Neural networks for optimal control

Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process. The process model is the well-known Innovation State Space model. Firstly, the observer network is trained with a Recursive Prediction Error Method using a Gauss-Newton search direction to minimize the the prediction error. Next, the trained observer network is applied in a closed-loop simulation to train another neural network, the controller. During this training an optimal control cost function is minimized using a recursive, off-line, backward training method, similar to the Back Propagation Through Time (BPTT) method. Finally, a practical, non-linear, noisy and multi-variable example confirms, that the model and the training methods are a promising technique to control non-linear processes, which are difficult to model.