Ellipsoid method

Control (management)

Ecology

Ellipsoid

Biology

Convex analysis

Materials science

Poaceae

Computer science

Mathematical optimization

Polynomial

Controller (irrigation)

Matrix (chemical analysis)

Physics

Mathematics

Politics

Astronomy

Image (mathematics)

Political science

Agronomy

Lemma (botany)

Mathematical analysis

Artificial intelligence

Geometry

Composite material

Representation (politics)

Linear matrix inequality

Control theory (sociology)

Noise (video)

Convex optimization

Regular polygon

Automatica

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an open-loop experiment. In the presence of noise in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen's lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen's lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through (convex) sum-of-squares programs. The findings are illustrated numerically.

Data-driven control via Petersen’s lemma