Adaptive Directions for Bernstein-Based Polynomial Set Evolution.

Dynamical systems are systems in which states evolve according to some laws. Their simple definition hides a powerful tool successfully adopted in many domains from physics to economy and medicine. Many techniques have been proposed so far to study properties, forecast behaviors, and synthesize controllers for dynamical systems, in particular, for the continuous-time case. Recently, methods based on Bernstein polynomials emerged as tools to investigate non-linear evolutions for sets of states in discrete-time dynamical systems. These approaches represent sets as parallelotopes having fixed axis/directions, and, during the evolution, they update the parallelotope boundaries to over-approximate the reached set. This work suggests a heuristic to identify a new set of axis/directions to reduce over-approximation. The heuristic has been implemented and successfully tested in some examples.