## 1 Introduction  
In recent years, with the gradual scarcity of non-renewable energy resources, people have been eager to find alternatives to fossil fuel. Against this background, many researchers have considered fuel cell electricity generation with higher energy efficiency, which produces water, heat, less noise, no radiation and negligible amounts of pollutants [1; 2; 3; 4; 5]. The solid oxide fuel cell (SOFC) is a type of fuel cell that uses solid oxide material as the electrolyte to send negative oxygen ions from the cathode to the anode, where a chemical reaction related to the electrochemical oxidation occurs [6; 7; 8; 9; 10]. SOFCs have many advantages, such as flexibility in selecting fuel, long-term stability and no need for an expensive catalyst. However, some serious problems due to sluggish dynamics, nonlinearity, fuel starvation, external disturbance, unavailability of some key measurements and tight operating constraints often occur in the actual control process of an SOFC [11]. Therefore, the control strategy of the SOFC system is still a challenging problem. The complex dynamical system of an SOFC is often subject to imprecise models and a priori unknown disturbances. Therefore, some model-based control methods cannot satisfy the control objective due to the model-reality discrepancy [12; 13]. To obtain an approximate model of the SOFCunder unknown parameters, many algorithms based on the neural network model [14; 15; 16] have been proposed. In this paper, a Wiener-type neural network is employed to achieve the identification of the model of SOFC. On the one hand, neural networks are widely used in identification and control of nonlinear systems with complex dynamics due to their ability to approximate any nonlinear function. They have several advantages, for example, the unique learning ability of a neural network makes it able to adapt to the changes of the system and environment. The powerful parallel computing ability makes it possible to carry out a large number of complex operations quickly. Besides, the multi-input multi-output model structure makes it possible to facilitate identification and control of multivariable systems. In [14], a fuzzy neural network controller was proposed for the control of active and reactive power of an SOFC-based system. In [15], an artificial neural network was used to establish the model of SOFC and predict the performance and parameters of SOFC. In [16], a nonlinear predictive controller based on an improved radial basis function neural network identification model was designed to guarantee the fuel utilization to operate within a safe range. On the other hand, the Wiener model composed of a linear dynamic system and a static nonlinear system in series has a clear internal structure and can be used to express the nonlinear characteristics of common systems in most cases. Besides, the model is often employed based on some intelligence algorithms like a neural network [17; 18]. It has attracted wide attention for a long time and has been applied in many research fields. In [17], the authors gave a method of the Wiener identification model in series connected by a linear dynamic neuron and static BP neural network. In [18], a nonlinear Wiener model combined with the Laguerre function and a BP network was presented, which had strong robustness due to the information of the model being non-essential. In addition, the problem of input constraints, which can impact the system performance and stability, is ignored by many researchers. Notice that in terms of preventing fuel from being overused in an SOFC system, the expected scope of fuel utilization must be maintained from 0.7-0.9, which should further take the input constraints into consideration. Then, various constraint problems have been considered in closed-loop control systems [19; 20; 21; 22; 23]. At present, most of the constrained control approaches for the SOFC system focus on model predictive control (MPC) [5; 24; 25; 26; 27].