Prediction of Optimal Trajectories with Neural Networks

Optimal control problems arise naturally in many fields of application. Often, they need to be solved many times with only small changes in their dependent variables, or to respond to new choices of dependent variables in real time. However, most of the commonly used numerical solvers are computationally expensive and often unable to make predictions in very short amounts of time. Each new scenario usually results in a complete rerun of the numerical solver. In this thesis, we propose a deep learning approach to optimal control, that predicts optimal trajectories in a supervised manner. For this purpose, a deep learning model is presented with a series of examples of already solved optimal control trajectories. After a computationally expensive training phase, the deep learning model predicts optimal trajectories with instantaneous response time. A simple feed forward neural network and an autoencoder approach for dimensionality reduction of the high-dimensional trajectory data are presented and applications to both fixed and free end-time optimal control problems are discussed.