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

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Abstract

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.

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Abbreviations

\({{\text{a}}_i}\) :

Input weight of the ith hidden node

\({b_i}\) :

Bias of the ith hidden node

\({e_{k+1}}\) :

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

\(G({{\text{a}}_i},{b_i},{{\varvec{x}}_k})\) :

Mapping function of the ith hidden node

\({{\varvec{H}}_g}\) :

Hidden layer output for function \(g\)

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

Hidden layer output for function \(\varphi\)

\({\varvec{I}}\) :

Identity matrix

\({{\varvec{P}}_0}\) :

Initial updating term for ITF-OSELM

\({{\varvec{P}}_{k+1}}\) :

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

t :

Time

\({u_k}\) :

Control signal of the kth step

\({v_t}\) :

Time varying factor

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

System state at the kth step

\({y_{k+1}}\) :

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

\({\varvec{\beta}^0}\) :

Initial output weights

\({\varvec{\beta}^{({\varvec{k}}+1)}}\) :

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

\({\varvec{\beta}_g}\) :

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

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

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

\(\gamma\) :

Regularization factor

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

Measured lambda value at time \(t\)

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

Desired lambda value at time \(t\)

\(\rho\) :

Forgetting factor

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

Part of system to be identified

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

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

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Electromechanical Engineering, University of Macau, Macau, China

    Pak Kin Wong & Zhi-Xin Yang

  2. Key Laboratory of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding, Hebei, China

    Xiang Hui Gao

  3. Institute for the Development and Quality, Macau, China

    Ka In Wong

  4. Department of Computer and Information Science, University of Macau, Macau, China

    Chi Man Vong

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  1. Pak Kin Wong
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Correspondence to Pak Kin Wong.

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Wong, P.K., Gao, X.H., Wong, K.I. et al. Initial-training-free online sequential extreme learning machine based adaptive engine air–fuel ratio control. Int. J. Mach. Learn. & Cyber. 10, 2245–2256 (2019). https://doi.org/10.1007/s13042-018-0863-0

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