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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)
  • Received : 2021.10.31
  • Accepted : 2022.02.18
  • Published : 2022.05.25

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

Acknowledgement

The authors are grateful for the research grants given to ZY Chen from the Projects of Talents Recruitment of GDUPT (NO. 2021rc002) in Guangdong Province, Peoples R China, RY Wang from the Projects of Talents Recruitment of GDUPT (NO. 2019rc098), and Guangdong Provincial Key Lab.of Petrochemical Equipment and Fault Diagnosis, School of Science, Guangdong University of Petrochemical Technology, Maoming, Guangdong 525000, China as well as to the anonymous reviewers for constructive suggestions.

References

  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).
  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).
  3. 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.
  4. 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.
  5. 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.
  6. Chawla, K.K. (2012), Fatigue and Creep, 3rd Edition, Springer, New York.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. Connor, J.J. (2003), Introduction to Structural Motion Control, Prentice-Hall, Upper Saddle River, NJ, USA.
  25. Fossen, T.I. (1994), Guidance and Control of Ocean Vehicles, John Wiley and Sons, 448-451.
  26. 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.
  27. 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.
  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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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).
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. 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.
  43. 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.
  44. 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).
  45. 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.
  46. Maciejowski, J.M. (1989), Multivariable Feedback Design, Addition-Wesley Publishing Co., Chapter 5, 222-264.
  47. 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.
  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.
  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.
  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.
  51. 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.
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  56. 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.
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
  63. 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.
  64. 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.
  65. 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.
  66. 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.
  67. 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.
  68. 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.
  69. 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.
  70. 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.
  71. 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.
  72. 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.
  73. 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.
  74. 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.
  75. 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.
  76. 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.