Abstract
In this paper, we propose a heterogeneous hidden layer consisting of both sigmoid functions and RBFs (Radial Basis Functions) in multi-layered neural networks and present a method for implementing the neural network to control systems. Focusing on the orthogonal relationship between the sigmoid function and its derivative, a derived RBF that is a derivative of the sigmoid function is used as the RBF in the neural network, so the proposed neural network is called an ONN (Orthogonal Neural Network) and the function mapping with the ONN can be treated as a kind of an orthogonal function series model. Identification results using a nonlinear function confirm both the ONN's feasibility and characteristics by comparing with those obtained using a conventional neural network which has sigmoid function or RBF in hidden layer. Using the ONN, a parallel type neural controller, which uses both the ONN output and the conventional control output as an objective system control input, is proposed. Simulation results for discrete-time nonlinear SISO system demonstrate the applicability of the neural controller for controlling nonlinear systems and experimental results for controlling angular velocity of a DC servo motor demonstrate its usefulness for controlling practical systems.
