Optimal Control with Aerospace Applications

286 Pages·2014·2.29 MB·English

by  James M Longuski

Space Technology Library
James M. Longuski
José J. Guzmán
John E. Prussing
Optimal Control
with Aerospace
Applications
Optimal Control with Aerospace Applications
SPACETECHNOLOGY LIBRARY
PublishedjointlybyMicrocosmPressandSpringer
TheSpaceTechnologyLibraryEditorialBoard
ManagingEditor:JamesR.Wertz,Microcosm,Inc.,ElSegundo,CA
EditorialBoard: Roland Dore´, Professor and Director InternationalSpace Univer-
sity,Strasbourg
Tom Logsdon, Senior member of Technical Staff, Space Division,
RockwellInternational;ret.
F.LandisMarkley,NASA,GoddardSpaceFlightCenter;ret.
Robert G. Melton, Professor of Aerospace Engineering, Pennsyl-
vaniaStateUniversity
Keiken Ninomiya, Professor, Institute of Space & Astronautical
Science
JehangirJ.Pocha,Letchworth,Herts.
RexW.Ridenoure,JetMicrocosm,Inc.,Torrance
Gael Squibb, Jet Propulsion Laboratory, California Institute of
Technology
MartinSweeting,ProfessorofSatelliteEngineering,Universityof
Surrey
Forfurthervolumes:
http://www.springer.com/series/6575
James M. Longuski • Jose´ J. Guzma´n
John E. Prussing
Optimal Control with
Aerospace Applications
S
TT
L
Published jointly by
Microcosm Press
El Segundo, California
123
JamesM.Longuski Jose´J.Guzma´n
PurdueUniversity OrbitalSciencesCorporation
Lafayette,IN,USA Chantilly,VA,USA
JohnE.Prussing
UniversityofIllinois
atUrbana-Champaign
Urbana,IL,USA
ISBN978-1-4614-8944-3 ISBN978-1-4614-8945-0(eBook)
DOI10.1007/978-1-4614-8945-0
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2013949151
©SpringerScience+BusinessMediaNewYork2014
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting, reproduction onmicrofilmsorinanyotherphysical way,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynow
knownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnectionwith
reviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeingenteredandexecuted
onacomputersystem,forexclusiveusebythepurchaserofthework.Duplicationofthispublicationor
partsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthePublisher’slocation,inits
currentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Permissionsforusemaybe
obtainedthroughRightsLinkattheCopyrightClearanceCenter.Violationsareliabletoprosecutionunder
therespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpublication,
neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforanyerrorsor
omissions thatmaybemade.Thepublisher makes nowarranty, express orimplied, withrespect tothe
materialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
Optimalcontroltheoryhasbecomesuchanimportantfieldinaerospaceengineering
that no graduate student or practicing engineer can afford to be without a working
knowledge of it. Unfortunately, there is no modern text which begins from scratch
to teach the reader the basic principles of the calculus of variations, to develop the
necessary conditions step-by-step, and to introduce the elementary computational
techniquesofoptimalcontrol.
Our book assumes that the reader has only the usual background of an under-
graduateengineering,science,ormathematicsprogram,namely,calculus,differential
equations,andnumericalintegration.
Weassumenootherknowledge.Wedonotrequirethereadertoknowwhatcalculus
ofvariationsis,whatnecessaryconditionsmean,norwhatatwo-pointboundary-value
problementails.ItdoesnotmatterifthereaderhasneverheardoftheEuler-Lagrange
theorem, the Weierstrass condition, Pontryagin’s Minimum Principle, or Lawden’s
primervector.
Our goal is to provide the reader with sufficient knowledge so that he or she
cannotonlyreadtheliteratureandstudythenext-leveltextbook(suchasBrysonand
Ho’sAppliedOptimalControl)butalsoapplythetheorytofindoptimalsolutionsin
practice.
Toaccomplishthegoalsofthisintroductorytext,wehaveincorporatedanumber
of features as follows. Several theorems are presented along with “proof outlines”
that favor a heuristic understanding over mathematical rigor. Numerous rigorous
treatmentsarecitedinthereferencesandthebookbibliographytosupportthereader’s
advancedstudies.
In presenting the Euler-Lagrangetheorem, we treat two differentversions which
appear in the literature. In the first method (followed by Bryson and Ho [1975]),
we adjoin terminal constraints to the cost functional through the use of additional
Lagrange multipliers. We refer to this approach as the “adjoined method” and note
thatit has becomea sort of gold standardin the literature since the revised printing
of Bryson and Ho’s Applied Optimal Control in 1975. This approach leads to a
form of the transversality condition which we refer to as the “algebraic form.” In
publications prior to 1975, a number of authors use an approach which we refer to
v
vi Preface
as the “un-adjoined method” which does not adjoin the terminal constraints to the
costfunctionalandhencedoesnotintroduceanyadditionalmultiplierstobesolved.
Theun-adjoinedmethodleadstoa“differentialform”ofthetransversalitycondition
asgivenbyCitron[1969],Hestenes[1966],KennethandMcGill [1966],andPierre
[1969].Theun-adjoinedmethodisparticularlyamenabletosimpleproblemsinwhich
theterminalconstraintsarealgebraicallyeliminatedfromthetransversalitycondition.
Each method has its strengths and weaknesses as observed by Citron [1969], who
is one of the few authors who discuss both methods. Introducingthe reader to both
methods,withapplicationstocurrentaerospaceproblems,isanimportantfeatureof
thepresenttext.
Throughoutthe book, we make use of the time-optimallaunch of a satellite into
orbitasanimportantcasestudy,andweprovideadetailedanalysisoftwoexamples:
launch from the Moon and launch from the Earth. In the Moon-launch case, we
assumeconstantacceleration(fromthrusters),nodrag,anduniformflat-Moongravity.
For Earth launch we include time-varying acceleration, drag from an exponential
atmosphere,and uniformflat-Earthgravity.AppendicesA and B provideMATLAB
code to solve the resulting two-point boundary-valueproblems. In Appendix C, we
also set up and provide MATLAB code to solve a geocentric low-thrust transfer
problem.
A modern approach to Lawden’s primer vector theory is presented for optimal
rocket trajectories. The important special cases of constant-specific impulse and
variable-specificimpulsearetreatedindetail.
Anextensiveannotatedbookbibliographyliststhereferenceswefoundmostuseful
inthepreparationofthistext.Thesesourcesrangefromhighlypragmaticapplication
approaches (for engineers) to rigorous, theoretical treatments (for mathematicians).
Thesecondbibliographylistsnumerouspapersandreportsthatdemonstratethevast
rangeofrelatedaerospaceapplications.
Finally, for the weary and the worried, we provide a few “Curious Quotations”
(inAppendixD)toletthereaderknowthatmanygreatmindsandrenownedauthors
have expressed their own concerns, often in humble and humorousways, about the
vastchallengesthatthecalculusofvariationsandoptimalcontrolpresenttoallofus.
Lafayette,IN,USA JamesM.Longuski
Chantilly,VA,USA Jose´ J.Guzma´n
Urbana,IL,USA JohnE.Prussing
Acknowledgments
FirstandforemostIthankDr.WilliamF.Powers,whotaughtmehisgraduatecourse
onoptimizationofspacetrajectoriesinthewinterof1974whenhewasaprofessorof
aerospaceengineeringattheUniversityofMichigan.Dr.Powershashadanillustrious
career as a leader in the application of control theory, as a professor, as a NASA
consultant for the Space Shuttle, and as the vice president of research for the Ford
MotorCompany.HeisamemberoftheNationalAcademyofEngineering,theRoyal
SwedishAcademyofEngineeringSciences,andtheUniversityofFloridaFoundation
BoardofDirectors.
This book is largely based on the lecture notes I obtained from Dr. Powers, and
I have received his permission and encouragementto flesh out those notes to form
thepresenttext.Ihaveextendedthematerialovermyyearsofteachingoptimization
ofspacetrajectories.Inmy effortto teachandlearnmoreaboutthisfascinatingand
importantsubject,IhaveoftenmarveledatwhatanexcellentcourseDr.Powerstaught
me. I hasten to add that any errorsin the text are entirely my own—andshould not
reflectinanywayonDr.Powers.
I thank my colleagues, my doctoral students, the graduate and undergraduate
studentswhotookmycourseonOptimizationinAerospaceEngineering(AAE508),
andthestaffatPurdueUniversitywhohelpedinmanysignificantwaystomakethe
finalmanuscriptasclear,accurate,andusefulaspossible.
In particular I thank Prof. Mohammad Ayoubi, Dr. Julia L. Bell, Ms. Nicole
Bryan,Ms.ErinCalderwood,Ms.JasmineCashbaugh,Mr.AlanCastillejoRobles,Dr.
K.JosephChen,Dr.DianeCraig,Mr.MichaelCroon,Ms.AshwatiDas,Ms.Meredith
Evans, Lt. Jennifer Fuka, Mr. Giacinto Genco, Mr. Filippo Genco, Mr. Seung
Yeob Han, Mr. Adam Harden, Mr. Patrick Hayes, Mr. Evan Helmeid, Mr. Gregory
Henning, Mr. Kyle Hughes, Mr. Junichi Kanehara, Ms. Aizhan Kinzhebayeva,
Mr.MichaelKean,Dr.KevinKloster,Mr.RichardLang,Mr.FrankLaipert,Mr.Karl
Madon, Mr. Nicholas Makarowski, Dr. Belinda Marchand, Ms. Kaela Martin (nee
Rasmussen), Dr. T. Troy McConaghy, Mr. Wesley McDonald, Prof. Ken Mease,
Mr.JamesMoore,Ms.BhuviNirudhoddi,Dr.JeffreyOnken,Mr.Jose´ F.PazSolda´n
Guerra,Dr.AnastassiosPetropoulos,Ms.LuciePoulet,Mr.BlakeRogers,Mr.Saverio
Rotella, Mr. Sarag J. Saikia, Dr. Oleg Sindiy, Ms. Nissa Smith, Ms. Tracey Smith,
vii
viii Acknowledgments
Mr. Christopher Spreen, Mr. Nathan Strange, Prof. Dengfeng Sun, Prof. Steven G.
Tragesser,Prof. Brad Wall, Dr. Geoff Wawrzyniak,Ms. Rozaine Wijekularatne,Mr.
AndyWiratama,andDr.ChitHong“Hippo”Yam.
Special thanks go to Mr. Peter Edelman, Mr. Rob Falck, Dr. Joseph Gangestad,
Mr.KshitijMall,Dr.GeorgeE.PollockIV,andProf.MarcWilliams.
ThankstothePurduephysicslibrarians,Ms. LilConarroeandMs. DonnaSlone,
for their professionalismand their patiencein helpingme find importantreferences.
I also thank Ms. Karen Johnson, Ms. Jennifer LaGuire, and Ms. Vickie Schlene for
theirsecretarialassistance.
IthanktheeditorialstaffatSpringerfortheirprofessionalandunswervingsupport,
inparticularDr.Harry(J.J.)Blom,Ms.MaurySolomon,andMs.NoraRawn.Thanks
also to my friend and colleague, Dr. James R. Wertz of Microcosm Press for co-
publishingourbook.
Finally my most grateful thanks to my wife and best friend, Holly, for her
unwaveringsupport,herenthusiasticencouragement,andespeciallyforherlove.
I apologizeto any contributorI shouldhave acknowledged—pleaselet me know
whoyouaresoIcanthankyouinafutureedition.
J.M.Longuski
Acknowledgments ix
Itisoftendifficultfortheworkingengineertousecalculusofvariations(COV)in
thenormalcourseofbusiness.We hopethatthisbookmakesthatprocesseasierand
fasterforproblemsamenabletotheapplicationofCOV.Forexample,forcontinuous
thrust-steeringsystemsencounteredduringpoweredascent(launch),powereddescent
(landing), and low-thrust trajectories, COV can provide a great set of tools for the
mission analyst. The material presented in this book and in the extensive list of
referenceswillguidetheengineerinusingthetheoryforpracticalproblems.Perhaps
more importantly, the practicing engineer could use this book to understand the
software tools available for trajectory optimization and to provide these software
toolswithinitialapproximationsthatwillspeeduptheconvergenceprocess.Iwould
like to thank the professors that inspired me to pursue trajectory optimization: Dr.
KathleenC.Howell,Dr.JamesM.Longuski,Dr.StephenJ.Citron,andDr.MartinJ.
Corless. I would like to thank a.i. solutions (Mr. Daryl Carrington, Mr. Jeff Dibble,
Dr. Conrad Schiff, Dr. Ariel Edery, Dr. Peter Demarest, and Mrs. Laurie Mann
(neeMailhe))and NASA GoddardSpace FlightCenter (Mr. David Folta, Mr. Mark
Beckmnan,Mr.StevenCooley,andMr.StevenHughes)allwithwhomIworkedand
discussed many challengingoptimizationproblems. I would like to thank the Johns
Hopkins Applied Physics Laboratory (APL) for providing funding under the Stuart
S. Janney program (spring 2005). This funding allowed the development of some
of the numerical work and illustrations in the book. Also at APL, I would like to
thankDr.RobertW.Farquhar,Dr.DavidW.Dunham,Mr.PeterJ.Sharer,Mr.James
T. Kaidy, Dr. J. Courtney Ray, Dr. Uday Shankar, and Dr. Thomas E. Strikwerda
for invaluable discussions on mission design, trajectory optimization, and attitude
control. While at APL, I also had a chance to work with Mr. Jerry L. Horsewood
fromSpaceFlightSolutions.WorkingwithJerryallowedmetounderstandsomeofthe
finer pointsof low-thrusttrajectoryoptimization.Also, many thanksto Dr. Gregory
Chirikjianand Dr. Joseph Katz from the Johns HopkinsUniversity and to Dr. Chris
D. Hall from Virginia Tech for part-time teaching opportunities at their respective
institutions. I would like to thank Orbital Sciences and Dr. James W. Gearhart for
providing a challenging work environment and great applied problems to work on.
Finally,I’dliketothankmywife,Natalia,andmydaughter,Sofia,fortheirloveand
patience.
J.J.Guzma´n