Constrained time-optimal control for nonlinear systems: a fast explicit approximation

We present a method for the calculation of approximate explicit solutions to constrained time-optimal control problems for nonlinear discrete-time systems. We aim to pre-compute offline a low complexity control law that provides feasibility guarantees and fast online computation. Related approaches build on hyperrectangular state space partitions that, unfortunately, lead to a large number of regions. We introduce a method based on a hierarchy of Voronoi diagrams, which leads to partitions with fewer elements. Thereby, we use the aforementioned hyperrectangular partitions as initializations and try to systematically reduce the number of regions.