Control and Analysis of Nonlinear Systems using Neural Networks

D. Karimanzira and P. Otto (Germany)


Neural networks, linearization, predictive control, selftuning control, system analysis


Nonlinear processes are very difficult to control and analyze with conventional methods. This paper presents a scheme based on a method for extracting linear models from a nonlinear neural network and using these in the control system design and analysis of the system's nonlinear behavior. A neural network (NN) is used for modeling the process and a gain-scheduling type of General Predictive Controller (GPC) is subsequently designed. In our work we have chosen to restrict the attention to the so-called multilayer perceptron neural networks (MLP). To illustrate some of the major characteristics of the scheme, it is applied to control and analyze a propeller arm and a pneumatic positioning system. To investigate the nonlinearities, the coefficients of the extracted linear models are plotted. This plot gives a good indication of the "degree of nonlinearity". Perhaps a better illustration of the variations in process dynamics is accomplished by showing the location of the poles in the complex plane. Naturally the method has its shortcomings. When the nonlinearities are not reasonably smooth, the linearized models will be valid only in the proximity of the current operating point. In practice this implies that the design will also be highly sensitive to overparameterized models. In fact, it may be advantageous to underparameterize the network deliberately (or use a large weight decay) to impose certain smoothness on the network.

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