Switching and Learning in Feedback Systems: European Summer School on Multi-Agent Control, Maynooth, Ireland, September 8-10, 2003, Revised Lectures and Selected Papers

353 Pages·2005·17.128 MB·English

by  Kumpati S. Narendra (auth.), Roderick Murray-Smith, Robert Shorten (eds.)

Lecture Notes in Computer Science 3355
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DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
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ETHZurich,Switzerland
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StanfordUniversity,CA,USA
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UniversityofCalifornia,Berkeley,CA,USA
MosheY.Vardi
RiceUniversity,Houston,TX,USA
GerhardWeikum
Max-PlanckInstituteofComputerScience,Saarbruecken,Germany
Roderick Murray-Smith Robert Shorten (Eds.)
Switching
and Learning in
Feedback Systems
European Summer School on Multi-Agent Control
Maynooth, Ireland, September 8-10, 2003
Revised Lectures and Selected Papers
1 3
VolumeEditors
RoderickMurray-Smith
GlasgowUniversity,Dept.ofComputingScience
GlasgowG128QQ,Scotland,UK
E-mail:[email protected]
RobertShorten
HamiltonInstitute,NUIMaynooth
Co.Kildare,Ireland
E-mail:[email protected]
LibraryofCongressControlNumber:2004118125
CRSubjectClassification(1998):F.1,C.3,G.3,I.2,I.6
ISSN0302-9743
ISBN3-540-24457-3SpringerBerlinHeidelbergNewYork
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Preface
A central theme in the study of dynamic systems is the modelling and control
of uncertain systems. While ‘uncertainty’ has long been a strong motivating
factor behind many techniques developed in the modelling, control, statistics
and mathematics communities, the past decade, in particular, has witnessed
remarkable progress in this area with the emergence of a number of powerful
newmethodsforbothmodellingandcontrollinguncertaindynamicsystems.The
specific objective of this book is to describe and review some of these exciting
new approacheswithin a single volume. Our approachwas to invite some of the
leading researchers in this area to contribute to this book by submitting both
tutorial papers on their specific area of research, and to submit more focussed
research papers to document some of the latest results in the area. We feel
that collecting some of the main results together in this manner is particularly
important as many of the important ideas that emerged in the past decade
werederivedinavarietyofacademicdisciplines.Byprovidingbothtutorialand
researchpaperswehopetobeabletoprovidetheinterestedreaderwithsufficient
background to appreciate some of the main concepts from a variety of related,
but nevertheless distinct fields, and to provide a flavor of how these results are
currently being used to cope with ‘uncertainty.’ It is our sincere hope that the
availability of these results within a single volume will lead to further cross-
fertilization of ideas and act as a spark for further research in this important
area of applied mathematics.
It is a huge challenge to completely characterize methods for dealing with
‘uncertainty’ in a concise manner, and it is impossible to document all of the
methods that have emerged over the past decade. The work that is included in
this book is work that to a large extent is due to the widespread availability of
cheap computation power. Identification paradigms based upon non-parametric
statisticsandMonteCarlosimulationthatwereonceconsideredtooimpractical
to be of interest to engineers, are now the subject of great interest in the com-
munity, and form the basis of many practically useful nonlinear system identifi-
cation techniques. Similarly, complex supervisory (switching) control strategies
thatwerealsoonceconsideredtoocomplextomanageinpracticalsituationsare
nowprovidingthebasisforthecontrolofuncertainandrapidlytime-varyingdy-
namic systems. Switching controlstrategies can also be considered Multi-Agent
or Multiple Model systems, although each research area has tended to use dif-
ferent tools, and to apply their methods to different application areas. It is our
hope that this book provides, in particular, a rigorous snapshot of some of the
developments that have taken place in these areas over the past decade, and
alsopresentsstate-of-theartresearchinselectedareasofswitchingandlearning
systems. In the context of this overallobjective,our aim was to produce a book
that would be of use to a graduate researcher wishing to undertake research in
thisvastfield,andthatwouldhavebothintroductorychaptersandleading-edge
VI Preface
research, together with example applications of the methods. Toward this aim,
we divided the book into three parts:
Part I introduces the challenges in switching systems for feedback control
systems, with a broad overviewby K. Narendra.This is followed by a review of
someofthe stabilityissuesthatariseinsupervisorycontrolsystemsbyShorten,
MasonandWulff.GrancharovaandJohansenthensurveyexplicitapproachesto
constrained optimal control for complex systems, which is of particular interest
for practical application.
PartIIcoverstheuseofGaussianProcesspriorsinfeedbackcontrolcontexts.
Recentlyitwasobservedthatwhenthenumberofsubmodelsinamultiple-model
system increases towardsinfinity, the system tends towards a Gaussianprocess.
GaussianProcesspriorswerealsofoundtobewell-suitedtononlinearregression
tasks,andwereverycompetitivewithmethodssuchasartificialneuralnetworks.
There has, to date, been very little published work in the combination of Gaus-
sianProcesspriorsinfeedbackcontrolcontexts.Thisseriesofpapersisintended
to provide an overview of the ways in which the approach can be used, and its
effectiveness. One of the challenges in the use of Gaussian Process priors which
has to be overcome before they are likely to be accepted for control purposes is
theirhighcomputationalcostformediumtolargedatasets.Quin˜onero-Candela
and Rasmussen introduce Gaussian Process priors, discuss the link with linear
models, and propose a reduced rank GP approach that would reduce the com-
putational load. The topic of efficient GPs for large data sets is continued in
the following chapter by Shi et al. which provides an alternative approach, one
also of interest in applications where the nonlinear system is convolved with
a known system before measurement. An adaptive variant of single-step-ahead
model-predictive control is presented by Sbarbaro and Murray-Smith, showing
how Gaussian Process priors are well suited for cautious control, while simul-
taneously learning about a new plant. In order to use Gaussian processes in
multiple-step-aheadcontrol,theissueofpropagationofuncertaintyintime-series
predictions needs to be resolved. An approach to this for Gaussian processes is
presented in Girard and Murray-Smith. The following chapter by Kocijan pro-
vides an illustrative example of the use of Girard’s propagation algorithm in a
model-predictive control setting, controlling a simulated pH process.
Part III is composed of papers making more specific research contributions
or applying switching and learning techniques to a range of application do-
mains. Vilaplana et al. present the results of tests of a new controller for cars
equippedwith4-wheelsteer-by-wire,andprovidesaveryclearapplicationexam-
ple of the individual channel design approach. This is followed by two chapters
on applications in communications systems: Wong et al. present a geometric
approach to designing minimum-variance beamformers that are robust against
steering vector uncertainties; Xiao et al. consider allocation of communication
resources in wireless communication channels, demonstrating their approachon
the design of a networked linear estimator and on the design of a multivariable
networked LQG controller. Ragnoli and Leithead present a theoretical contri-
bution, investigating inconsistencies in the theory of linear systems. Tresp and
Preface VII
Yu present an introduction to nonparametric hierarchical Bayesian modelling
with Dirichlet distributions, and apply this in a multiagent learning context for
a recommendation engine, allowing a principled combination of content-based
and collaborative filtering. Roweis and Salakhutdinov investigate simultaneous
localizationandsurveyingwith multiple agents,basedonthe use ofconstrained
HiddenMarkovmodels,allowingagentstonavigateandlearnaboutanunknown
static environment. In the final chapter, Williamson and Murray-Smith present
an application of adaptive nonlinear control methods to user interface design.
The Hex system is a gestural interface for entering text on a mobile device via
a continuous controltrajectory.The dynamics of the systemdepend onthe lan-
guagemodelandchangeasnewlettersareenteredsuchthatusersaresupported
without being constrained.
ThebookdocumentstheworkbehindpresentationsattheEuropeanSummer
School on Multi-Agent Control, held at the Hamilton Institute in Maynooth,
Ireland, in September 2003. The meeting was partially supported by the EC-
fundedresearchtrainingnetworkMAC:Multi-AgentControl,andincludedmany
of the outcomes of the project. The participants in the summer school brought
insight, techniques and language from very diverse theoretical backgrounds to
bear on a range of leading-edge applications. We hope that the publication of
this book will bring these exciting cross-disciplinary developments to a broader
audience.
October 2004 Roderick Murray-Smith, Robert Shorten
Glasgow and Maynooth
VIII Organization
Organization
TheMaynoothSummerSchoolwasjointlyorganizedbytheEC-fundedresearch
training network MAC: Multi-Agent Control, and the Hamilton Institute, NUI
Maynooth.
Conference Chair Robert Shorten (Hamilton Institute, Ireland)
Network Coordinator Roderick Murray-Smith (Glasgow University,
UK and Hamilton Institute, Ireland)
Local Organizing Committee Rosemary Hunt
Oliver Mason
Kai Wulff (Hamilton Institute, Ireland)
Table of Contents
Switching and Control
From Feedback Control to Complexity Management: A Personal
Perspective....................................................... 1
Kumpati S. Narendra (Yale University)
Convex Cones, Lyapunov Functions, and the Stability of Switched
Linear Systems ................................................... 31
Robert Shorten, Oliver Mason, Kai Wulff (Hamilton Institute)
Survey of Explicit Approaches to Constrained Optimal Control ......... 47
Alexandra Grancharova (Norwegian University of Science and
Technology & Bulgarian Academy of Sciences), Tor Arne Johansen
(Norwegian University of Science and Technology)
Gaussian Processes
Analysis of Some Methods for Reduced Rank Gaussian Process
Regression ....................................................... 98
Joaquin Quin˜onero-Candela (Technical University of Denmark &
Max-Planck Institute), Carl Edward Rasmussen (Max-Planck Institute)
Filtered Gaussian Processes for Learning with Large Data-Sets ......... 128
Jian Qing Shi (University of Newcastle), Roderick Murray-Smith,
D. Mike Titterington, (Glasgow University) Barak A. Pearlmutter
(Hamilton Institute)
Self-tuning Control of Non-linear Systems Using Gaussian Process
Prior Models ..................................................... 140
Daniel Sbarbaro (Univ. of Concepcion), Roderick Murray-Smith
(University of Glasgow & Hamilton Institute)
Gaussian Processes: Prediction at a Noisy Input and Application to
Iterative Multiple-Step Ahead Forecasting of Time-Series .............. 158
Agathe Girard (University of Glasgow), Roderick Murray-Smith
(University of Glasgow & Hamilton Institute)
Nonlinear Predictive Control with a Gaussian Process Model ........... 185
Juˇs Kocijan (Jozef Stefan Institute & Nova Gorica Polytechnic),
Roderick Murray-Smith (University of Glasgow & Hamilton Institute)
X Table of Contents
Applications of Switching & Learning
Control of Yaw Rate and Sideslip in 4-Wheel Steering Cars with
Actuator Constraints .............................................. 201
Miguel A. Vilaplana, Oliver Mason, Douglas J. Leith,
William E. Leithead (Hamilton Institute)
A Second-Order Cone Bounding Algorithm for Robust Minimum
Variance Beamforming............................................. 223
Ngai Wong (University of Hong Kong), Venkataramanan Balakrishnan
(Purdue University), Tung-Sang Ng (University of Hong Kong)
Joint Optimization of Wireless Communication and Networked Control
Systems ......................................................... 248
Lin Xiao (Stanford University), Mikael Johansson (KTH),
Haitham Hindi (PARC), Stephen Boyd, Andrea Goldsmith (Stanford
University)
Reconciliation of Inconsistencies in the Theory of Linear Systems ....... 273
Emanuele Ragnoli, William Leithead (Hamilton Institute)
An Introduction to Nonparametric Hierarchical Bayesian Modelling
with a Focus on Multi-agent Learning ............................... 290
Volker Tresp, Kai Yu (Siemens AG)
Simultaneous Localization and Surveying with Multiple Agents ......... 313
Sam T. Roweis, Ruslan R. Salakhutdinov (University of Toronto)
Hex: Dynamics and Probabilistic Text Entry ......................... 333
John Williamson (University of Glasgow), Roderick Murray-Smith
(University of Glasgow & Hamilton Institute)
Author Index ................................................ 343