A Neural Approximation to Continuous Time Reachability Computations

A method for approximating viability computations using neural networks is developed, with the aim of combating the "curse of dimensionality". The viability problem is first formulated in an optimal control setting. Our algorithm extracts random initial conditions and then uses randomization to explore the space of bang-bang controls in an attempt to find viable trajectories starting at the given initial condition. The cost for the best among these randomly selected controls is then used to train the neural network. We demonstrate our approach on 2- and 3-dimensional examples in aerodynamic envelope protection