Continuous-Time Robust Dynamic Programming

Abstract: This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze the robustness of DP algorithms, and in par- ticular, to develop novel adaptive optimal control and reinforcement learning methods. In order to demonstrate the potential of this new framework, four illustrative applications in the fields of stochastic optimal control and adaptive DP are presented. Three numerical examples arising from both finance and engineering industries are also given, along with several possible extensions of the proposed framework.