Joint Learning-Based Stabilization of Multiple Unknown Linear Systems

Study of reinforcement learning algorithms for sequential learning-based decision-making in unknown linear systems has become increasingly popular in the recent years. In the canonical version of the problem, the true dynamics matrices of the plant are unknown, and the goal consists of adaptive design of the control input for minimizing deviations from optimal policy. Still, the control actions must be diverse enough to lead to accurate identification of the unknown parameters [1]. The existing literature is notably rich, including adaptive policies based on optimistic approximations of the dynamics matrices over a confidence region [2, 3], as well as plugin estimates of unknown parameters after leveraging a dither signal [4, 5, 6], Bayesian approaches [7, 8, 9], and statistical bootstrap [10]. An important problem in in different areas of control theory is that of stabilization.