A tutorial on the informativity framework for data-driven control

Abstract

The purpose of this paper is to provide a tutorial on the so-called informativity framework for direct data-driven control. This framework views data-driven analysis and design through the lens of robust control, and aims at assessing system properties and determining controllers for sets of systems unfalsified by the data. We will first introduce the informativity approach at an abstract level. Thereafter, we will study several case studies where we highlight the strength of the approach in the context of stabilizability analysis and stabilizing feedback design in different setups involving exact and noisy data, and for both input-state and input-output measurements. Finally, we provide an account of other applications of the data informativity framework.

Data Informativity: A New Perspective on Data-Driven Analysis and Control

“…Recall that the controller (118) is a stabilizing controller for the input-ouput system (123) if and only if the autonomous system (120) is stable. As an immediate consequence of Theorem 24 we then have Lemma 7 (A QMI condition for stabilization [80])…”

“…Of course, when changing the model class one needs to balance the benefits of more general model classes and the tractability of the resulting robust control problems. Some classes of systems have shown a favorable trade-off in this regard, such as bilinear systems [44], [49], polynomial systems [45], [48], rational systems [46] and systems with quadratic or sector bounded nonlinearities [47], [70]. As was shown in the aforementioned works, a thorough understanding of the linear case often remains invaluable for the proposal of nonlinear extensions.…”

“…The conclusion is that Assumption 11 also covers the case in which the noise is constrained to a known subspace, which is captured by the noise bound (38) with Φ in (45). 4) As shown in [70,Section 5.4], these noise models can also be applied in settings of Gaussian noise. To be precise, such sets can be employed as confidence intervals corresponding to a given probability.…”

“…for Π ∈ S q +r , and we refer to [70] for more details. In what follows, we assume that Π ∈ S q +r is partitioned as…”

“…In a continuoustime context, the connection between stability and QDFs was studied in [106], while the discrete-time version was considered in [107]. The following proposition holds: Proposition 2 (A QDF as Lyapunov function [80]) Let P(ξ) be a nonsingular polynomial matrix. The corresponding autonomous system P(σ)y = 0 is stable if and only if there exists a QDF Q Ψ such that Q Ψ 0 on B(P) and Q ∇Ψ < 0 on B(P).…”