Hope for the best, prepare for the worst: optimal path planning under uncertainty.
Alex Vladimirsky (Math, Cornell)

Practical optimal control problems involve uncertainty, which often has stochastic characterization. Canonical dynamic programming yields Hamilton-Jacobi PDEs for optimizing either the "average" or the "worst" case scenario. I will describe several models for optimizing the former subject to guarantees on the latter. We will also discuss semi-Lagrangian and Eulerian numerical schemes for the resulting augmented PDEs. The emphasis of the talk will be on the computational consequences of modeling assumptions.