Skip to main content
Springer Nature Link
Log in

Adaptive nonparametric evolving fuzzy controller for uncertain nonlinear systems with dead zone

  • Original Paper
  • Published:
Evolving Systems Aims and scope Submit manuscript

Abstract

This paper presents an adaptive nonparametric evolving fuzzy controller for uncertain nonlinear systems with dead zone. The unknown nonlinear- ities caused by the dead zone are approximated using a nonparametric data clouds-based evolving fuzzy systems (EFSs), based on which the controller is designed via the Backstepping procedure. The data clouds- based EFSs impose the local and global density as the learning schemes to adapt the structure of the controller using the information extracted from nonstationary data streams. The stable parameter adjustment laws with projection operator are derived under the Lyapunov theorem to update the parameters of the controller. To further reduce the in uence of the approximation errors brought by the data clouds-based approxima- tors, a sliding mode control term is designed to augment the controller. The stability of the proposed controller is proven under the Lyapunov synthesis, and its effectiveness is verified by the simulation results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Aguilar-Ibanez C, Moreno-Valenzuela J, García-Alarcón O, Martinez-Lopez M, Ángel Acosta J, Suarez-Castanon MS (2021) PI-type controllers and \(\Sigma\)-\(\Delta\) modulation for saturated DC-DC buck power converters. IEEE Access 9:20346–20357

    Article  Google Scholar 

  • Alves KSTR, de Aguiar EP (2021) A novel rule-based evolving fuzzy system applied to the thermal modeling of power transformers. Appl Soft Comput 112:107764

    Article  Google Scholar 

  • Andonovski G, Angelov P, Blažičč S, Škrjanc I (2016) A practical implementation of robust evolving cloud-based controller with normalized data space for heat-exchanger plant. Appl Soft Comput 48:29–38

    Article  Google Scholar 

  • Andonovski G, Costa BSJ, Blažičč S, Škrjanc I (2018) Robust evolving controller for simulated surge tank and for real two-tank plant. at-Automatisierungstechnik 66(9):725–734

    Article  Google Scholar 

  • Andonovski G, Costa BSJ, Blažičč S, Škrjanc I (2018) Robust evolving controller for simulated surge tank and for real two-tank plant. at - Automatisierungstechnik 66(9):725–734

    Article  Google Scholar 

  • Andonovski G, Angelov SBP, Škrjanc I (2015) Robust evolving cloud-based controller in normalized data space for heat-exchanger plant. In: 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp 1–7

  • Angelov P (2012) Autonomous Learning Systems: From Data Streams to Knowledge in Real-time. John Wiley and Sons, Chichester

    Book  Google Scholar 

  • Angelov PP, Filev DP (2004) An approach to online identification of takagi-sugeno fuzzy models. IEEE Trans Syst Man Cybern Part B (Cybernetics) 34(1):484–498

    Article  Google Scholar 

  • Angelov P, Yager R (2012) A new type of simplified fuzzy rule-based system. Int J Intell Syst 41(2):163–185

    MathSciNet  MATH  Google Scholar 

  • Angelov P, K D, Gu X (2017) Empirical data analytics. Int J Intell Syst 32(12):1261–1284

    Article  Google Scholar 

  • Angelov P, Buswell R (2001) Evolving rule-based models: A tool for intelligent adaptation. In: Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569), vol. 2, pp. 1062–1067

  • Burton JA, Zinober ASI (1986) Continuous approximation of variable structure control, international journal of systems science. Int J Syst Sci 17(6):875–885

    Article  MATH  Google Scholar 

  • Chen S-Y, Liu T-S (2017) Intelligent tracking control of a PMLSM using self-evolving probabilistic fuzzy neural network. IET Electr Power Appl 11(6):1043–1054

    Article  Google Scholar 

  • Choi JY, Farrell JA (2001) Adaptive observer backstepping control using neural networks. IEEE Trans Neural Netw 12(5):1103–1112

    Article  Google Scholar 

  • Costa B, Skrjanc I, Blazic S, Angelov P (2013) A practical implementation of self-evolving cloud-based control of a pilot plant. In: 2013 IEEE International Conference on Cybernetics (CYBCO), pp. 7–12

  • de Campos Souza PV, Lughofer E (2021) An evolving neuro-fuzzy system based on uni-nullneurons with advanced interpretability capabilities. Neurocomputing 451:231–251

    Article  Google Scholar 

  • de Jesús Rubio J, Bouchachia A (2017) MSAFIS: an evolving fuzzy inference system. Soft Comput 21:2357–2366

    Article  Google Scholar 

  • de Jesús Rubio J, Lughofer E, Pieper J, Cruz P, Martinez DI, Ochoa G, Islas MA, Garcia E (2021) Adapting H-infinity controller for the desired reference tracking of the sphere position in the maglev process. Inf Sci 569:669–686

    Article  MathSciNet  Google Scholar 

  • Du H, Zhang N, Ji JC, Gao W (2010) Robust fuzzy control of an active magnetic bearing subject to voltage saturation. IEEE Trans Control Syst Technol 18(1):164–169

    Article  Google Scholar 

  • Ferdaus MM, Pratama M, Anavatti SG, Garratt M (2018) A generic self-evolving neuro-fuzzy controller based high-performance hexacopter altitude control system. In: 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp 2784–2791

  • Ferdaus MM, Pratama M, Anavatti SG, Garratt MA, Lughofer E (2020) Pac: A novel self-adaptive neuro-fuzzy controller for micro aerial vehicles. Inf Sci 512:481–505

    Article  MathSciNet  MATH  Google Scholar 

  • Ge D, Zeng X-J (2020) Learning data streams online-an evolving fuzzy system approach with self-learning/adaptive thresholds. Inf Sci 507:172–184

    Article  Google Scholar 

  • Gu X (2021) Multilayer ensemble evolving fuzzy inference system. IEEE Trans Fuzzy Syst 29(8):2425–2431

    Article  Google Scholar 

  • Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501

    Article  Google Scholar 

  • Jiang Z-P, Hill DJ (1999) A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics. IEEE Trans Autom Control 44(9):1705–1711

    Article  MathSciNet  MATH  Google Scholar 

  • Juang C-F, Lin C-T (1999) A recurrent self-organizing neural fuzzy inference network. IEEE Trans Neural Netw 10(4):828–845

    Article  Google Scholar 

  • Kasabov NK, Song Q (2002) DENFIS: dynamic evolving neural-fuzzy inference system and its application for time-series prediction. IEEE Trans Fuzzy Syst 10(2):144–154

    Article  Google Scholar 

  • Le T-L, Lin C-M, Huynh T-T (2018) Self-evolving type-2 fuzzy brain emotional learning control design for chaotic systems using PSO. Appl Soft Comput 73:418–433

    Article  Google Scholar 

  • Leite D, Palhares RM, Campos VCS, Gomide F (2015) Evolving granular fuzzy model-based control of nonlinear dynamic systems. IEEE Trans Fuzzy Syst 23(4):923–938

    Article  Google Scholar 

  • Lemos A, Caminhas W, Gomide F (2011) Multivariable Gaussian evolving fuzzy modeling system. IEEE Trans Fuzzy Syst 19(1):91–104

    Article  Google Scholar 

  • Li D-P, Liu Y-J, Tong S, Chen CLP, Li D-J (2018) Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE Trans Cybern, 1–10

  • Lin C-M, Le T-L, Huynh T-T (2018) Self-evolving function-link interval type-2 fuzzy neural network for nonlinear system identification and control. Neurocomputing 275:2239–2250

    Article  Google Scholar 

  • Liu W, Lim C-C, Shi P, Xu S (2017) Backstepping fuzzy adaptive control for a class of quantized nonlinear systems. IEEE Trans Fuzzy Syst 25(5):1090–1101

    Article  Google Scholar 

  • Lughofer ED (2008) FLEXFIS: A robust incremental learning approach for evolving Takagi-Sugeno fuzzy models. IEEE Trans Fuzzy Syst 16(6):1393–1410

    Article  Google Scholar 

  • Lughofer E, Cernuda C, Kindermann S, Pratama M (2015) Generalized smart evolving fuzzy systems. Evol Syst 6(4):269–292

    Article  Google Scholar 

  • Lughofer E, Pratama M, Skrjanc I (2018) Incremental rule splitting in generalized evolving fuzzy systems for autonomous drift compensation. IEEE Trans Fuzzy Syst 26(4):1854–1865

    Article  Google Scholar 

  • Maciel L, Ballini R, Gomide F (2017) Evolving possibilistic fuzzy modeling for realized volatility forecasting with jumps. IEEE Trans Fuzzy Syst 25(2):302–314

    Article  MATH  Google Scholar 

  • Mahmoud MS (2018) Basics of Fuzzy Control. Fuzzy Control, Estimation and Diagnosis: Single and Interconnected Systems, pp. 15–44. Springer, Cham

  • Martinez DI, de Jesús Rubio J, Garcia V, Vargas TM, Islas MA, Pacheco J, Gutierrez GJ, Meda-Campaña JA, Mujica-Vargas D, Aguilar-Ibañez C (2021) Transformed structural properties method to determine the controllability and observability of robots. Appl Sci11(7)

  • Martinez DI, Rubio JdJ, Aguilar A, Pacheco J, Gutierrez GJ, Garcia V, Vargas TM, Ochoa G, Cruz DR, Juarez CF (2020) Stabilization of two electricity generators. Complexity 2020

  • Mendes J, Maia R, Araújo R, Souza FAA (2020) Self-evolving fuzzy controller composed of univariate fuzzy control rules. Appl Sci 10(17)

  • Pires DS, de Oliveira Serra GL (2019) Methodology for evolving fuzzy Kalman filter identification. Int J Control Autom Syst 17:793–800

    Article  Google Scholar 

  • Pratama M, Anavatti SG, Angelov PP, Lughofer E (2014) PANFIS: A novel incremental learning machine. IEEE Trans Neural Netw Learn Syst 25(1):55–68

    Article  Google Scholar 

  • Pratama M, Anavatti SG, Lughofer E (2014) GENEFIS: Toward an effective localist network. IEEE Trans Fuzzy Syst 22(3):547–562

    Article  Google Scholar 

  • Pratama M, Lu J, Lughofer E, Zhang G, Er MJ (2017) An incremental learning of concept drifts using evolving type-2 recurrent fuzzy neural networks. IEEE Trans Fuzzy Syst 25(5):1175–1192

    Article  Google Scholar 

  • Precup R-E, Bojan-Dragos C-A, Hedrea E-L, Rarinca M-D, Petriu EM (2017) Evolving fuzzy models for the position control of magnetic levitation systems. In: 2017 Evolving and Adaptive Intelligent Systems (EAIS), pp 1–6

  • Precup R-E, Radac M-B, Petriu EM, Roman R-C, Teban T-A, Szedlak-Stinean A-I (2016) Evolving fuzzy models for the position control of twin rotor aerodynamic systems. In: 2016 IEEE 14th International Conference on Industrial Informatics (INDIN), pp. 237–242

  • Precup R-E, Teban T-A, Albu A, Borlea A-B, Zamfirache IA, Petriu M (2020) Evolving fuzzy models for prosthetic hand myoelectric-based control. IEEE Trans Instrum Meas 69(7):4625–4636

    Article  Google Scholar 

  • Rocha Filho OD, de Oliveira Serra GL (2018) Recursive fuzzy instrumental variable based evolving neuro-fuzzy identification for non-stationary dynamic system in a noisy environment. Fuzzy Sets Syst 338:50–89

    Article  MathSciNet  MATH  Google Scholar 

  • Rong H-J, Yang Z-X, Wong PK, Vong CM (2017) Adaptive self-learning fuzzy autopilot design for uncertain bank-to-turn missiles. J Dyn Syst Meas Control 139(4)

  • Rong H-J, Sundararajan N, Huang G-B, Saratchandran P (2006) Sequential adaptive fuzzy inference system (SAFIS) for nonlinear system identification and prediction. Fuzzy Sets Syst 157(9):1260–1275

    Article  MathSciNet  MATH  Google Scholar 

  • Rong H-J, Yang Z-X, Wong PK, Vong CM, Zhao G-S (2017) A novel meta-cognitive fuzzy-neural model with Backstepping strategy for adaptive control of uncertain nonlinear systems. Neurocomputing 230:332–344

    Article  Google Scholar 

  • Rong H-J, Angelov PP, Gu X, Bai JM (2018) Stability of evolving fuzzy systems based on data clouds. IEEE Trans Fuzzy Syst 26(5):2774–2784

    Article  Google Scholar 

  • Silva-Ortigoza R, Hernandez-Marquez E, Roldan-Caballero A, Tavera-Mosqueda S, Silva-Ortigoza G (2021) Sensorless tracking control for a “full-bridge buck inverter-DC motor’’ system: Passivity and flatness-based design. IEEE Access 9:132191–132204

    Article  Google Scholar 

  • Škrjanc I, Iglesias JA, Sanchis A, Leite D, Lughofer E, Gomide F (2019) Evolving fuzzy and neuro-fuzzy approaches in clustering, regression, identification, and classification: A survey. Inf Sci 490:344–368

    Article  Google Scholar 

  • Slotine JJE, Li WP (1991) Applied Nonlinear Control. Prentice-Hall, Englewood, Cliffs, New Jersey

    MATH  Google Scholar 

  • Soriano LA, Zamora E, Vazquez-Nicolas JM, Gerardo H, Balderas D (2020) PD control compensation based on a cascade neural network applied to a robot manipulator. Front Neurorobot 14

  • Subramanian K, Suresh S, Babu RV (2012) Meta-cognitive neuro-fuzzy inference system for human emotion recognition. In: The 2012 International Joint Conference on Neural Networks (IJCNN), pp. 1–7

  • Tong S, Wang T, Li Y, Zhang H (2014) Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics. IEEE Trans Cybern 44(6):910–921

    Article  Google Scholar 

  • Wong PK, Huang W, Vong CM, Yang Z (2020) Adaptive neural tracking control for automotive engine idle speed regulation using extreme learning machine. Neural Comput Appl 232:14399–14409

    Article  Google Scholar 

  • Yang Z-X, Rong H-J, Angelov PP, Yang Z-X (2021) Statistically evolving fuzzy inference system for non-Gaussian noises. IEEE Trans Fuzzy Syst

  • Yang Z-X, Rong H-J, Wong PK, Angelov P, Yang Z-X, Wang H (2021) Self-evolving data cloud-based PID-like controller for nonlinear uncertain systems. IEEE Trans Industr Electron 68(5):4508–4518

    Article  Google Scholar 

  • Yue W, Wang Y, Li T, Yang Z (2021) A new fault tolerant control scheme for non-linear systems by T-S fuzzy model approach. IET Control Theory Appl 15(106):1915–1930

    Google Scholar 

  • Zhou J (2008) Decentralized adaptive control for large-scale time-delay systems with dead-zone input. Automatica 44(7):1790–1799

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. These authors contributed equally to this work.

Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, and School of Aerospace Engineering, Xi’an Jiaotong University, West Xianning Road, Xi’an, 710049, Shaanxi, China

    Zhao-Xu Yang & Hai-Jun Rong

  2. State Key Laboratory of Internet of Things for Smart City, and Department of Electromechanical Engineering, University of Macau, Avenida da Universidade, Taipa, 999078, Macau SAR, China

    Zhao-Xu Yang & Zhi-Xin Yang

Authors
  1. Zhao-Xu Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zhi-Xin Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Hai-Jun Rong
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Hai-Jun Rong.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported in part by the National Natural Sci- ence Foundation of China (Grant Nos. 61976172 and 12002254), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant Nos.2020JQ-013 and 2020JM-072), the Science and Technology Development Fund, Macau SAR (Grant Nos. 0018/2019/AKP and SKL-IOTSC(UM)-2021-2023), the Zhuhai Science and Technology Innovation Bureau Zhuhai-Hong Kong-Macau Special Cooperation Project (Grant No. ZH22017002200001PWC). Besides, the authors would like to thank the support from the Macao Young Scholar Program under Grant No. AM201909.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, ZX., Yang, ZX. & Rong, HJ. Adaptive nonparametric evolving fuzzy controller for uncertain nonlinear systems with dead zone. Evolving Systems 13, 637–651 (2022). https://doi.org/10.1007/s12530-022-09424-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12530-022-09424-6

Keywords