Introduction to Neural Network Control Systems

Neural networks have been applied 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 topic introduces three popular neural network architectures for prediction and control that have been implemented in the Deep Learning Toolbox™ software, and presents brief descriptions of each of these architectures and shows how you can use them:

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

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

System identification
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 topic, the system identification stage is identical. The control design stage, however, is different for each architecture:

For 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 NARMA-L2 control, the controller is simply a rearrangement of the plant model.
For 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 discuss model predictive control, NARMA-L2 control, and model reference control. Each section consists of a brief description of the control concept, followed by an example of the use of the appropriate Deep Learning Toolbox function. These three controllers are implemented as Simulink^® blocks, which are contained in the Deep Learning 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. (This is true for all three control architectures.) The controller, however, requires a significant amount of online computation, because 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 these three architectures. 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. (Identification of the NARMA-L2 Model describes the companion form model.)
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 offline, in addition to the neural network plant model. The controller training is computationally expensive, because 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.