Numerical Awareness in Control

Algorithm development, sensitivity and accuracy issues, large-scale computations, and high-performance numerical softwar

Coprime Factor Reduction of H-infinity Controllers

We consider the efficient solution of the coprime factorization based H infinity controller approximation problems by using frequency-weighted balancing related model reduction approaches. It is shown that for a class of frequency-weighted performance preserving coprime factor reduction as well as for a relative error coprime factor reduction method, the computation of the frequency-weighted controllability and observability grammians can be done by solving Lyapunov equations of the order of the controller. The new approach can be used in conjunction with accuracy enhancing square-root and balancing-free techniques developed for the balancing related coprime factors based model reduction

Computational issues in fault detection filter design

We discuss computational issues encountered in the design of residual generators for dynamic inversion based fault detection filters. The two main computational problems in determining a proper and stable residual generator are the computation of an appropriate leftinverse of the fault-system and the computation of coprime factorizations with proper and stable factors. We discuss numerically reliable approaches for both of these computations relying on matrix pencil approaches and recursive pole assignment techniques for descriptor systems. The proposed computational approach to design fault detection filters is completely general and can easily handle even unstable and/or improper systems

Computation of transfer function matrices of periodic systems

We present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state-space representations as constant systems. The proposed pole-zero method determines each entry of the transfer function matrix in a minimal zeros-poles- gain representation. A basic computational ingredient for this method is the extended periodic real Schur form of a periodic matrix, which underlies the computation of minimal realizations and system poles. To compute zeros and gains, fast algorithms are proposed, which are specially tailored to particular single-input single-output periodic systems. The new method relies exclusively on reliable numerical computations and is well suited for robust software implementations

Balanced truncation model reduction of periodic systems

The balanced truncation approach to model reduction is considered for linear discrete-time periodic systems with time-varying dimensions. Stability of the reduced model is proved and a guaranteed additive bound is derived for the approximation error. These results represent generalizations of the corresponding ones for standard discrete-time systems. Two numerically reliable methods to compute reduced order models using the balanced truncation approach are considered. The square-root method and the potentially more accurate balancing-free square-root method belong to the family of methods with guaranteed enhanced computational accuracy. The key numerical computation in both methods is the determination of the Cholesky factors of the periodic Gramian matrices by solving nonnegative periodic Lyapunov equations with time-varying dimensions directly for the Cholesky factors of the solutions

Enhanced LFR-toolbox for MATLAB and LFT-based gain scheduling

We describe recent developments and enhancements of the LFR-Toolbox for MATLAB for building LFT-based uncertainty models and for LFT-based gain scheduling. A major development is the new LFT-object definition supporting a large class of uncertainty descriptions: continuous- and discrete-time uncertain models, regular and singular parametric expressions, more general uncertainty blocks (nonlinear, time-varying, etc.). By associating names to uncertainty blocks the reusability of generated LFT-models and the user friendliness of manipulation of LFR-descriptions have been highly increased. Significant enhancements of the computational efficiency and of numerical accuracy have been achieved by employing efficient and numerically robust Fortran implementations of order reduction tools via mex-function interfaces. The new enhancements in conjunction with improved symbolical preprocessing lead generally to a faster generation of LFT-models with significantly lower orders. Scheduled gains can be viewed as LFT-objects. Two techniques for designing such gains are presented. Analysis tools are also considered

Brentano's Influence on Husserl's Early Notion of Intentionality

The influence of Brentano on the emergence of Husserl's notion of intentionality has been usually perceived as the key of understanding the history of intentionality, since Brentano was credited with the discovery of intentionality, and Husserl was his discipline. This much debated question is to be revisited in the present essay by incorporating recent advances in Brentano scholarship and by focusing on Husserl's very first work, his habilitation essay (Über den Begriff der Zahl), which followed immediately after his study years at Brentano, and also on manuscript notes from the same period. It is to be shown that (i) although Brentano failed to enact a direct influence on Husserl's notion of intentionality (much in line with K. Schuhmann's claim), (ii) yet the core of Brentano's notion remained operative in Husserl's theory of relations, which is seemingly influenced by John Stuart Mill and Hermann Lotze. This investigation is intended as a contribution towards the proper understanding of the complexities of Husserl's early philosophy

Henri Temianka Correspondence; (varga)

This collection contains material pertaining to the life, career, and activities of Henri Temianka, violin virtuoso, conductor, music teacher, and author. Materials include correspondence, concert programs and flyers, music scores, photographs, and books.https://digitalcommons.chapman.edu/temianka_correspondence/4228/thumbnail.jp

Die SLICOT-Toolboxen für MatlabThe SLICOT Toolboxes for Matlab

SLICOT ist eine umfangreiche Softwarebibliothek zur numerischen Behandlung von Fragestellungen aus der System- und Regelungstheorie, die mit dem Ziel entwickelt wurde, hohe Leistungsfähigkeit mit Robustheit, Verlässlichkeit, sowie Benutzerfreundlichkeit zu vereinen. Dies wird mittels einer Kombination von Fortran-Kernroutinen und Matlab- bzw. Scilab-Schnittstellen erreicht. In dieser Übersicht soll der Funktionsumfang der folgenden SLICOT-Toolboxen beschrieben und erläutert werden: (1) Grundaufgaben der System- und Regelungstheorie, (2) Systemidentifizierung, (3) Modell- und Reglerreduktion. Der Einsatz der Toolboxen in der Praxis wird durch verschiedene Beispiele veranschaulich