Data-driven online convex optimization for control of dynamical systems

TL;DR

This paper introduces a data-driven online convex optimization method for controlling unknown dynamical systems using output feedback, capable of handling time-varying costs with sublinear regret guarantees.

Contribution

It presents a novel control algorithm that leverages behavioral systems theory and initial input-output data, requiring only output feedback for unknown linear systems.

Findings

Achieves sublinear regret under sublinear cost variation

Effective even with noisy measurements

Demonstrated via simulation example

Abstract

We propose a data-driven online convex optimization algorithm for controlling dynamical systems. In particular, the control scheme makes use of an initially measured input-output trajectory and behavioral systems theory which enable it to handle unknown discrete-time linear time-invariant systems as well as a priori unknown time-varying cost functions. Further, only output feedback instead of full state measurements is required for the proposed approach. Analysis of the closed loop's performance reveals that the algorithm achieves sublinear regret if the variation of the cost functions is sublinear. The effectiveness of the proposed algorithm, even in the case of noisy measurements, is illustrated by a simulation example.