We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance 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 alternate (convex) sum-of-squares programs. The findings are illustrated numerically.

Data-driven control via Petersen's lemma / Andrea Bisoffi; Claudio De Persis; Pietro Tesi. - In: AUTOMATICA. - ISSN 0005-1098. - STAMPA. - 145:(2022), pp. 110537-110537. [10.1016/j.automatica.2022.110537]

Data-driven control via Petersen's lemma

Pietro Tesi
2022

Abstract

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance 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 alternate (convex) sum-of-squares programs. The findings are illustrated numerically.
2022
145
110537
110537
Andrea Bisoffi; Claudio De Persis; Pietro Tesi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1279960
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