Initial-training-free online sequential extreme learning machine based adaptive engine air–fuel ratio control

  • Pak Kin WongEmail author
  • Xiang Hui Gao
  • Ka In Wong
  • Chi Man Vong
  • Zhi-Xin Yang
Original Article


In modern automotive engines, air–fuel ratio (AFR) strongly affects exhaust emissions, power, and brake-specific consumption. AFR control is therefore essential to engine performance. Most existing engine built-in AFR controllers, however, are lacking adaptive capability and cannot guarantee long-term control performance. Other popular AFR control approaches, like adaptive PID control or sliding mode control, are sensitive to noise or needs prior expert knowledge (such as the engine model of AFR). To address these issues, an initial-training-free online sequential extreme learning machine (ITF-OSELM) is proposed for the design of AFR controller, and hence a new adaptive AFR controller is developed. The core idea is to use ITF-OSELM for identifying the AFR dynamics in an online sequential manner based on the real-time engine data, and then use the ITF-OSELM model to calculate the necessary control signal, so that the AFR can be regulated. The contribution of the proposed approach is the integration of the initial-training-free online system identification algorithm in the controller design. Moreover, to guarantee the stability of the closed-loop control system, a stability analysis is also conducted. To verify the feasibility and evaluate the performance of the proposed AFR control approach, simulations on virtual engine and experiments on real engine have been carried out. Both results show that the proposed approach is effective for AFR regulation.


Automotive engine Air–fuel ratio Online sequential extreme learning machine Adaptive control 



Input weight of the ith hidden node


Bias of the ith hidden node


Error between system output and reference

\({\hat {e}_{k+1}}\)

Error between system output and model prediction

\(g\left( {{{\varvec{x}}_k}} \right)\)

Part of system to be identified

\(\hat {g}({{\varvec{x}}_k},{\varvec{\beta}_g})\)

Approximating function for function \(g\left( {{{\varvec{x}}_k}} \right)\)


Mapping function of the ith hidden node


Hidden layer output for function \(g\)

\({{\varvec{H}}_\varphi }\)

Hidden layer output for function \(\varphi\)


Identity matrix


Initial updating term for ITF-OSELM


Updated term by using the \((k+1)\)th arriving training data




Control signal of the kth step


Time varying factor


System state at the kth step


System output for control signal \({u_k}\)

\({\hat {y}_{k+1}}\)

Model prediction for control signal \({u_k}\)

\({y_{r\left( {k+1} \right)}}\)

Tracking reference of the (k + 1)th step


Initial output weights


Updated output weights by using the \((k+1)\)th arriving training data


Output weights of approximating function \(\hat {g}\)

\({\varvec{\beta}_\varphi }\)

Output weights of approximating function \(\hat {\varphi }\)


Regularization factor

\(\lambda \left( t \right)\)

Measured lambda value at time \(t\)

\({\lambda _d}\left( t \right)\)

Desired lambda value at time \(t\)


Forgetting factor

\(\varphi ({{\varvec{x}}_k})\)

Part of system to be identified

\(\hat {\varphi }({{\varvec{x}}_k},{\varvec{\beta}_\varphi })\)

Approximating function for function \(\varphi ({{\varvec{x}}_k})\)



This study is funded by the University of Macau Research Grant under Grant numbers: MYRG2017-00135-FST, MYRG2016-00134-FST and MYRG2016-00212-FST and the Science and Technology Development Fund of Macau S.A.R. under Grant numbers: 050/2015/A, 012/2015/A and 015/2015/AMJ.


  1. 1.
    EndTuning (2007) Air fuel ratios and stoichiometry. Accessed 10 Jan 2017
  2. 2.
    Kumar M, Shen T (2015) Estimation and feedback control of air-fuel ratio for gasoline engines. Control Theory Technol 13:151–159. MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ranga A, Surnilla G, Thomas J, Sanborn E, Linenberg M (2017) Adaptive algorithm for engine air–fuel ratio control with dual fuel injection systems. SAE technical paper 2017-01-0588.
  4. 4.
    Franceschi EM, Muske KR, Jones JCP, Makki I (2007) An adaptive delay-compensated PID air fuel ratio controller. SAE Paper no. 2007-01-1342.
  5. 5.
    Ebrahimi B, Tafreshi R, Masudi H, Franchek M, Mohammadpour J, Grigoriadis K (2012) A parameter-varying filtered PID strategy for air-fuel ratio control of spark ignition engines. Control Eng Pract 20:805–815. CrossRefGoogle Scholar
  6. 6.
    Choi SB, Hedrick JK (1998) An observer-based controller design method for improving air/fuel characteristics of spark ignition engines. IEEE Trans Control Syst Technol 6:325–334. CrossRefGoogle Scholar
  7. 7.
    Yoon P, Sunwoo M (2001) An adaptive sliding mode controller for air-fuel ratio control of spark ignition engines. Proc Inst Mech Eng Part D J Automob Eng 215:305–315. CrossRefGoogle Scholar
  8. 8.
    Pace S, Zhu GMG (2012) Sliding mode control of both air-to-fuel and fuel ratios for a dual-fuel internal combustion engine. ASME Trans J Dyn Syst Meas Control 134:1–12. CrossRefGoogle Scholar
  9. 9.
    Ebrahimi B, Tafreshi R, Mohammadpour J, Franchek M, Grigoriadis K, Masudi H (2014) Second-order sliding mode strategy for air-fuel ratio control of lean-burn SI engines. IEEE Trans Control Syst Technol 22:1374–1384. CrossRefGoogle Scholar
  10. 10.
    Wu HM, Tafreshi R (2018) Fuzzy sliding-mode strategy for air–fuel ratio control of lean-burn spark ignition engines. Asian J Control 20(1):149–158. MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Pan YP, Yu HY (2016) Composite learning from adaptive dynamic surface control. IEEE Trans Autom Control 61(9):2603–2609. MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Liu H, Pan YP, Li SG, Chen Y (2017) Adaptive fuzzy backstepping control of fractional-order nonlinear systems. IEEE Trans Syst Man Cyber Syst 47(8):2209–2217. CrossRefGoogle Scholar
  13. 13.
    Gao XH, Wong KI, Wong PK, Vong CM (2016) Adaptive control of rapidly time-varying discrete-time system using initial-training-free online extreme learning machine. Neurocomputing 194:117–125. CrossRefGoogle Scholar
  14. 14.
    Rong HJ, Wei JT, Bai JM, Zhao GS, Liang YQ (2015) Adaptive neural control for a class of MIMO nonlinear systems with extreme learning machine. Neurocomputing 149:405–414. CrossRefGoogle Scholar
  15. 15.
    Rong HJ, Zhao GS (2013) Direct adaptive neural control of nonlinear systems with extreme learning machine. Neural Comput Appl 22(3–4):577–586. CrossRefGoogle Scholar
  16. 16.
    Rong HJ, Suresh S, Zhao GS (2011) Stable indirect adaptive neural controller for a class of nonlinear system. Neurocomputing 74(16):2582–2590. CrossRefGoogle Scholar
  17. 17.
    Wong KI (2017) Machine-learning-based modeling of biofuel engine systems with applications to optimization and control of engine performance. Dissertation, University of MacauGoogle Scholar
  18. 18.
    Liang NY, Huang GB, Saratchandran P, Sundararajan N (2006) A fast and accurate online sequential learning algorithm for feedforward networks. IEEE Trans Neural Netw 17:1411–1423. CrossRefGoogle Scholar
  19. 19.
    Huynh HT, Won Y (2011) Regularized online sequential learning algorithm for single-hidden layer feedforward neural networks. Pattern Recognit Lett 32:1930–1935. CrossRefGoogle Scholar
  20. 20.
    Mirza B, Lin Z, Toh KA (2013) Weighted online sequential extreme learning machine for class imbalance learning. Neural Process Lett 38:465–486. CrossRefGoogle Scholar
  21. 21.
    Li XL, Jia C, Liu DX, Ding DW (2014) Adaptive control of nonlinear discrete-time systems by using OS-ELM neural networks. Abstr Appl Anal (Article ID 267609) MathSciNetGoogle Scholar
  22. 22.
    LeCun YA, Bottou L, Orr GB, Müller KR (2012) Efficient backprop. In: Montavon G, Orr GB, Müller KR (eds) Neural networks: tricks of the trade. Springer, Berlin, pp 9–48. CrossRefGoogle Scholar
  23. 23.
    Li GY (2007) Application of intelligent control and MATLAB to electronically controlled engines (in Chinese). Publishing House of Electronics Industry, BeijingGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Pak Kin Wong
    • 1
    Email author
  • Xiang Hui Gao
    • 2
  • Ka In Wong
    • 3
  • Chi Man Vong
    • 4
  • Zhi-Xin Yang
    • 1
  1. 1.Department of Electromechanical EngineeringUniversity of MacauMacauChina
  2. 2.Key Laboratory of Machine Learning and Computational Intelligence, College of Mathematics and Information ScienceHebei UniversityBaodingChina
  3. 3.Institute for the Development and QualityMacauChina
  4. 4.Department of Computer and Information ScienceUniversity of MacauMacauChina

Personalised recommendations