Sampling Strategies for Data-Driven Inference of Input–Output System Properties
Reads0
Chats0
TLDR
These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input–output data samples, and their convergence properties are discussed in continuous time and discrete time.Abstract:
Due to their relevance in controller design, we consider the problem of determining the $\mathcal {L}^2$ -gain, passivity properties, and conic relations of an input–output system. While, in practice, the input–output relation is often undisclosed, input–output data tuples can be sampled by performing (numerical) experiments. Hence, we present sampling strategies for discrete time and continuous time linear time-invariant systems to iteratively determine the $\mathcal {L}^2$ -gain, the shortage of passivity and the cone with minimal radius that the input–output relation is confined to. These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input–output data samples. This leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time.read more
Citations
More filters
L2 Gain And Passivity Techniques In Nonlinear Control
TL;DR: L2 gain and passivity techniques in nonlinear control is downloaded for free to help people who are facing with some harmful virus inside their desktop computer.
Posted Content
Provably robust verification of dissipativity properties from data
TL;DR: This paper presents a framework for verifying dissipativity properties from measured data with desirable guarantees in the case of input-state measurements, and extends this approach to input-output data, where similar results hold in the noise-free case.
Posted Content
Determining optimal input-output properties: A data-driven approach
TL;DR: 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 is introduced.
Journal ArticleDOI
Dissipativity learning control (DLC): Theoretical foundations of input–output data-driven model-free control
Wentao Tang,Prodromos Daoutidis +1 more
TL;DR: The statistical conditions on dissipativity learning that enable control performance guarantees are analyzed, and theoretical results on performance under nominal conditions as well as in the presence of statistical errors are established.
References
More filters
Book
System Identification: Theory for the User
TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.
Book
Feedback Systems: Input-output Properties
TL;DR: In this paper, the Bellman-Gronwall Lemma has been applied to the small gain theorem in the context of linear systems and convolutional neural networks, and it has been shown that it can be applied to linear systems.
Book
Optimization Algorithms on Matrix Manifolds
TL;DR: Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis and will be of interest to applied mathematicians, engineers, and computer scientists.
Journal ArticleDOI
Numerical solution of saddle point problems
TL;DR: A large selection of solution methods for linear systems in saddle point form are presented, with an emphasis on iterative methods for large and sparse problems.