A novel constraint tightening approach for robust data-driven predictive control

TL;DR

This paper introduces a data-driven model predictive control method that stabilizes unknown linear systems with disturbances using only measured data and a novel constraint tightening approach.

Contribution

It develops a new data-driven MPC scheme with constraint tightening for stabilizing unknown systems, including unstable ones, using only data and system bounds.

Findings

Guarantees practical exponential stability and recursive feasibility.

Ensures closed-loop constraint satisfaction.

Effective in controlling a priori unstable systems.

Abstract

In this paper, we present a data-driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time-invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured data and knowledge of an upper bound on the system order. First, we develop a state-feedback MPC scheme, based on input-state data, which guarantees closed-loop practical exponential stability and recursive feasibility as well as closed-loop constraint satisfaction. The scheme is extended by a suitable constraint tightening, which can also be constructed using only data. In order to control a priori unstable systems, the presented scheme contains a pre-stabilizing controller and an associated input constraint tightening. We first present the proposed data-driven MPC scheme for the case of full state measurements, and also provide extensions for obtaining similar closed-loop guarantees in case of output feedback. The presented scheme is applied to a numerical example.