Set-Theoretic Direct Data-driven Predictive Control

TL;DR

This paper introduces a set-theoretic, data-driven predictive control method for constrained LTI systems with unknown delays, achieving stability and feasibility without explicit models or terminal costs.

Contribution

It proposes a novel set-theoretic approach to direct data-driven predictive control that guarantees stability without requiring terminal costs or explicit state estimation.

Findings

Guarantees finite-time convergence and recursive feasibility

Does not require explicit state estimation or prediction models

Successfully stabilizes systems where previous methods fail

Abstract

Designing the terminal ingredients of direct data-driven predictive control presents challenges due to its reliance on an implicit, non-minimal input-output data-driven representation. By considering the class of constrained LTI systems with unknown time delays, we propose a set-theoretic direct data-driven predictive controller that does not require a terminal cost to provide closed-loop guarantees. In particular, first, starting from input/output data series, we propose a sample-based method to build N-step input output backward reachable sets. Then, we leverage the constructed family of backward reachable sets to derive a data-driven control law. The proposed method guarantees finite-time convergence and recursive feasibility, independent of objective function tuning. It requires neither explicit state estimation nor an explicit prediction model, relying solely on input-output measurements; therefore, unmodeled dynamics can be avoided. Finally, a numerical example highlights the effectiveness of the proposed method in stabilizing the system, whereas direct data-driven predictive control without terminal ingredients fails under the same conditions.