Neural network enhancement of closed-loop controllers for nonlinear systems

The actual trend is to combine traditional control methods with neural network's in parallel. This paper places the neural network inside the closed loop, in series with the existing controller. With the neural network, inside the closed-loop, randomly initialized weights, unknown performance levels, and multiple reinitializations are more difficult. A problem not so readily seen is that the weights update rules for neural networks were not designed to workin a feedback setting but in a feed-forward setting. The derivation of update rules, particularly for back propagation, were based on the independence of the weights and the input to the neural network. For a neural network, in the closed-loop, the assumption is no more valid; therefore, a new update rule had to be derived.