Randomized Algorithms for Data-Driven Stabilization of Stochastic Linear Systems

Abstract: Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the decision-maker about the dynamical parameter. Two randomized algorithms are proposed for this problem, but the performance is not sufficiently investigated. Further, the effect of key parameters of the algorithms such as the magnitude and the frequency of applying the randomizations is not currently available. This work studies the stabilization speed and the failure probability of data-driven procedures. We provide numerical analyses for the performance of two methods: stochastic feedback, and stochastic parameter. The presented results imply that as long as the number of statistically independent randomizations is not too small, fast stabilization is guaranteed.