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Online Support Vector Regression Based Adaptive NARMA-L2 Controller for Nonlinear Systems

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Abstract

NARMA model is a simple and effective way to represent nonlinear systems, based on the NARMA model, NARMA-L2 controller is designed and has been successfully applied in the literature. Success of NARMA-L2 controller is directly related to the precision with which controlled systems’ dynamics can be estimated. In this paper, online SVR is utilized to obtain controlled plant’s subdynamics and consequently this information is used in the construction of NARMA-L2 controller. Hence functionality of NARMA-L2 controllers and high generalization capability of SVR are combined. Also, SVR formulates a convex optimization problem and therefore guarantees global optimum solution. The proposed method is assessed by performing simulations on a nonlinear CSTR system, the robustness of the designed controller is also tested under noisy and uncertainty conditions.

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References

  1. Narendra KS, Mukhopadhyay S (1997) Adaptive control using neural networks and approximate models. IEEE Trans Neural Netw 8(3):475–485. https://doi.org/10.1109/72.572089

    Article  Google Scholar 

  2. Majstorovic M, Nikolic I, Radovic J, Kvascev G (2008) Neural network control approach for a two-tank system. In: 9th symposium on neural network applications in electrical engineering (NEUREL 2008). Belgrade, Serbia

  3. Pedro JO, Nyandoro OTC, John S (2009) Neural network based feedback linearisation slip control of an anti-lock braking system. In: Asian control conference (ASCC 2009). Hong Kong, China

  4. De Jesus O, Pukrittayakamee A, Hagan MT (2001) A comparison of neural network control algorithms. In: International joint conference on neural networks(IJCNN’01). Washington, D.C

  5. Pukrittayakamee A, De Jesus O, Hagan MT (2002) Smoothing the control action for NARMA-L2 controllers. In: 45th midwest symposium on circuits and systems (MWSCAS 2002). Tulsa, OK

  6. Hagan MT, Demuth HB, De Jesus O (2002) An introduction to the use of neural networks in control systems. Int J Robust Nonlinear Control 12(11):959–985. https://doi.org/10.1002/rnc.727

    Article  MATH  Google Scholar 

  7. Wahyudi, Mokri SS, Shafie AA (2008) Real time implementation of NARMA L2 feedback linearization and smoothed NARMA L2 controls of a single link manipulator. In: International conference on computer and communication engineering. Kuala Lumpur, Malaysia

  8. Akbarimajd A, Kia S (2010) NARMA-L2 controller for 2-DoF underactuated planar manipulator. In: International conference on control, automation, robotics and vision (ICARCV 2010). Singapore

  9. Vesselenyi T, Dzitac S, Dzitac I, Manolescu MJ (2007) Fuzzy and neural controllers for a pneumatic actuator. Int J Comput Commun Control 2(4):375–387

    Article  Google Scholar 

  10. Awwad A, Abu-Rub H, Toliyat HA (2008) Nonlinear autoregressive moving average (NARMA-L2) controller for advanced AC motor control. In: 34th annual conference of the ieee industrial electronics society (IECON 2008). Orlando, FL

  11. Pedro J, Ekoru J (2013) NARMA-L2 control of a nonlinear half-car servo-hydraulic vehicle suspension system. Acta Polytech Hung 10(4):5–26

    Google Scholar 

  12. Lutfy OF, Selamat H (2015) Wavelet neural network-based narma-l2 internal model control utilizing micro-artificial immune techniques to control nonlinear systems. Arab J Sci Eng 40(9):2813–2828

    Article  Google Scholar 

  13. Paul R, Chokkadi S (2016) Implementation of NARMA-L2 controller for shell and tube heat exchanger temperature process. Indus Eng Chem Res 55(19):5644–5653

    Article  Google Scholar 

  14. Al-Dunainawi Y, Abbod MF, Jizany A (2017) A new MIMO ANFIS-PSO based NARMA-L2 controller for nonlinear dynamic systems. Eng Appl Artif Intell 62:265–275

    Article  Google Scholar 

  15. Yang Y, Xiang C, Gao SH, Lee TH (2018) Data-driven identification and control of nonlinear systems using multiple NARMA-L2 models. Int J Robust Nonlinear Control 28(12):3806–3833 Special Issue: SI

    Article  MathSciNet  Google Scholar 

  16. Vapnik VN (1999) An overview of statistical learning theory. IEEE Trans Neural Netw 10(5):988–999. https://doi.org/10.1109/72.788640

    Article  Google Scholar 

  17. Uçak K, Günel GÖ (2016) A novel adaptive NARMA-L2 controller based on online support vector regression for nonlinear systems. Neural Process Lett 44(3):857–886

    Article  Google Scholar 

  18. Şen GD, Günel GÖ (2019) A NARMA-L2 controller based on online LSSVR for nonlinear systems. In: 15th european workshop on advanced control and diagnosis

  19. Wanfeng S, Shengdun Z, Yajing S (2008) Adaptive PID controller based on online LSSVM identification. in: IEEE/ASME international conference on advanced intelligent mechatronics (AIM 2008). Xian, China

  20. Zhao J, Li P, Wang Xs (2009) Intelligent PID controller design with adaptive criterion adjustment via least squares support vector machine. In: 21st chinese control and decision conference (CCDC 2009). Guilin, China

  21. Yuan XF, Wang YN, Wu LH (2008) Composite feedforward-feedback controller for generator excitation system. Nonlinear Dynam 54(4):355–364. https://doi.org/10.1007/s11071-008-9334-6

    Article  MATH  Google Scholar 

  22. Iplikci S (2010) A comparative study on a novel model-based PID tuning and control mechanism for nonlinear systems. Int J Robust Nonlinear Control 20(13):1483–1501

    Article  MathSciNet  Google Scholar 

  23. Takao K, Yamamoto T, Hinamoto T, (2006) A Design of PID Controllers with a Switching Structure by a Support Vector Machine. In: IEEE International Joint Conference on Neural Network (IJCNN). Vancouver, Canada

  24. Liu X, Yi J, Zhao D (2005) Adaptive inverse control system based on least squares support vector machines. In: 2nd international symposium on neural networks (ISNN 2005). Chongqing, China

  25. Wang H, Pi DY, Sun YX (2007) Online SVM regression algorithm-based adaptive inverse control. Neurocomputing 70(4–6):952–959. https://doi.org/10.1016/j.neucom.2006.10.021

    Article  Google Scholar 

  26. Yuan XF, Wang YN, Wu LH (2008) Adaptive inverse control of excitation system with actuator uncertainty. Neural Process Lett 27(2):125–136. https://doi.org/10.1007/s11063-007-9064-7

    Article  Google Scholar 

  27. Zhao ZC, Liu ZY, Xia ZM, Zhang JG (2012) Internal model control based on LS-SVM for a class of nonlinear process. In: International conference on solid state devices and materials science (SSDMS). Macao, China

  28. Zhong WM, Pi DY, Sun YX, Xu C, Chu SZ (2006) SVM based internal model control for nonlinear systems. In: 3rd international symposium on neural networks (ISNN 2006). Chengdu, China

  29. Sun CY, Song JY (2007) An adaptive internal model control based on ls-svm. In: International symposium on neural networks (ISNN 2007). Nanjing, China

  30. Wang YN, Yuan XF (2008) SVM approximate-based internal model control strategy. Acta Automatica Sinica 34(2):172–179. https://doi.org/10.3724/SP.J.1004.2008.00172

    Article  MathSciNet  MATH  Google Scholar 

  31. Iplikci S (2006) Online trained support vector machines-based generalized predictive control of non-linear systems. Int J Adapt Control Signal Process 20(10):599–621. https://doi.org/10.1002/acs.919

    Article  MathSciNet  MATH  Google Scholar 

  32. Iplikci S (2006) Support vector machines-based generalized predictive control. Int J Robust Nonlinear Control 16(17):843–862. https://doi.org/10.1002/rnc.1094

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhiying D, Xianfang W (2008) Nonlinear generalized predictive control based on online SVR. In: 2nd international symposium on intelligent information technology application. Shanghai, China

  34. Shin J, Kim HJ, Park S, Kim Y (2010) Model predictive flight control using adaptive support vector regression. Neurocomputing 73(4–6):1031–1037. https://doi.org/10.1016/j.neucom.2009.10.002

    Article  Google Scholar 

  35. Wang DS, Shen JJ, Zhu SH, Jiang GP (2020) Model predictive control for chlorine dosing of drinking water treatment based on support vector machine model. Desalin Water Treat 173:133–141

    Article  Google Scholar 

  36. Pourjafari E, Reformat M (2019) A support vector regression based model predictive control for volt-var optimization of distribution systems. IEEE Access 7:93352–93363

    Article  Google Scholar 

  37. Uçak K, Günel GÖ (2016) An adaptive support vector regressor controller for nonlinear systems. Soft Comput 20(7):2531–2556

    Article  Google Scholar 

  38. Uçak K, Günel GÖ (2017) Generalized self-tuning regulator based on online support vector regression. Neural Comput Appl 28:S775–S801

    Article  Google Scholar 

  39. Uçak K, Günel GÖ (2019) Model free adaptive support vector regressor controller for nonlinear systems. Eng Appl Artif Intell 81:47–67

    Article  Google Scholar 

  40. Uçak K, Günel GÖ (2020) An adaptive sliding mode controller based on online support vector regression for nonlinear systems. Soft Comput 24(6):4623–4643

    Article  Google Scholar 

  41. Ma J, Theiler J, Perkins S (2003) Accurate online support vector regression. Neural Comput 15(11):2683–2703

    Article  Google Scholar 

  42. Wang X, Du Z, Chen Z, Pan F (2009) Dynamic modeling of biotechnical process based on online support vector machine. J Comput 4(3):251–258

    Google Scholar 

  43. Uçak K, Üstoğlu İ, Günel GÖ (2018) Safety-critical support vector regressor controller for nonlinear systems. Neural Process Lett 48:419–440

    Article  Google Scholar 

  44. Uçak K (2016) Support vector regression based controller design methods for nonlinear systems. Dissertation, Istanbul Technical University

  45. Mario M (2002) On-Line Support Vector Machine Regression. In: 13th european conference on machine learning (ECML 2002). Helsinki, Finland

  46. Kravaris C, Palanki S (1988) Robust nonlinear state feedback under structured uncertainty. AIChE J 34(7):1119–1127

    Article  MathSciNet  Google Scholar 

  47. Wu W, Chou YS (1999) Adaptive feedforward and feedback control of non-linear time-varying uncertain systems. Int J Control 72(12):1127–1138

    Article  MathSciNet  Google Scholar 

  48. Levenspiel O (1999) Chemical reaction engineering. Wiley, USA

    Google Scholar 

  49. Fogler HS (2006) Elements of reaction engineering. Pearson Education, London

    Google Scholar 

  50. Ungar LH (1990) Neural networks for control. In: Miller III WT, Werbos PJ (eds) A bioreactor benchmark for adaptive network based process control. MIT Press, USA, Sutton RS, pp 387–402

    Google Scholar 

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Authors and Affiliations

  1. Massachusetts Institute of Technology Cambridge, MA, 02139, USA

    Kemal Uçak

  2. Muğla Sıtkı  Koçman University Kötekli, 48000, Muğla, Turkey

    Kemal Uçak

  3. Istanbul Technical University Maslak, 34469, Istanbul, Turkey

    Gülay Öke Günel

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  1. Kemal Uçak
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  2. Gülay Öke Günel
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Correspondence to Kemal Uçak.

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Uçak, K., Günel, G.Ö. Online Support Vector Regression Based Adaptive NARMA-L2 Controller for Nonlinear Systems. Neural Process Lett 53, 405–428 (2021). https://doi.org/10.1007/s11063-020-10403-8

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