Data-Driven Control: Part Two of Two: Hot Take: Why not go with Models?
Florian Dörfler
Abstract
A recurring question that all authors of this special issue encounter is, “Why not go with models?” Two terms need to be clarified: In this context, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">model</i> is understood as a parametric system representation often endowed with an interpretable structure, for example, a state-space representation with a readily discernible <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> = <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> · <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> equation. Further, the term <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">data-driven control</i> , as we employ it in this special issue, is not just about using data from a black box to inform decision making. Researchers are exploring different paradigms, among others, model-based control design, where the model and uncertainty estimates are learned from data using contemporary system identification and uncertainty quantification techniques. In classical adaptive control terminology <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , this two-stage approach is referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">indirect</i> . In contrast, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct</i> data-driven control bypasses models in the decision making; see <xref ref-type="fig" rid="fig1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Figure 1</xref> for a graphical illustration of the two paradigms. Hence, the more precise question should be, “When should we embrace direct or indirect data-driven control?” I will delve into the expected “it depends” answer in this “Editorial” column.