Control of Dynamical Systems with Multiplicative Observation Noise with Unknown Distribution Parameters

Eric Xu, Gireeja Ranade

Abstract:

In this work, we consider the problem of stabiliz-
ing a linear dynamical system with multiplicative observation
noise (MON), where the precise distribution generating the
MON is unknown. We propose a control algorithm that first
uses system identification to estimate the necessary parameters
for the optimal policy and then applies the resulting control
policy using those parameter estimates. We provide theoretical
guarantees for our algorithm which show that (1) our estimation
scheme requires O(log(1/δ)2/ε2) samples to obtain estimates
with ε accuracy and high probability 1 − 3δ, (2) the resulting
controller guarantees second-moment stability conditioned on
a good estimation event. This controller has a bounded gap to
the performance of the optimal linear memoryless controller
that knows the distribution of the noise a-priori.