Computational Methods for Approximation of Large-Scale Dynamical Systems

Summary

These days, computer-based simulation is considered as the quintessential approach to exploring new ideas in the different disciplines of  science, engineering and technology.  To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first or second order differential-algebraic equations (DAEs) or descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity thus restricting frequent simulations as required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through Model Order Reduction (MOR) techniques. This book discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of   descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems.
The book also discusses the low-rank alternating direction implecit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors.
Note that the low-rank Gramian factors are important ingredients for implementing the Gramin based MOR.

This book can be a text book for the graduate (i.e.  Masters and Ph.D.) students/researchers of varies disciplines of science and engineerings. While the basic contents of this book can be helpful to the advanced Bachelor level students in any discipline. It would be highly valuable reference  to   researchers working in both academics and industries.

Features:

• This book provides an up-to-date step-by-step guide for its readers.
  Each chapter develops theories, provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic;
• The MATLAB® codes for some selected  algorithms are provided in the book. The solution to the exercise problems, experiment data sets and a digital copy of the software are provided in the book's website;
• The numerical experiments  use real-world data sets  obtained from industries and research institutes and they have not been used any text book yet;
• The methodologies discussed in this book are updated and efficient.
  

Table of Contents

I Preliminaries. Review of Linear Algebra. Dynamic Systems and Control Theory. Iterative Solution of Lyapunov Equations. Model Reduction of Generalized State Space Systems. II Model Reduction of Descriptor Systems. Introduction to Descriptor Systems. Model Reduction of First-Order Index 1 Descriptor Systems. Model Reduction of First-Order Index 2 Descriptor Systems. Model Reduction of First-Order Index 2 Unstable Descriptor Systems. Model Reduction of First-Order Index 3 Descriptor Systems. Model Reduction of Second-Order Index 1 Descriptor Systems. Model Reduction of Second-Order Index 3 Descriptor Systems. III Appendices. Appendix A Data of Benchmark Model Examples. Appendix B MATLAB® Codes. Bibliography. Index.

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