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

TL;DR

This paper introduces a data-driven control method for unknown stochastic linear systems that directly estimates system transfer functions from experiments and uses them to solve convex optimization problems without explicit system identification.

Contribution

It presents a novel approach to control unknown stochastic systems by directly estimating transfer functions from data and applying a gradient-based controller for optimization.

Findings

Transfer functions can be estimated directly from control experiments.

The proposed controller converges to the optimization problem's solution without system knowledge.

Method applied successfully to mobility-on-demand scheduling case study.

Abstract

This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available methods critically rely on a precise knowledge of the system dynamics (thus requiring off-line system identification and model refinement). To this aim, in this paper we first show that the steady-state transfer function of a linear system can be computed directly from control experiments, bypassing explicit model identification. Then, we leverage the estimated transfer function to design a controller -- which is inspired by stochastic gradient descent methods -- that regulates the system to the solution of the prescribed optimization problem. A distinguishing feature of our methods is that they do not require any knowledge of the system dynamics, disturbance terms, or their distributions. Our technical analysis combines concepts and tools from behavioral system theory, stochastic optimization with decision-dependent distributions, and stability analysis. We illustrate the applicability of the framework on a case study for mobility-on-demand ride service scheduling in Manhattan, NY.