Neural Network Toolbox

Introduction

Neural networks have been applied very successfully in the identification and control of dynamic systems. The universal approximation capabilities of the multilayer perceptron make it a popular choice for modeling nonlinear systems and for implementing general-purpose nonlinear controllers [HaDe99]. This chapter introduces three popular neural network architectures for prediction and control that have been implemented in the Neural Network Toolbox:

• Model Predictive Control
• NARMA-L2 (or Feedback Linearization) Control
• Model Reference Control

This chapter presents brief descriptions of each of these architectures and demonstrates how you can use them.

There are typically two steps involved when using neural networks for control:

1. System Identification
2. Control Design

In the system identification stage, you develop a neural network model of the plant that you want to control. In the control design stage, you use the neural network plant model to design (or train) the controller. In each of the three control architectures described in this chapter, the system identification stage is identical. The control design stage, however, is different for each architecture.

• For the model predictive control, the plant model is used to predict future behavior of the plant, and an optimization algorithm is used to select the control input that optimizes future performance.
• For the NARMA-L2 control, the controller is simply a rearrangement of the plant model.
• For the model reference control, the controller is a neural network that is trained to control a plant so that it follows a reference model. The neural network plant model is used to assist in the controller training.

The next three sections of this chapter discuss model predictive control, NARMA-L2 control and model reference control. Each section consists of a brief description of the control concept, followed by a demonstration of the use of the appropriate Neural Network Toolbox function. These three controllers are implemented as Simulink® blocks, which are contained in the Neural Network Toolbox blockset.

To assist you in determining the best controller for your application, the following list summarizes the key controller features. Each controller has its own strengths and weaknesses. No single controller is appropriate for every application.

• Model Predictive Control. This controller uses a neural network model to predict future plant responses to potential control signals. An optimization algorithm then computes the control signals that optimize future plant performance. The neural network plant model is trained offline, in batch form, using any of the training algorithms discussed in Chapter 5. (This is true for all three control architectures.) The controller, however, requires a significant amount of on-line computation, since an optimization algorithm is performed at each sample time to compute the optimal control input.
• NARMA-L2 Control. This controller requires the least computation of the three architectures described in this chapter. The controller is simply a rearrangement of the neural network plant model, which is trained offline, in batch form. The only online computation is a forward pass through the neural network controller. The drawback of this method is that the plant must either be in companion form, or be capable of approximation by a companion form model. (The companion form model is described later in this chapter.)
• Model Reference Control. The online computation of this controller, like NARMA-L2, is minimal. However, unlike NARMA-L2, the model reference architecture requires that a separate neural network controller be trained off-line, in addition to the neural network plant model. The controller training is computationally expensive, since it requires the use of dynamic backpropagation [HaJe99]. On the positive side, model reference control applies to a larger class of plant than does NARMA-L2 control.

Control Systems

NN Predictive Control

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