Data-Driven Synthesis of Optimization-Based Controllers for Regulation of Unknown Linear Systems

TL;DR

This paper introduces a data-driven approach to design controllers for unknown linear systems, enabling regulation to optimization solutions without system identification, leveraging behavioral theory and gradient-based methods.

Contribution

It develops a novel data-driven framework that computes system transfer functions from samples and designs controllers without prior system knowledge or disturbance estimation.

Findings

Controller successfully regulates unknown systems to optimization solutions.

Method applies to cost functions satisfying Polyak-ojasiewicz inequality.

Eliminates need for system identification phase.

Abstract

This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization problem is a central goal in many modern engineering applications. Yet, the available methods critically rely on a precise knowledge of the system dynamics, thus mandating a preliminary system identification phase before a controller can be designed. In this work, we leverage results from behavioral theory to show that the steady-state transfer function of a linear system can be computed from data samples without any knowledge or estimation of the system model. We then use this data-driven representation to design a controller, inspired by a gradient-descent optimization method, that regulates the system to the solution of a convex optimization problem, without requiring any knowledge of the time-varying disturbances affecting the model equation. Results are tailored to cost functions satisfy the Polyak-\L ojasiewicz inequality.