Venue+scope:
The workshop will be held at the Eindhoven University of Technology. In order to reserve sufficient time for discussions amongst the members of the Working Group, the workshop will span 2 days. The date has been fixed to October 8-9, 2001. Renowned experts in the field of model reduction will present lectures on the present state of the field, both from the mathematical point of view and from the practical point of view. 
Date:  October 8-9, 2001 
Location: Eindhoven University of Technology, Eindhoven, The Netherlands 
Auditorium, Room 12 
How to get there

Abstracts:
“Model reduction for linear systems” 
Maarten Steinbuch
Current tools for modelling physical systems are nowadays widespread and at a high level. The consequence is that the resulting models are becoming detailed and rather accurate, and this means that the dynamic complexity (‘order’) can be relatively high. Especially for model based control design methods this yields equally high order controllers, obstructing implementation and experimental validation. In addition, it is well-known that the feedback controllers normally only see part of the dynamics of the model, namely that part that is relevant for the input/output behaviour. 
In this talk on linear techniques for model reduction we will give an overview of the relevance of model and controller reduction, and we will give overview of Pade-based, modal based and Grammian based methods, with emphasis on the latter one. Slides 

“Input-output representations of nonlinear systems” 
Henk Nijmeijer
One of the equivalent ways of representing a linear input-output system is by means of the impulse-response matrix of the system. In contrast to, for instance, the transfer matrix of a system, the notion of an impulse-response matrix admits an analogon in the context of nonlinear systems. This is the so-called Wiener-Volterra series expansion, that was mostly developed in the 1970s. The purpose of this contribution is to review the theory on Wiener-Volterra representations of nonlinear systems, and also introduce a slightly different series expansion that was developed in the 1980s by Michel Fliess and co-workers. In this review, attention will be paid to some of the computational aspects involving the use of Wiener-Volterra or Fliess' series. Slides 
 

"Model reduction by proper orthogonal decompositions" 
Siep Weiland and Patricia Astrid
slides 

“Statistical bilinearization in stochastic nonlinear dynamics” 
Nathan van de Wouw
A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original, nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the difference between the original system and the bilinear system in a statistical sense. Application to a piece-wise linear system illustrates the effectiveness of this approach in approximating truly nonlinear, stochastic response phenomena in both the statistical moments and the power spectral density of the response of this system in case of a white noise excitation. 

“Component modes in nonlinear dynamic modelling” 
Bram de Kraker 
Numerical models for realistic nonlinear dynamic problems (for example in turbomachinry) can be build very frequently from one or more large linear substructures (the housing and the shaft) and some local nonlinearities (the bearings and seals). In general the linear substructures will lead to multi-degree-of-freedom models which after introducing the nonlinearities gives a model which can hardly be used in a design or control situaton. The Component Mode Synthesis technique allows us to reduce the order of the models and generate accurate models in a specific frequency range. The basic technique and some practically important versions will be presented. As a practical illustration the nonlinear control of a beam system with impact will be discussed. 
 

“Model reduction for eigenvalue problems” 
Henk van der Vorst
Many scientific and engineering models for studying sensitivities in phenomena lead to eigenvalue problems: magnetohydrodynamic stability, acoustic resonance problems, structural dynamics, attachment line flow instabilities, etc. The resulting eigenproblems may be very high-dimensional. We will show how the given eigenproblem can be reduced to a low-dimensional problems over a subspace that can be generated automatically. This leads to tremendous reductions in comparison with standard eigenvalue computation methods.

 “Passive reduced order multiport modeling: the Pade-Laguerre, Krylov-Arnoldi-SVD connection” 
Luc Knockaert and Daniel De ZutterCircuit simulation tasks generally require the solution of very large linear networks. Since the main point is the behavior of the interconnect structure at given ports over a given frequency range, it is of the utmost importance to obtain a reduced but accurate model of the network. For this reason, a reduced order multiport modeling algorithm based on the decomposition of the system transfer matrix into orthogonal scaled Laguerre functions has been developed. The link with Pade approximation, the block Arnoldi method and singular value decomposition leads to a simple and stable implementation of the algorithm. The method is provably passive.
Slides part 1 
Slides part 2

 “Lattice differential equations and coupled lattice maps – An overview of recent results” 
Sjoerd Verduyn LunelWe survey recent results in the theory of lattice differential equations and coupled lattice maps. Coupled lattice maps are systems that model spatial structures where the state of a site is determined dynamically by the previous state at that site and that of its neighbours. Such models have a wide range of applications to physics (crystals), biology (nervous systems, population dynamics), economics (interaction of different markets) and reaction-diffusion equations. Numerically, one can observe the formation of waves, patterns, synchronisation in which coupling plays an important role. Lattice differential equations are continuous-time dynamical systems, usually infinite-dimensional, which possess a discrete spatial structure modelled on a lattice. Recent research focuses on  travelling waves in discrete spatial media such as lattices and leads to differential equations with retarded and advanced arguments. slides 
 

“Model reduction within control system design” 
Pepijn Wortelboer
Model reduction for linear high-order systems is best performed in a configuration that is close to the operating conditions of the true system. For mechanical servo-systems such as a CD-player, the reduction of the mechanics part with numerous vibration modes, is needed to derive effective simulation models and to design controllers. The usage of closed-loop reduction techniques combined with iterative schemes for reduction and evaluation, is key in finding dedicated low-order models. Slides 

Efficiency of model-order reduction through TSL and 4SID techniques 
Prof. Irina Munteanu
Two model order reduction techniques are described and compared. When a space-discretized system of equations for the analyzed device 
is available, the established Pade via Lanczos (PVL) method for model order reduction can yield very small reduced models, at a relatively high computational cost. A new Two-Step Lanczos (TSL) technique is described, which is meant to drastically reduce the computational cost. 
On the other hand, for devices whose port- or terminal- behaviour is known i.e. from measurements, reduction techniques based on input/output data can be used. Such a technique is the 4SID/MOESP method. The two methods are discussed in terms of computational efficiency, stability of 
the reduced-order models, and ease of equivalent-circuit synthesis. Slides 

Model Reduction for VLSI Physical Verification 
Nick van der Meijs 
slides