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Workshop on Multiple Model approaches to modelling and Control

Interfaces between Control theory and Statistics

Monday 12th April 1999, IMM, DTU.

PRELIMINARY PROGRAMME

The multiple model approach to modelling nonlinear systems has been attracting increasing levels of interest. This workshop aims to bring together researchers from statistics/neural networks with control researchers working in the area of blended or switching systems.

Participation:

Anyone interested in participating should send a mail to Roderick Murray-Smith (rod@imm.dtu.dk) so that we have an idea of numbers etc.

Anyone wishing to present a poster, or give a demo of relevant software is also encouraged to mail the same address with details of the poster/demo.

Practical info:

How to get to IMM, DTU etc.

The workshop will take place in room 053 (the room beside the library, in the basement linking IMM's building 321 with building 305.
 
9:00-9:40
Coffee, and Welcome, R. Murray-Smith, L.K.  Hansen
9:40-10:30

Common quadratic Lyapunov functions: Necessary or sufficient conditions for asymptotic stability for a class of hybrid system? 

Robert Shorten 
Department of Computer Science  National University of Ireland, Maynooth  Co. Kildare, Ireland 
http://www.cs.may.ie/~rshorten/ 

Abstract: In this talk we derive necessary and sufficient conditions for the existence of a common quadratic Lyapunov function (CQLF) for a class of stable linear switching systems. These conditions suggest a stronger relationship between necessary conditions for asymptotic stability and the existence of a CQLF, than might be expected. 

10:30-11:00 Coffee, Posters
11:00-11:50

Multi-objective system identification with application to blended multiple models 

T. A. Johansen 
Norwegian University of Science and Technology,  Department of Engineering Cybernetics,  N-7034 Trondheim, Norway 
http://www.itk.ntnu.no/ansatte/Johansen_Tor.Arne/index.html

Abstract: Identification of model parameters can be viewed as a problem with  multiple objectives and constraints derived from empirical data dynamic and steady-state), physical models and knowledge, empirical and qualitative knowledge, desired properties etc.  We suggest an approach to multi-objective system identification  based on constrained optimization and regularization.  The analysis and selection of tradeoffs between conflicting objectives and constraints is discussed, and particular attention is  paid to the robust identification of models that are formulated as a blend of multiple models. 

12:00-13:00 Lunch, Posters, demos
Statistical Approaches
13:00-14:00

Countably Infinite Bayesian Gaussian Mixture Density Models

Carl Edward Rasmussen, Dept. Mathematical Modelling, Technical University of Denmark http://bayes.imm.dtu.dk 

Conventional models based on mixtures require specification of the number of mixture components, a task which is fraught with technical difficulties. In a Bayesian setting this problem may neatly be sidestepped by using mixture models with an infinite number of components. Such models do not overfit the data, and perhaps somewhat surprisingly, may be handled efficiently in an MCMC framework using a finite amount of computation. Examples with application to multivariate density modelling will be given.

14:00-14:45

Gaussian Process Implementations of  Multiple Model ideas

Roderick Murray-Smith, Dept. Mathematical Modelling, Technical University of Denmark
http://www.imm.dtu.dk/~rms

Abstract: I will discuss the Gaussian process prior approach to nonparametric regression, and relate this to the multiple model approach. I will highlight some practical advantages of Gaussian process priors compared to conventional multiple model parameterisations, and then discuss the pros and cons of the two approaches, showing that they can be combined to both theoretical and practical advantage. This will include discussion of the supposed 'interpretability' of multiple model representations.

14:45-15:00 Coffee, Posters
Velocity-based approaches
15:00-15:45

Velocity-Based Modelling of Nonlinear Systems 

Doug Leith, Bill Leithead 
Industrial Control Unit, University of Strathclyde, Glasgow http://www.icc.strath.ac.uk/~doug 

Abstract: Depending on the task at hand, a number of different representations are typically utilised for the analysis and design of complex nonlinear systems; for example, Bond Graphs, Ordinary Differential Equations. Each representation possesses particular advantages and disadvantages which make it more, or less, suitable for a particular purpose. Representations based on equilibrium linearisations are often employed for the analysis and design of nonlinear systems. While conventional linearisation-based analysis is only valid locally to a specific equilibrium operating point, it has the considerable advantage that it maintains continuity with established linear analysis techniques for which a substantial body of experience has been accumulated. A powerful new approach, the velocity-based linearisation, is a generalisation of equilibrium linearisation which resolves many of the deficiencies of the latter, including the restriction to near equilibrium operation. Since linearisation is a critical technology which underpins the great majority of analysis and design approaches, the potential applications of velocity-based representations are extremely wide ranging. Applications discussed in this presentation include velocity-based representations supporting genuinely modular analysis/design of complex large-scale nonlinear systems, representations for the real-time simulation of large-scale systems and representations which provide direct support the gain-scheduling and predictive control design approaches.

15:45-16:15
Wrap up open discussion session - Why is the multiple model approach interesting?
18:00-? Open ended appreciation of Danish culinary and brewing skills.....