Balanced truncation for time-delay systems via approximate gramians

In circuit simulation, when a large RLC network is connected with delay elements, such as transmission lines, the resulting system is a time-delay system (TDS). This paper presents a new model order reduction (MOR) scheme for TDSs with state time delays. It is the first time to reduce a TDS using balanced truncation. The Lyapunov-type equations for TDSs are derived, and an analysis of their computational complexity is presented. To reduce the computational cost, we approximate the controllability and observability Gramians in the frequency domain. The reduced-order models (ROMs) are then obtained by balancing and truncating the approximate Gramians. Numerical examples are presented to verify the accuracy and efficiency of the proposed algorithm. ©2011 IEEE.published_or_final_versionThe 16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011), Yokohama, Japan, 25-28 January 2011. In Proceedings of the 16th ASP-DAC, 2011, p. 55-60, paper 1C-

Block oriented model order reduction of interconnected systems

Unintended and parasitic coupling effects are becoming more relevant in currently designed, small-scale/highfrequency RFICs. Electromagnetic (EM) based procedures must be used to generate accurate models for proper verification of system behaviour. But these EM methodologies may take advantage of structural sub-system organization as well as information inherent to the IC physical layout, to improve their efficiency. Model order reduction techniques, required for fast and accurate evaluation and simulation of such models, must address and may benefit from the provided hierarchical information. System-based interconnection techniques can handle some of these situations, but suffer from some drawbacks when applied to complete EM models. We will present an alternative methodology, based on similar principles, that overcomes the limitations of such approaches. The procedure, based on structure-preserving model order reduction techniques, is proved to be a generalization of the interconnected system based framework. Further improvements that allow a trade off between global error and block size, and thus allow a better control on the reduction, will be also presented

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Passivity-preserving parameterized model order reduction using singular values and matrix interpolation

We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique

Theoretical and practical aspects of linear and nonlinear model order reduction techniques

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 133-142).Model order reduction methods have proved to be an important technique for accelerating time-domain simulation in a variety of computer-aided design tools. In this study we present several new techniques for model reduction of the large-scale linear and nonlinear systems. First, we present a method for nonlinear system reduction based on a combination of the trajectory piecewise-linear (TPWL) method with truncated-balanced realizations (TBR). We analyze the stability characteristics of this combined method using perturbation theory. Second, we describe a linear reduction method that approximates TBR model reduction and takes advantage of sparsity of the system matrices or available accelerated solvers. This method is based on AISIAD (approximate implicit subspace iteration with alternate directions) and uses low-rank approximations of a system's gramians. This method is shown to be advantageous over the common approach of independently approximating the controllability and observability gramians, as such independent approximation methods can be inefficient when the gramians do not share a common dominant eigenspace. Third, we present a graph-based method for reduction of parameterized RC circuits. We prove that this method preserves stability and passivity of the models for nominal reduction. We present computational results for large collections of nominal and parameter-dependent circuits. Finally, we present a case study of model reduction applied to electroosmotic flow of a marker concentration pulse in a U-shaped microfluidic channel, where the marker flow in the channel is described by a three-dimensional convection-diffusion equation. First, we demonstrate the effectiveness of the modified AISIAD method in generating a low order models that correctly describe the dispersion of the marker in the linear case; that is, for the case of concentration-independent mobility and diffusion constants.(cont) Next, we describe several methods for nonlinear model reduction when the diffusion and mobility constants become concentration-dependent.by Dmitry Missiuro Vasilyev.Ph.D