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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Vapnik VN (1999) An overview of statistical learning theory. IEEE Trans Neural Netw 10(5):988–999. https://doi.org/10.1109/72.788640
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
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
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
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
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
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
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
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
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
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
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
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
Sun CY, Song JY (2007) An adaptive internal model control based on ls-svm. In: International symposium on neural networks (ISNN 2007). Nanjing, China
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
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
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
Zhiying D, Xianfang W (2008) Nonlinear generalized predictive control based on online SVR. In: 2nd international symposium on intelligent information technology application. Shanghai, China
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
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
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
Uçak K, Günel GÖ (2016) An adaptive support vector regressor controller for nonlinear systems. Soft Comput 20(7):2531–2556
Uçak K, Günel GÖ (2017) Generalized self-tuning regulator based on online support vector regression. Neural Comput Appl 28:S775–S801
Uçak K, Günel GÖ (2019) Model free adaptive support vector regressor controller for nonlinear systems. Eng Appl Artif Intell 81:47–67
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
Ma J, Theiler J, Perkins S (2003) Accurate online support vector regression. Neural Comput 15(11):2683–2703
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
Uçak K, Üstoğlu İ, Günel GÖ (2018) Safety-critical support vector regressor controller for nonlinear systems. Neural Process Lett 48:419–440
Uçak K (2016) Support vector regression based controller design methods for nonlinear systems. Dissertation, Istanbul Technical University
Mario M (2002) On-Line Support Vector Machine Regression. In: 13th european conference on machine learning (ECML 2002). Helsinki, Finland
Kravaris C, Palanki S (1988) Robust nonlinear state feedback under structured uncertainty. AIChE J 34(7):1119–1127
Wu W, Chou YS (1999) Adaptive feedforward and feedback control of non-linear time-varying uncertain systems. Int J Control 72(12):1127–1138
Levenspiel O (1999) Chemical reaction engineering. Wiley, USA
Fogler HS (2006) Elements of reaction engineering. Pearson Education, London
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
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Ethical Approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-020-10403-8