Robust Adaptive Fourier Neural Network Control for Unknown Nonlinear Systems

The past two decades have witnessed major advances in neural network based control, which has proven to be an efficient technique for unknown nonlinear systems. However, due to heavy computation cost and slow convergent speed, many existing NN may not be suitable for on-line control applications. Moreover, both the determination of network topology and stability analysis of closed-loop system are not easy to be carried out. These drawbacks have prevented them from being widely used in control design. In this talk, a robust adaptive Fourier neural network (FNN) based control scheme is proposed for the control of unknown nonlinear systems. A class of nonlinear systems to be considered is described in a new reduced-order model in the state space. Via the new model, all the nonlinearities and uncertainties of a system are included in a nonlinear function, and therefore the control problem is converted into a function approximation problem. In order to solve this problem and avoid the abovementioned drawbacks of conventional NNs, a new type of NN, Fourier NN, is developed in the light of complex Fourier analysis and neural network theory. Because the choice of basis functions will strongly influence the performance of an NN, we employ orthogonal complex Fourier exponentials as the basis functions of the FNN. Due to the orthogonality of the basis functions, the FNN has a rich knowledge representation capability and is suitable for real time control applications.