Abstraction-based branch and bound approach to Q-learning for hybrid optimal control

Abstract

In this paper, we design a theoretical framework allowing to apply model predictive control on hybrid systems. For this, we develop a theory of approximate dynamic programming by leveraging the concept of alternating simulation. We show how to combine these notions in a branch and bound algorithm that can further refine the Q-functions using Lagrangian duality. We illustrate the approach on a numerical example.

13 pages, 1 figure, submitted to the 3rd Annual Learning for Dynamics & Control Conference (L4DC 2021)