This study used Xilinx Field Programmable Gate Arrays (FPGAs) to implement a functional neuro-fuzzy network (FNFN) for solving nonlinear control problems. A functional link neural network (FLNN) was used as the consequent part of the proposed FNFN model. This study adopted the linear independent functions and the orthogonal polynomials in a functional expansion of the FLNN. Thus, the design of the FNFN model could improve the control accuracy. The learning algorithm of the FNFN model was divided into structure learning and parameter learning. The entropy measurement was adopted in the structure learning to determine the generated new fuzzy rule, whereas the gradient descent method in the parameter learning was used to adjust the parameters of the membership functions and the weights of the FLNN. In order to obtain high speed operation and real-time application, a very high speed integrated circuit hardware description language (VHDL) was used to design the FNFN controller and was implemented on FPGA. Finally, the experimental results demonstrated that the proposed hardware implementation of the FNFN model confirmed the viability in the temperature control of a water bath and the backing control of a car.Electronics 2018, 7, 145 2 of 22 the accuracy of functional approximation. Corresponding to a FLNN, each fuzzy rule comprises a functional expansion of inputs. The linearly independent functions and orthogonal polynomials are used in FLNN. The learning algorithm was divided into structure learning and parameter learning and used for constructing the FNFN automatically. Initially, no rules existed in the FNFN model. In the structure learning algorithm, the entropy measure was used to determine a whether a new node needed to be added. In the parameter learning, the backpropagation leaning method was used to adjust the parameters of the FNFN model.Real-time control is very important in industrial process control system applications. For rapid computing hardware engineering, real-time control becomes more feasible [10]. Recently, there has been a focus on the hardware implementation [11] of artificial neural networks (ANNs). Furthermore, the realization that a hybrid of neural networks and fuzzy systems presents an even more powerful form of computational intelligence [12] provides additional motivation to complete hardware implementation. The main reason for hardware implementation is that it has high speed processing and real-time operating capability. In many applications, hardware implementation requires larger arrays and has resorted to digital simulation, which are usually built using digital integrated circuits. Development of digital integrated circuits such as FPGA [13] makes the hardware implementation process programmable and flexible. Recently, the hardware implementation of neural networks has been successfully implemented. Li et al.[10] discussed various aspects of the hardware implementation of an artificial neural network (ANN), e.g., generic architecture, back propagation, precision, etc. One of the b...