Neural network approaches to some model flow control problems

The application of two neural network approaches (supervised neural network and adaptive neural network) to control some flows modeled by the Burgers equation and the Wave equation is studied. Due to its capability of handling nonlinearity and its parallel processing structure, a neural network is suitable as an adaptive controller in real time. The simple mapping type feedforward multilayer neural network controller is trained with the data set obtained from the optimal and robust control laws, while the adaptive neural network controller is obtained by applying a feedback linearization method. The neural network is used to estimate the function of the system. The simple mapping type neural network requires off-line (or supervised) training with the sets of data while the adaptive neural network controller does not require an off-line training phase. The dynamic sequential recursive backpropagation algorithm is used to train the adaptive neural network on-line according to a modeling error. Both approaches result in successfully obtaining the controller for randomly disturbed flows. It should be noted, however, that the simple mapping type neural network controller results in offset from zero, even though the offset is very small and is adjusted easily.