Data-based guarantees of set invariance properties

TL;DR

This paper presents a data-driven method for designing feedback controllers that ensure set invariance and constraint satisfaction in linear systems, using only data from a single experiment and linear programming.

Contribution

It introduces a data-based approach to guarantee set invariance without requiring a system model, leveraging classical invariance results and a rank condition for equivalence.

Findings

Data-driven controller guarantees invariance and constraints.

Feasibility is checked via linear programming.

Equivalence with model-based solutions under rank condition.

Abstract

For a discrete-time linear system, we use data from a single open-loop experiment to design directly a feedback controller enforcing that a given (polyhedral) set of the state is invariant and given (polyhedral) constraints on the control are satisfied. By building on classical results from model-based set invariance and a fundamental result from Willems et al., the controller designed from data has the following desirable features. The satisfaction of the above properties is guaranteed only from data, it can be assessed by solving a numerically-efficient linear program, and, under a certain rank condition, a data-based solution is feasible if and only if a model-based solution is feasible.