arXiv subjects

Jaap Eising

Publications and source records attributed to Jaap Eising.

27 records · Page 2Linked to original sources

arXiv2022

Informativity for centralized design of distributed controllers for networked systems

Recent work in data-driven control has led to methods that find stabilizing controllers directly from measurements of an unknown system. However, for multi-agent systems we are often interested in finding controllers that take their distributed nature into account. For instance, the full state might not be available for feedback at every agent. In order to deal with such information, we consider the problem of finding a feedback controller with a given block structure based on measured data. Moreover, we provide an algorithm that, if it converges, leads to a maximally sparse controller.

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arXiv2022

A behavioral approach to data-driven control with noisy input-output data

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

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arXiv2022

On eigenvectors of convex processes in non-pointed cones

Spectral analysis of convex processes has led to many results in the analysis of differential inclusions with a convex process. In particular the characterization of eigenvalues with eigenvectors in a given cone has led to results on controllability and stabilizability. However, these characterizations can handle only pointed cones. This paper will generalize all known results characterizing eigenvalues of convex processes with eigenvectors in a given cone. In addition, we reveal the link between the assumptions on our main theorem and classical geometric control theory.

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arXiv2021

A geometric approach to convex processes: from reachability to stabilizability

This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of convex processes. This will allow us to characterize reachability, stabilizability and (null-)controllability of nonstrict convex processes in terms of spectral properties. These characterizations generalize all previously known results regarding for instance linear processes and specific classes of nonstrict convex processes.

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arXiv2021

On reachability and null-controllability of nonstrict convex processes

This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are constrained to lie within a convex cone. After developing a geometric framework for convex processes relying on invariance properties, we provide necessary and sufficient conditions for both reachability and null-controllability in terms of the spectrum of dual processes.

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arXiv2021

Data informativity for analysis of linear systems with convex conic constraints

This paper studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of exact state trajectories of finite length. We are interested in performing system analysis of such an unknown system on the basis of the measured data. However, from such measurements it is only possible to obtain a unique system explaining the data in very restrictive cases. This means that we can not approach this problem using system identification combined with model based analysis. As such, we will formulate conditions on the data under which any such system consistent with the measurements is guaranteed to be reachable or null-controllable. These conditions are stated in terms of spectral conditions and subspace inclusions, and therefore they are easy to verify.

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arXiv2020

Informativity of noisy data for structural properties of linear systems

This paper deals with developing tests for checking whether an unknown system has certain structural properties. The tests that we are aiming at are in terms of noisy input-state-output data obtained from the unknown system. Since, in general, the data do not determine the unknown system uniquely, many systems are compatible with the same set of data. Therefore we can not apply system identification and apply existing, model based, tests. Instead, we will use the concept of informativity, and establish tests for informativity of the given noisy data. We will do this for a range of system properties, among which strong observability and detectability and strong controllability and stabilizability. These informativity tests will be in terms of rank tests on polynomial matrices that can be constructed from the noisy data. We will also set up a geometric framework for informativity analysis. Within that framework we will give geometric tests for informativity for strong observability, observability, and left-invertibilty.

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arXiv2020

On Duality for Lyapunov Functions of Nonstrict Convex Processes

This paper provides a novel definition for Lyapunov functions for difference inclusions defined by convex processes. It is shown that this definition reflects stability properties of nonstrict convex processes better than previously used definitions. In addition the paper presents conditions under which a weak Lyapunov function for a convex process yields a strong Lyapunov function for the dual of the convex process.

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arXiv2020

Data informativity: a new perspective on data-driven analysis and control

The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.

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