Set oriented construction of globally optimal controllers

Recently, techniques for the design of optimal controllers have been developed which are based on a piecewise constant approximation of the value function of the underlying optimal control problem. They combine ideas from set oriented numerics with shortest path algorithms from graph theory. The approach is particularly well suited for problems with highly irregular value function, complicated state constraints and naturally handles hybrid systems. In this contribution, we give an overview of the approach and illustrate it by several numerical examples.