Robust composite adaptive neural network control for air management system of PEM fuel cell based on high-gain observer


Polymer electrolyte membrane (PEM) fuel cell system is usually affected negatively by external disturbance, model uncertainties and unmeasured variables. In this paper, a robust composite adaptive neural network controller using high-gain observer is proposed to achieve stable oxygen excess ratio control for PEM fuel cell air management system. First, the derivatives of system output, which are unavailable due to the limited sensors, are estimated via high-gain observer. Then, a neural network is adopted to estimate the unknown system dynamics and the additional robust term is used to attenuate the compound disturbance including unknown external disturbance and neural network approximation error. Finally, a composite adaptive updating laws are constructed by utilizing estimated tracking error and modeling error to improve the tracking performance. In contrast to the existing controllers applied in PEM fuel cell air management system, this controller has a better control performance in the practical application. By means of Lyapunov stability analysis, it is theoretically proved that the system tracking error is uniformly ultimately bounded. The effectiveness and practicability of the proposed controller are validated by hardware-in-loop experiment.

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Polymer electrolyte membrane


Oxygen excess ratio




Radial basis function neural network


Composite adaptive radial basis function neural network




Root mean square error


Standard deviation


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Natural Science Foundation of China (Grand No. 51775103).

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Correspondence to Yongfu Wang.

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In this appendix, we define the values of the constants \(\mu _{1}\)\(\mu _{4}\) and \(c_{1}\)\(c_{16}\) in Table 5 and the detailed parameters of model in Table 6.

Table 5 Expression of parameters \(\mu _{i}\) and \(c_{i}\) [12]
Table 6 Physical parameters of fuel cell system [12]

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Wang, Y., Wang, Y. & Chen, G. Robust composite adaptive neural network control for air management system of PEM fuel cell based on high-gain observer. Neural Comput & Applic 32, 10229–10243 (2020).

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  • Composite adaptive control
  • Neural network
  • High-gain observer
  • Polymer electrolyte membrane (PEM) fuel cell