A scalable sampling method to high-dimensional uncertainties for optimal and reinforcement learning-based controls

Abstract

Modern dynamical systems often operate in environments of high-dimensional uncertainties that modulate system dynamics in a complicated fashion. These high-dimensional uncertainties, non-Gaussian in many realistic scenarios, complicate real-time system analysis, design, and control tasks. In this letter, we address the scalability of computation for systems of high-dimensional uncertainties by introducing new sampling methods, the multivariate probabilistic collocation method (M-PCM), and its extension called M-PCM-orthogonal fractional factorial design (OFFD) which integrates M-PCM with the OFFDs to break the curse of dimensionality. We explore the capabilities of M-PCM and M-PCM-OFFD-based optimal control and adaptive control using the reinforcement learning approach. The analyses and simulation studies illustrate the efficiency and effectiveness of these two approaches.