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This paper proposes a data-driven control framework to regulate an unknown,stochastic linear dynamical system to the solution of a (stochastic) convexoptimization problem. Despite the centrality of this problem, most of theavailable methods critically rely on a precise knowledge of the system dynamics(thus requiring off-line system identification and model refinement). To thisaim, in this paper we first show that the steady-state transfer function of alinear system can be computed directly from control experiments, bypassingexplicit model identification. Then, we leverage the estimated transferfunction to design a controller -- which is inspired by stochastic gradientdescent methods -- that regulates the system to the solution of the prescribedoptimization problem. A distinguishing feature of our methods is that they donot require any knowledge of the system dynamics, disturbance terms, or theirdistributions. Our technical analysis combines concepts and tools frombehavioral system theory, stochastic optimization with decision-dependentdistributions, and stability analysis. We illustrate the applicability of theframework on a case study for mobility-on-demand ride service scheduling inManhattan, NY.

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis