What should a planner do if a list of possible targets are known initially (instead of a single deterministic one), and the true one is revealed only after a certain time? What if the information can be obtained gradually? Can the planner make robust decisions? 
Why do some computed optimal paths show numerical artifacts? How to develop a scheme to make them disappear? 
Deep learning and optimal control are mutually influencing each other in scientific research nowadays. Can we use control theory to improve the training of DNN? Can we use deep learning to improve classical numerical optimal control algorithms? 
In surveillance evasion game, what if the surveillance intensity is a priori unknown but has to be learned on-line, as the evader conducts repetitive path planning? Is there a strategic method to explore the relevant regions? 