Controller design for robust invariance from noisy data

TL;DR

This paper presents a method to design robust controllers for unknown linear systems using noisy data, ensuring state invariance despite disturbances, with a linear program-based solution and demonstrated through a vehicle platoon example.

Contribution

It introduces a necessary and sufficient linear programming condition for robust invariance controller design directly from noisy data, without system identification.

Findings

Linear program guarantees robust invariance under disturbances.

Rich data sets improve controller design.

Numerical example demonstrates practical applicability.

Abstract

For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design a linear feedback controller that guarantees robust invariance of a given polyhedral set of the state in the presence of disturbances. The main result is a necessary and sufficient condition for the existence of such a controller, and amounts to the solution of a linear program. The benefits of large and rich data sets for the solution of the problem are discussed. A numerical example about a simplified platoon of two vehicles illustrates the method.