Multiresolution discrete abstraction for optimal control

This paper presents a method that computes an approximate solution to a class of optimal control problems in arbitrary precision based on a discrete abstraction technique. Using a discrete abstract model, one can obtain upper and lower bounds on the optimal cost of an optimal control problem. By making use of this property, the method initially constructs a coarse discrete model, and then it gradually increases the resolution of discretization to tighten the bound on the optimal cost until the required precision is satisfied. The effectiveness of the method is demonstrated in a path-planning problem on a 2D plane.