow Energy Syst., 134, 107343. https://doi.org/10.1016/j.ijepes.2021.107343.   DOI
69 Chawla, K.K. (2012), Fatigue and Creep, 3rd Edition, Springer, New York.
70 Akhavan Alavi, S.M., Mohammadimehr, M. and Ejtahed, S.H. (2021), "Vibration analysis and control of micro porous beam integrated with FG-CNT distributed piezoelectric sensor and actuator", Steel Compos. Struct., 41(4), 595-608. https://doi.org/10.12989/scs.2021.41.4.595.   DOI
71 Chen, C.W. (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
72 Chen, C.W. (2014a), "Interconnected TS fuzzy technique for nonlinear time-delay structural systems", Nonlin. Dyn., 76(1), 13-22. https://doi.org/10.1007/s11071-013-0841-8.   DOI
73 Chen, C.W., Chiang, W.L., Tsai, C.H., Chen, C.Y. and Wang, M.H. (2005), "Fuzzy Lyapunov method for stability conditions of nonlinear systems", Int. J. Artif. Intell. Tool., 15, 163-171. https://doi.org/10.1142/S0218213006002618.   DOI
74 Chen, C.Y., Shen, C.W., Chen, C.W., Liu, K.F.R. and Cheng, M.J. (2009b), "A stability criterion for time-delay tension leg platform systems subjected to external force", China Ocean Eng., 23, 49-57.
75 Choi, B.J., Kwak, S.W. and Kim, B.K. (2000), "Design and stability analysis of single-input fuzzy logic controller", IEEE Trans. Syst. Man Cybernet. Part B (Cybernetics), 30(2), 303-309. https://doi.org/10.1109/3477.836378.   DOI
76 Katebi, J., Shoaei-parchin, M., Shariati, M., Trung, N.T. and Khorami, M. (2019), "Developed comparative analysis of metaheuristic optimization algorithms for optimal active control of structures", Eng. Comput., 36(4), 1539-1558. https://doi.org/10.1007/s00366-019-00780-7.   DOI