Data-driven control via Petersen's lemma

Abstract

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.

References in corpus (5)

• Data-driven control via Petersen's lemma
• Trade-offs in learning controllers from noisy data
• Certainty Equivalence is Efficient for Linear Quadratic Control
• On the Certainty-Equivalence Approach to Direct Data-Driven LQR Design
• Learning controllers for performance through LMI regions

Cited by in corpus (16)

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• Controller synthesis for input-state data with measurement errors
• Notes on data-driven output-feedback control of linear MIMO systems
• The Non-Strict Projection Lemma
• Learning controllers for performance through LMI regions
• Controller Synthesis from Noisy-Input Noisy-Output Data
• Derivative free data-driven stabilization of continuous-time linear systems from input-output data
• Data-driven input-to-state stabilization with respect to measurement errors
• Data Informativity for Quadratic Stabilization under Data Perturbation
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• Setpoint control of bilinear systems from noisy data
• Data-Driven Identification of Attack-free Sensors in Networked Control Systems