Table Of ContentCommunications and Control Engineering
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Graham C. Goodwin, Mar´ıa M. Seron and
Jose´ A. De Dona´
Constrained Control
and Estimation
An Optimisation Approach
With 109 Figures
Graham C. Goodwin, PhD
Jose´ A. De Dona´, PhD
Department of Electrical Engineering, University of Newcastle, Australia
Mar´ıa M. Seron, PhD
Departamento de Electro´nica, Universidad Nacional de Rosario, Argentina
Series Editors
E.D. Sontag • M. Thoma • A. Isidori • J.H. van Schuppen
BritishLibraryCataloguinginPublicationData
Goodwin,GrahamC.(GrahamClifford),1945–
Constrainedcontrolandestimation:anoptimisation
approach.—(Communicationsandcontrolengineering)
1. Automaticcontrol
I. Title II. Seron,M.(Maria),1963– III. DeDona,JoseA.
629.8
ISBN1852335483
LibraryofCongressCataloging-in-PublicationData
DeDona,Jose.
Constrainedcontrolandestimation:andoptimisationapproach/JoseDeDona´,Graham
Goodwin,andMar´ıaSeron.
p.cm.—(Communicationsandcontrolengineering;ISSN0178-5354)
ISBN1-85233-548-3(alk.paper)
1. Predictivecontrol. 2. Controltheory. I. Goodwin,GrahamC.(GrahamClifford),
1945– II. Seron,M.(Mar´ıa),1963– III. Title. IV. Series.
TJ217.6.D4 2004
629.8—dc21 2001049308
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Preface
This book gives an introduction to the fundamental principles underlying
constrainedcontrolandestimation.Thissubjecthasalonghistoryinpractice,
particularlyinthecontrolofchemicalprocessesandinchannelequalisationin
digitalcommunications.Recently,significantadvanceshavealsobeenmadein
thesupportingtheory.Inthiscontext,theobjectiveofthisbookistodescribe
thefoundationsofconstrainedcontrolandestimation.Thetreatmentisaimed
at researchers and/or practitioners and builds on core principles in signals
and systems, optimisation theory and optimal control. We also emphasise
the common links and connections that exist between estimation and control
problems.
What Is Constrained Control?
It is generally true in controlsystem design that higher levels of performance
areassociatedwith“pushingthesystemhard”.Thelatter,however,isusually
limited by the presence of physical constraints on system components. As a
simple, commonworld example, consider the case of automobile control.It is
well knownthat rapid accelerationand decelerationare associatedwith large
throttledisplacementandstrongbrakingaction,respectively.Itisalsoknown
thatthereexistmaximumandminimumavailablethrottledisplacementsand
brakingcapacity,thatis,theinputtothesystemisconstrained.Furthermore,
we might suspect that variables other than the system input are subject to
constraints; for example, acceleration and deceleration have to be limited to
prevent wheels from losing traction. These are constraints on the output or
state ofthe system.Similarconstraintsariseinvirtuallyallcontrolproblems.
Forexample,valvesinchemicalprocesscontrolhaveamaximumdisplacement
(whenfullyopen)andaminimumdisplacement(whenfullyclosed).Theseare
examples of input constraints. Also, for safety or other operational reasons,
it is usual to impose limits on allowable temperatures, levels and pressures.
These are examples of state constraints.
vi Preface
One possible strategy for dealing with constraints is to modify the design
so that limits are never violated. However, it is heuristically reasonable that
this may be counterproductive. Indeed, because it is usually true that higher
performance levels are associated with pushing the limits, there is a strong
incentive to operate the system on constraint boundaries. Within this con-
text, the subject of optimal constrained control provides the necessary tools
required to solve this class of problems. Specifically, the aim is to maximise
performancewhilstensuringthattherelevantconstraintsonbothinputs(ma-
nipulated variables) and states (process variables) are not violated.
What Is Constrained Estimation?
Constraints occur in estimation problems for similar reasons as they do in
control problems, save that in estimation, the constraints typically arise as
a priori known conditions rather than as required conditions. For example,
in estimating the concentrationin a distillation column, it is typically known
that the liquid levels in the trays must lie between given lower and upper
limits. By enforcing these kinds of constraints during estimation, one should
expectmore accurateandrealisticresults.Another areainwhichconstrained
estimation occurs is the case where the signal to be estimated is known, a
priori,tobelongtoafinitealphabet.Thisisthecoreproblem,forexample,in
signalrecoveryindigitalcommunications.Well-knownconstrainedestimators
usedinthelattercontextincludedecisionfeedbackequalisersandthe Viterbi
algorithm.
Why a Special Treatment of Constrained Control and
Estimation?
Most of the existing literature on the topic of control and estimation deals
with unconstrained problems. However, as discussed above, there are strong
practical reasons why constraints cannot be ignored if one is seeking high
performance. Also, from a theoretical perspective, constrained control and
estimationrepresentstheobvious“nextstep”beyondtraditionallineartheory.
In fact we shall see that adding constraints to an otherwise linear control or
estimationproblemstillleadsto aproblemthatis computationallytractable.
Indeed,atthe presentstateofdevelopment,the theoryofconstrainedcontrol
and/or estimation for linear systems is approaching the completeness of the
traditional theory for the unconstrained case. Thus there remains no real
impediment to teaching this theory alongside traditional treatments of linear
estimation and control. In summary, constrained control and estimation lies
at the junction of practical importance and theoretical tractability.
Preface vii
Why a Book at this Particular Time?
Therehasrecentlybeenasurgeofinterestinconstrainedestimationandcon-
trol problems and many new results have appeared which underpin practical
applications in many areas.
For example, constrained control has been utilised in industry for three
or four decades,primarily in the area of processcontrolwhere long-time con-
stants of the systems facilitated the necessary calculations. However, there
have recently been several advances that have significantly broadened the
realm of application of constrained control. These advances include:
• Computer speeds have increased dramatically making it feasible to apply
constrained control methods to high speed systems, including electrome-
chanical and aerospace systems.
• Newinsightshavebeenobtainedintoconstrainedcontrolwhichshowthat,
inmanycasesofpracticalinterest,thenecessarycomputationscanoftenbe
significantlysimplified.Thishasfurtherenhancedthedomainofpotential
application of the ideas.
• Theoretical support for the topic is growing. This gives increased confi-
dence in the application of the methods.
• The topic builds onmany core principles frommathematical systems the-
ory. Thus, it is a useful vehicle by which neophyte researchers can be
acquainted with a broad range of tools in systems theory, convex optimi-
sation, and optimal control and estimation.
Book Philosophy
Thisbookisaimedatgoingastepbeyondtraditionallinearcontroltheoryto
includeconsiderationofconstraints.Ourpremiseisthatoneshouldacceptthe
existenceofconstraintsanddealwiththemratherthanavoidthem.Thus,this
book addresseshighperformancecontrolsystemdesignandsignalestimation
in the presence of constraints. We adopt an optimisation-based approach to
these problems. The principal tools used are prediction and optimisation.
Primetopicsarerecedinghorizoncontrolandmovinghorizonestimation.We
treat related approaches in so far that they can be viewed as special cases
of this philosophy. For example, it has recently been shown that anti-windup
methods can sometimes be viewed as simplified forms of receding horizon
control. Also, decision feedback equalisers turn out to be a special case of a
more general moving horizon optimisation problem.
Book Content
Thebookgivesacomprehensivetreatmentofconstrainedcontrolandestima-
tion. Topics to be addressed include:
viii Preface
• an overview of optimisation;
• linear and nonlinear receding horizon control;
• links to classical optimal control theory, including the discrete minimum
principle;
• input and state constraints in control system design;
• constrained control solutions having a finite parameterisation for specific
classes of problems;
• stability of constrained controllers;
• numerical procedures for solving constrained optimisation problems;
• output feedback;
• an overview of Bayesian estimation theory;
• constrained state estimation;
• links between constrained estimation and constrained control.
Related Literature
The book includes a comprehensive set of references to contemporary liter-
ature. We also note that there have recently been several excellent books
published that complement the material in the current book. In particular,
we point to the books by Camacho and Bordons (1999), Maciejowski (2002),
Borrelli (2003), and Rossiter (2003).
Intended Audience
The current book is aimed at those wishing to gain an understanding of the
fundamental principles underlying constrained control and estimation. The
book could be used as the basis of a junior level course for research students
or as the basis of a self-study program by practising engineers.
Flavour and Structure of the Book
The book emphasises the mathematical underpinnings of the topic. It sum-
marises and utilises core ideas from signals andsystems, optimisation theory,
classical optimal control and Bayesian estimation. Also, the book deals with
dual problems that arisein control,state estimation andsignalrecovery.The
book assumes that the reader has appropriate backgroundin systems theory,
includinglinearcontroltheory,stabilitytheoryandstatespacemethods.With
this as background, the book is self-contained and encompasses all necessary
material to understand constrained control and estimation, including:
• optimisation and quadratic programming;
• controller design in the presence of constraints;
Preface ix
• stability;
• Bayesianestimation;
• estimator design in the presence of constraints;
• optimisation with finite set constraints.
Thebookalsocontainsthreecasestudies.Thesecasestudiesareintended
to show how the theory described in the book can be put into practice on
problems of practical relevance. The chosen case studies are:
• rudder roll stabilisation of ships;
• cross directional control;
• control over communication networks.
These applications are described in sufficient detail so that the reader can
gain an appreciation of the practical issues involved.
The book is divided into three parts:
• Part I: Foundations
• Part II: Further Developments
• Part III: Case Studies
Part I was written by the principal authors. Parts II and III are based
on contributions prepared by other authors within our working group. Note,
however, that Parts II and III are not simply a collection of contributions;
the contentshavebeencarefully chosen,editedandarrangedby the principal
authorsandthusformanintegratedpresentationincombinationwithPartI.
The split into three parts is aimed at dividing the material into distinct ar-
eas (foundations, further developments and case studies) and at providing
appropriate recognition to those who assisted with the overall book project.
The book is accompanied by a website, which contains related material
such as papers by the authors, lecture slides, worked examples, Matlab rou-
tines, and so on (see http://murray.newcastle.edu.au/cce/).
Newcastle, Australia Graham C. Goodwin
June 2004 Mar´ıa M. Seron
Jos´e A. De Dona´
Acknowledgements
The authors gratefully acknowledge input from many colleagues and friends
who assistedwith the developmentof this book. Specialthanks go to Hernan
Haimovich, TristanPerez,Osvaldo Rojas,Daniel Quevedo and James Welsh,
whoeachcontributedmaterialforPartsIIandIII.Wealsoacknowledgeinput
from other students and colleagues at the University of Newcastle, including
AdrianWills,JuanI.YuzandJuanCarlosAgu¨ero.Inparticular,wearegrate-
fultoClausMu¨llerforthestabilityresultsofChapter4,Sections10.6and10.7
in Chapter 10, and his careful reading of other parts of the manuscript; we
are also grateful to Xiang W. Zhuo for contributing simulation examples for
Chapters 9 and 10. A special thanks is due to David Mayne who was instru-
mentalinintroducingtheauthorstothistopicandwhodirectlyinspiredmuch
ofthedevelopment.Also,partsofthebookwereinspiredbythecontributions
of many others, including (but not restricted to) Manfred Morari, Jim Rawl-
ings,HannahMichalska,PeterTøndel,ThorJohansen,Karl˚Astr¨om,Alberto
Bemporad,MogensBlanke,MikeCannon,LucienPolak,DavidClarke,Steven
Duncan,FrankAlgo¨wer,ThorFossen,ElmerGilbert,BasilKouvaritakis,Jan
Maciejowski,WookHyunKwon,ChristopherRao,EdoardoMosca,RickMid-
dleton,BobSkelton,ArieFeuer,GregStewart,ArthurJutan,WillHeathand
manyotherstoonumeroustoname.We alsoacknowledgeRosslyn,Jayneand
Dianne for their generous support. Finally, the third author wishes to ac-
knowledge his young son Stefano for the loss of shared moments, which were
as missed by his father as they were for him.