Joint Learning-Based Stabilization of Multiple Unknown Linear Systems

Abstract

Learning-based control of linear systems received a lot of attention recently. In popular settings, the true dynamical models are unknown to the decision-maker and need to be interactively learned by applying control inputs to the systems. Unlike the matured literature of efficient reinforcement learning policies for adaptive control of a single system, fast and reliable stabilization of multiple systems remains unexplored and is the focus of this work. We propose a novel algorithm for joint learning-based stabilization of multiple systems whose dynamics are unknown linear combinations of some unknown basis matrices. The presented procedure is effective for quickly learning from unstable state trajectories such that it stabilizes the family of dynamical systems in a short time period, significantly faster than individual-learning methods.