## 5 Conclusions  
In this paper, a new adaptive tracking constrained control strategy based on the online-updated Wiener-type neural network has been proposed for the SOFC, in which we provide a new effective alternative to overcome the control difficulty of the SOFC. Firstly, the nonlinear dynamical model of SOFC is investigated, and the volt-ampere characteristics for the SOFC are presented. Secondly, the dynamic model of the SOFC is approached using the Wiener model formulation, and the parameters of the model are estimated via adaptive Wiener model identification. Thirdly, an adaptive exponential  
Figure 10: The curves of the Wiener-type neural network weight coefficients.  
Figure 9: The curves of exponential PID parameters.  
PID controller is designed to achieve the tracking performance of voltage, with an anti-windup compensator utilized to eliminate the harm of saturation considering the input magnitude and rate constraints. Fourthly, the stability of the proposed control system is proven via the Lyapunov function. Finally, the simulation is carried out in the MATLAB/Simulink environment, and the simulation results are analyzed to show that the proposed adaptive tracking constrained control approach possesses good effectiveness when dealing with nonlinear systems with complicated dynamics. Future work will include solving the problem of output constraints, improving our control algorithm to obtain a better tracking performance, and so on.  
All authors contributed to designing and performing measurements, data analysis, scientific discussions, and writing the article.  
This work was partially supported by the National Natural Science Foundation of China (61503156), National Key Research and Development Program (2016 YFD0400301), Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network, Nanjing Institute of Technology (XTCX201806), National first-class discipline program of Food Science and Technology (JUFSTR20180205), and State Grid Zhejiang Province Technology Project (SGTYHT/17-JS-201)  
The authors declare no conflict of interest, and the founding sponsors had no role in the design of the study, in the collection, analyses or interpretation of data, in the writing of the manuscript, nor in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} \(T_{0}\) & Absolute temperature (K) \\ \(F_{0}\) & [PERSON]'s constant (C/mol) \\ \(R_{0}\) & Universal gas constant (J/mol \(\cdot\) K) \\ \(E_{0}\) & Ideal standard potential (V) \\ \(N_{0}\) & Number of cells in the stack \\ \(K_{r}\) & Constant, \(K_{r}=N_{0}/4F_{0}\) (mol/s \(\cdot\) A) \\ \(K_{\rm H_{2}}\) & Valve molar constant for hydrogen (mol/s \(\cdot\) Pa) \\ \(K_{\rm H_{2}O}\) & Valve molar constant for water (mol/s \(\cdot\) Pa) \\ \(K_{\rm O_{2}}\) & Valve molar constant for oxygen (mol/s \(\cdot\) Pa) \\ \(\tau_{\rm H_{2}}\) & Response time of hydrogen flow (s) \\ \(\tau_{\rm H_{2}O}\) & Response time of water flow (s) \\ \(\tau_{\rm O_{2}}\) & Response time of oxygen flow (s) \\ \(\tau_{\rm H-O}\) & Ratio of hydrogen to oxygen \\ \(r\) & Ohmic loss (\(\Omega\)) \\ \(\tau_{f}\) & Time constant for the fuel processor (s) \\ \(\delta\) & Tafel constant \\ \(\beta\) & Tafel slope \\ \(I_{L}\) & Limiting current density (A) \\ \(p_{\rm H_{2}}\) & Partial pressure for hydrogen (Pa) \\ \(p_{\rm H_{2}O}\) & Partial pressure for water (Pa) \\ \(p_{\rm O_{2}}\) & Partial pressure for oxygen (Pa) \\ \(q_{\rm H_{2}}^{\rm\mu}\) & Input flow rate for hydrogen (mol/s) \\ \(q_{\rm O_{2}}^{\rm\mu}\) & Input flow rate for oxygen (mol/s) \\ \(q_{\rm H_{2}}^{\rm\sigma}\) & Reacted flow rate for hydrogen (mol/s) \\ \(q_{\rm H_{2}}^{\rm\sigma}\) & Output flow rate for hydrogen (mol/s) \\ \(V_{dc}\) & The stack output voltage (V) \\ \(q_{f}\) & Natural gas flow rate (mol/s) \\ \(I\) & Load current (A) \\ \(\rho\) & Fuel utilization \\ \end{tabular}