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Determining optimal input-output properties: A data-driven approach

Authors :
Koch, Anne
Berberich, Julian
Köhler, Johannes
Allgöwer, Frank
Publication Year :
2020

Abstract

Due to their relevance in systems analysis and (robust) controller design, we consider the problem of determining control-theoretic system properties of an a priori unknown system from data only. More specifically, we introduce a necessary and sufficient condition for a discrete-time linear time-invariant system to satisfy a given integral quadratic constraint (IQC) over a finite time horizon using only one input-output trajectory of finite length. Furthermore, for certain classes of IQCs, we provide convex optimization problems in form of semidefinite programs (SDPs) to retrieve the optimal, i.e. the tightest, system property description that is satisfied by the unknown system. Finally, we provide bounds on the difference between finite and infinite horizon IQCs and illustrate the effectiveness of the proposed scheme in a variety of simulation studies including noisy measurements and a high dimensional system.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2002.03882
Document Type :
Working Paper