Speaker:

Prof. A. E. Krener

Abstract:

The Hamilton Jacobi Bellman partial differential equation arises in the solution of optimal control problems. It is a first order, nonlinear, hyperbolic PDE that is very difficult to solve because of the curse of dimensionality. Moreover the solution may not exist in the classical sense, i.e., the solution may not be differentiable everywhere. We describe an approach to approximately solve some of these equations on patches where the solution is smooth.