Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function
A number of applications to interplanetary trajectories have been recently proposed based on deep networks. These approaches often rely on the availability of a large number of optimal trajectories to learn from. In this project we show that it is possible to not only generate millions of optimal trajectories without solving the Optimal Control Problem millions of times, but also that there exist multiple methods of training deep neural networks such that the optimal controls can be computed from the state. 
It has already been established that deep network representations of the optimal control can be used for different scenarios  depending on the dynamical system involved. With this project we find deep network representations of not only the optimal control, but also the value function and its corresponding costates. This permits a more interesting representation as the same network can both predict the expected propellant that an optimal manouevre requires and the optimal control for that manouevre.
In this project, we have successfully trained and shown the efficacy of the generated database using deep network representations of the optimal control and the value function. The current method requires that the database contains not only the optimal controls, but also the costates associated with the problem. Since there is one costate per state variable, this nearly doubles the size of the needed database and the data throughput required during training. It is now being investigated whether these costates are really necessary in the database by training them indirectly.
- Izzo, D., E. Öztürk, and M. Märtens. 2019. “Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function.” In arXiv preprint arXiv:1904.08809.
- Sanchez-Sanchez, C., D. Izzo, and D. Hennes. 2016. “Learning the Optimal State-Feedback Using Deep Networks.” In 2016 IEEE Symposium Series on Computational Intelligence (SSCI).
- Sanchez-Sanchez, C., D. Izzo, and D. Hennes. 2016. “Optimal Real-Time Landing Using Deep Networks.” In 6th International Conference on Astrodynamics Tools and Techniques (ICATT).
- Sanchez-Sanchez, C., and D. Izzo. 2018. “Real-Time Optimal Control via Deep Neural Networks: Study on Landing Problems.” Journal of Guidance Control and Dynamics 41 (5): 1122–35.