A fast marching algorithm for hybrid systems

Abstract

Describes an approach to solving optimal hybrid control problems using level set methods. Level set methods are powerful techniques for generating equipotential contours with applications in the realm of fluid mechanics, computer vision, material science, robotics, and geometry. The paper specifically deals with the problem of determining an optimal control path in a hybrid system by extending the "fast marching" method to a hybrid setting. We formalize the hybrid problem, provide an algorithm to solve it, and give a constructive proof of the algorithm's correctness. We also solve two examples in our hybrid setup and discuss upper- and lower-bounds of numerical solutions.