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

arXiv: https://arxiv.org/abs/2103.16067 · HTML: https://mlsanity.com/paper/2103.16067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [Achievement and Fragility of Long-term Equitability](https://mlsanity.com/paper/2206.12333/) (2022)

## Abstract (arXiv)

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.