603 research outputs found
A duality perspective on Loewner rational interpolation and state-space modelling of vector-exponential trajectories
No full textWe explore some connections between the Loewner approach to interpolation and realization, and that based on bilinear differential forms arising in the behavioral framework. We show that a crucial concept underlying both approaches is that of duality of trajectories, and that many known results can be interpreted in its ligh
Bilinear differential forms and the Loewner framework for rational interpolation
No full textThe Loewner approach, based on the factorization of a special-structure matrix derived from data generated by a dynamical system, has been applied successfully to realization, generalized interpolation, and model reduction. We examine some connections between such approach and that based on bilinear- and quadratic differential forms arising in the behavioral framework
Model validation and consistency
No full textThis thesis addresses model validation, important in robust control system modeling, for the identification method developed by Antoulas. Given a system model, the problem is to assess whether the model is consistent with the data.
This work formulates the validation problem in the form of a quadratic optimization problem subject to a spherical constraint. This new, computationally tractable method allows us to find a necessary and sufficient condition on the energy of the input sequence required to invalidate a given model. Therefore, for a given energy level, not all the models can be invalidated. For fixed noise level, the set of invalidatable models decreases as the energy of the input sequence decreases. Moreover, even if infinite length measurements are taken, the set of plants which cannot be invalidated does not shrink to the true model. The true model, in addition, can never be invalidated using an input of finite energy
The Δρομοδείχτης της Ελλάδος of 1824 and Athanasios Stageirites (Τίτλος περίληψης)
No full textσ. [281]-290Κείμενο στα ελληνικά με περίληψη στα αγγλικά με τον τίτλο: The Δρομοδείχτης της Ελλάδος of 1824 and Athanasios StageiritesThe article first examines the close relationship between the publication “Δρομοδείχτης της Ελλάδος” [1824] and the publication “Ηπειρωτικά” (1819) by Athanasios Stageirites and then suggests that Athanasios Stageirites is the likeliest author of the “Δρομοδείχτης της Ελλάδος”.Δωδώνη: Τεύχος Πρώτο: επιστημονική επετηρίδα του Τμήματος Ιστορίας και Αρχαιολογίας της Φιλοσοφικής Σχολής του Πανεπιστημίου Ιωαννίνων; Τόμ. 43-44 (2014-2015
On Loewner data-driven control for infinite-dimensional systems
No full textInternational audienceIn this paper, we address extensions of the Loewner Data-Driven Control (L-DDC) methodology. First, this approach is extended by incorporating two alternative approximation methods known as Adaptive-Antoulas-Anderson (AAA) and Vector Fitting (VF). These algorithms also include least squares fitting which provides additional flexibility and enables possible adjustments for control tuning. Secondly, the standard model reference data-driven setting is extended to handle noise affecting the data and uncertainty in the closedloop objective function. These proposed adaptations yield a more robust data-driven control design
Data-Driven Model Reduction for Optimal Control of Large-scale Dynamical Systems
No full textIn the thesis, we investigate data-driven model reduction for optimal control of large-scale dynamical systems. Optimal control problems play an important role in many engineering applications. However, computational cost is the bottleneck for obtaining optimal control of large-scale dynamic systems. Model reduction which approximates the large-scale complex model accurately by a smaller reduced order model can largely reduce the computation cost. In the thesis, a new model reduction approach, the Loewner Framework, is investigated for generating reduced order models for linear-quadratic optimal control problems. The Loewner Framework is a data-driven model reduction method which can construct the reduced order models from measurements directly. The property gives Loewner framework more flexibility compared with other model-driven methods. Besides, the Loewner framework is an interpolation-based method that requires much less computation cost than SVD-based model reduction methods for large-scale dynamical systems. In this thesis, the iterative error system approximation approach which has an aposteriori error bound is developed for the model reduction of optimal control problems. On several optimal control problems involving CD player, damped Euler-Bernoulli beam and water pollution problem, Loewner framework shows unique performance compared with other methods like balanced truncation and rational Krylov method
Factorization of the Loewner Matrix Pencil and Its Consequences
No full textIn this thesis, we derive a factorization of the Loewner pencil in data-driven modeling and explore its consequences. The Loewner framework is a data-driven modeling and complexity reduction method that can be used to learn models of dynamical systems from measurements of their transfer function. One key feature of the Loewner framework consists in the fact that it does not need an exact description of the original dynamical system to start with, which is typically described by ordinary or partial differential equations (ODEs, PDEs). Instead of having full access to the coefficient matrices that scale these equations, one requires only transfer function measurement values. Finally, by arranging the given data in a specific way, one can construct with basically no computational effort a realization (dynamical system) that explains the data. The Loewner pencil plays a central role in the system realization constructed by the Loewner framework. More precisely, the two Loewner matrices that enter the pencil represent the coefficient matrices that scale the internal variable vector and its derivative. Consequently, the eigenvalues of the pencil are the poles of the surrogate Loewner model and are used to characterize the dynamics of the system.
In this thesis, the Loewner pencil is factorized in terms of generalized Cauchy matrices that are composed of poles, residues of the system, and measurement points. It is shown that the factors given by the generalized Cauchy matrices are Krylov projection matrices for a particular system realization. Using the factorization of the generalized Loewner matrix, the eigenvalue decomposition (EVD) of the Loewner pencil is hence available. Based on this EVD and eigenvalue perturbation theory for matrix pencils, we explore two types of eigenvalue sensitivities. The first one is defined for unstructured perturbations of the Loewner pencil, while the second one is defined for structured perturbations. The motivation for studying these two sensitivities is that they reflect the robustness of the Loewner surrogate model. We will show that the unstructured perturbation sensitivity is related to the numerical conditioning of the Loewner pencil and can be used in comparison to the pseudo spectrum of the pencil. Moreover, it is shown that the structured perturbation sensitivity can be used to estimate eigenvalue perturbations as a result of the noise in the data. We also discuss how the choice of data affects the two sensitivities. Finally, we will extend our framework to the time-series data and show its application in the research of biological rhythms
Modeling Systems from Measurements of their Frequency Response
No full textThe problem of modeling systems from frequency response measurements is of interest to many engineers. In electronics, we wish to construct a macromodel from tabulated impedance, admittance or scattering parameters to incorporate it into a circuit simulator for performing circuit analyses. Structural engineers employ frequency response functions to determine the natural frequencies and damping coefficients of the underlying structure. Subspace identification, popular among control engineers, and vector fitting, used by electronics engineers, are examples of algorithms developed for this problem. This thesis has three goals. 1. For multi-port devices, currently available algorithms arc expensive. This thesis therefore proposes an approach based on the Loewner matrix pencil constructed in the context of tangential interpolation with several possible implementations. They are fast, accurate, build low dimensional models, and are especially designed for a large number of terminals. For noise-free data, they identify the underlying system, rather than merely fitting the measurements. For noisy data, their performance is analyzed for different noise levels introduced in the measurements and an improved version, which identifies an approximation of the original system even for large noise values, is proposed. 2. This thesis addresses the problem of generating parametric models from measurements performed with respect to the frequency, but also with respect to one or more design parameters, which could relate to geometry or material properties. These models are suited for performing optimization over the design variables. The proposed approach generalizes the Loewner matrix to data depending on two variables. 3. This thesis analyzes the convergence properties of vector fitting, an iterative algorithm that relocates the poles of the model, given some "starting poles" chosen heuristically. It was recognized as a reformulation of the Sanathanan-Koerner iteration and several authors attempted to improve its convergence properties, but a thorough convergence analysis has been missing. Numerical examples show that for high signal to noise ratios, the iteration is convergent, while for low ones, it may diverge. Hence, incorporating a Newton step aims at making the iteration always convergent for "starting poles" chosen close to the solution. A connection between vector fitting and the Loewner framework is exhibited, which resolves the issue of choosing the starting poles
Discrete-time linear periodically time-varying systems: Analysis, realization and model reduction
No full textDiscrete-time linear periodically time-varying (LPTV) systems, considered as a bridge between the well-studied linear time-invariant (LTI) model and the nonlinear time-varying problems in real world, have been receiving increasing attention in recent a few decades.
In this research project, we try to understand discrete-time LPTV systems both internally and externally and derive basic theories for analysis, realization and model reduction of LPTV systems. Firstly we review the system model for LPTV systems, define its transfer function matrix, Markov parameters, stability, reachability and observability. Then we emphasize on the numerically efficient and stable methods to compute LPTV system grammians and to approximate the eigenvalue decay rate.
Another main result of this thesis is Krylov-based moment matching algorithm for model reduction of LPTV systems, which is derived afterwards, and is also compared to the other approach: balancing and balanced truncation of LPTV systems.
Almost any application of discrete-time LPTV systems, including periodic digital filters and periodic control theories, demands a periodic state-space model from input-output maps. This periodic realization problem is treated at the end of the thesis with demonstration of applicable non-minimal and quasi-minimal realization methods
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