Provably Stable Learning Control of Linear Dynamics With Multiplicative Noise

Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work, we show how these dynamics can be identified from state trajectories. The least-squares scheme enables the exploitation of prior information and comes with practical data-driven confidence bounds and sample complexity guarantees. We complement this scheme with an associated control synthesis procedure for linear quadratic regulator (LQR) that robustifies against distributional uncertainty, guarantees stability with high probability, and converges to the true optimum at a rate inversely proportional to the sample count. Throughout, we exploit the underlying multilinear problem structure through tensor algebra and completely positive operators. The scheme is validated through numerical experiments.