The tracking control problem of nonlinear systems has been a difficult and important subject in the literature. During the past two decades, much has been written about the neural network (NN) control method, which is regarded as a powerful control technique due to its ability to learn, adapt and approximate nonlinear functions to desired degrees of accuracy. Although it has been successful in many applications, some difficulties still exist, such as the determination of the network structure, the selection of parameters of the activation function, local minimum, and stability analysis of the closed-loop system. These problems have prevented the NNs from being widely adopted in the control field....[ Read more ]

The tracking control problem of nonlinear systems has been a difficult and important subject in the literature. During the past two decades, much has been written about the neural network (NN) control method, which is regarded as a powerful control technique due to its ability to learn, adapt and approximate nonlinear functions to desired degrees of accuracy. Although it has been successful in many applications, some difficulties still exist, such as the determination of the network structure, the selection of parameters of the activation function, local minimum, and stability analysis of the closed-loop system. These problems have prevented the NNs from being widely adopted in the control field.

In this thesis, a novel Fourier neural network (FNN) based control scheme is proposed to deal with the tracking control problems for a class of unknown nonlinear systems. A strong motivation for the research is to overcome the abovementioned problems currently existing in conventional NN controllers. The FNN is established in the light of Fourier analysis and neural network theory. Because the choice of activation functions strongly influences the performance of an NN, the orthogonal complex Fourier exponentials are employed to construct the proposed network. Therefore, the FNN has a rich representation capability and is suitable for real time control purpose.

Due to the clear physical meaning of the hidden layer neurons, the determination of network topology as well as the parameters of the activation functions becomes convenient. The learning algorithm of FNN is actually performed in the frequency domain, so that it is capable of changing both the magnitude and the phase of the input function. As a result the phase lag phenomenon can be well handled and the tracking control performance is greatly improved.

The proposed control method was implemented and tested with different setups. Without a priori knowledge of the system model, all the nonlinearities and uncertainties were lumped together and compensated for by the FNN. The experimental results have led to a more complete undertanding of the FNN and verified the effecitveness of the proposed control scheme.

Key words: Fourier neural network, orthogonal activation functions, unknown nonlinear systems, frequency domain, tracking control