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NARMA-L2 (Feedback Linearization) Control

The neurocontroller described in this section is referred to by two different names: feedback linearization control and NARMA-L2 control. It is referred to as feedback linearization when the plant model has a particular form (companion form). It is referred to as NARMA-L2 control when the plant model can be approximated by the same form. The central idea of this type of control is to transform nonlinear system dynamics into linear dynamics by canceling the nonlinearities. This section begins by presenting the companion form system model and demonstrating how you can use a neural network to identify this model. Then it describes how the identified neural network model can be used to develop a controller. This is followed by a demonstration of how to use the NARMA-L2 Control block, which is contained in the Neural Network Toolbox™ block set.

Identification of the NARMA-L2 Model

As with model predictive control, the first step in using feedback linearization (or NARMA-L2) control is to identify the system to be controlled. You train a neural network to represent the forward dynamics of the system. The first step is to choose a model structure to use. One standard model that is used to represent general discrete-time nonlinear systems is the nonlinear autoregressive-moving average (NARMA) model. The moving average model is essentially a finite impulse response filter with some additional interpretation placed on it. This is the identification procedure used for the NN Predictive Controller. The only problem with using this controller is that if you want to train a neural network to create the function G to minimize mean square error, you need to use dynamic backpropagation ([NaPa91] or [HaJe99]). This can be quite slow. One solution, proposed by Narendra and Mukhopadhyay [NaMu97], is to use approximate models to represent the system. The controller used in this section is based on the NARMA-L2 approximate model.