Behavioral systems theory in data-driven analysis, signal processing, and control

By Ivan Markovsky, Florian Dörfler. Annual Reviews in Control, 2021

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The behavioral approach to systems theory, put forward 40 years ago by Jan C. Willems, takes a representation-free perspective of a dynamical system as a set of trajectories. Till recently, it was an unorthodox niche of research but has gained renewed interest for the newly emerged data-driven paradigm, for which it is uniquely suited due to the representation-free perspective paired with recently developed computational methods. A result derived in the behavioral setting that became known as the fundamental lemma started a new class of subspace-type data-driven methods. The fundamental lemma gives conditions for a non-parametric representation of a linear time-invariant system by the image of a Hankel matrix constructed from raw time series data. This paper reviews the fundamental lemma, its generalizations, and related data-driven analysis, signal processing, and control methods. A prototypical signal processing problem, reviewed in the paper, is missing data estimation. It includes simulation, state estimation, and output tracking control as special cases. The direct data-driven control methods using the fundamental lemma and the non-parametric representation are loosely classified as implicit and explicit approaches. Representative examples are data-enabled predictive control (an implicit method) and data-driven linear quadratic regulation (an explicit method). These methods are equally amenable to certainty-equivalence as well as to robust control. Emphasis is put on the robustness of the methods under noise. The methods allow for theoretical certification, they are computationally tractable, in comparison with machine learning methods require small amount of data, and are robustly implementable in real-time on complex physical systems.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5a1df705cf521321509963d26f8829b9075bd386

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In Control and Systems Engineering

  1. Florian Dörfler
  2. Jeremy Coulson
  3. Ivan Markovsky

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