Approximate Time Optimal Control by Deep Neural Networks Trained with Numerically Obtained Optimal Trajectories

This paper focuses on online time optimal control of nonlinear systems. This is achieved by approximating the results of time optimal control problems (TOCP) with deep neural networks (DNN) depending on the initial and terminal system state. In general, solving a TOCP for nonlinear systems is a computationally challenging task. Especially in the context of time optimal nonlinear model predictive control (TMPC) with hard real time constraints successful termination of a TOCP within sample times suitable for controlling mechanical systems cannot be guaranteed. Therefore, our approach is to train three DNNs with different aspects of numerical solutions of TOCPs with random initial and terminal state. These networks can then be used to approximate the TMPC by a one step model predictive control scheme with a significantly simpler structure and decreased calculation time. In order to verify this procedure by simulation, it is applied to a prove of concept example as well as the model of an industrial robot.