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Control of linear dynamics with multiplicative noise naturally introducesrobustness against dynamical uncertainty. Moreover, many physical systems aresubject to multiplicative disturbances. In this work we show how these dynamicscan be identified from state trajectories. The least-squares scheme enablesexploitation of prior information and comes with practical data-drivenconfidence bounds and sample complexity guarantees. We complement this schemewith an associated control synthesis procedure for LQR which robustifiesagainst distributional uncertainty, guaranteeing stability with highprobability and converging to the true optimum at a rate inversely proportionalwith the sample count. Throughout we exploit the underlying multi-linearproblem structure through tensor algebra and completely positive operators. Thescheme is validated through numerical experiments.

Provably stable learning control of linear dynamics with multiplicative noise