Modeling and control of nonlinear systems with multilayer neural network and its Jacobian

Abstract

During past several years, modeling and control of nonlinear systems with neural networks have emerged as one of the most active and fruitful areas for research in the application of neural networks. Nonlinear systems which are often encountered in industrial processes, in general, do not lend themselves to model by conventional methods because of a lack of informations on parametric and nonparametric nonlinearities. But in case the number of the input-output samples is abundant, neural network modeling provides an efficient way of nonparametric modeling by learning the input-output data samples and resolves most parts of the parametric and nonparametric identification problems. In the modeling of nonlinear systems, multilayer neural networks have been widely accepted for their ability of generalizations and simple learning rules known as error backpropagation. In modeling nonlinear systems by learning the input-output data samples with neural networks, there may be some cases that Jacobian of system are available. Or in some cases, it is possible to extract Jacobian from input-output data, though it is very noisy. In this dissertation, we firstly develop the method of estimating Jacobian from multilayer neural networks and then the Jacobian learning method is developed. The Jacobian estimation can provide a valuable information in controlling the nonlinear systems. And the proposed Jacobian learning method is shown to be able to provide an efficient way of suppressing overfitting and acceleration of learning speed. The Jacobian learning method can be incorporated with conventional input-output data mapping and it is named as hybrid learning method. The proposed method is shown to be improve learning speed and promoting generalizations in modeling the highly nonlinear systems through numerical experiments. The basic architecture of controlling nonlinear system with neural network is inverse control. Though inversion control has simple structure, it shows some...