geometric contro theory 111111111

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1、GEOMETRICCONTROLTHEORYVELIMIRJURDJEVICUniversityofTorontoCAMBRIDGEUNIVERSITYPRESSContentsIntroductionpagexiiiAcknowledgmentsxviiPartone:Reachablesetsandcontrollability11Basicformalismandtypicalproblems31Differentiablemanifolds31.1Differentiablemappings61.2Thetangentspace71.3

2、Thecotangentspace82Vectorfields,flows,anddifferentialforms112.1Derivations112.2Thetangentbundleandcotangentbundle122.3Vectorfieldsanddifferentialforms143Controlsystems203.1Familiesofvectorfieldsandcontrolsystems27Notesandsources312Orbitsoffamiliesofvectorfields321Theorbittheo

3、rem321.1Submanifolds331.2Integralsubmanifolds351.3Proofoftheorbittheorem362Liebracketsofvectorfieldsandinvolutivity402.1Liebracketsofvectorfields402.2Liealgebras422.3Involutivityandintegralmanifolds433Analyticvectorfieldsandtheirorbitproperties483.1Liegroups50vnviiiContents3.

4、2Grouptranslationsandinvariantvectorfields513.3Orbitsofinvariantvectorfields523.4GLn(R)anditssubgroups543.5Homogeneousspaces554Zero-timeorbitsoffamiliesofvectorfields564.1Zero-timeorbitsofanalyticvectorfields59Notesandsources633ReachablesetsofLie-determinedsystems641Topologic

5、alpropertiesofreachablesets651.1ReachablesetsoftheformAf(x,

6、ntrollability89Notesandsources944Controlaffinesystems951Kinematicequationsofarollingsphere962Linearsystems1003Controlofarigidbodybymeansofjettorques1034Reachabilitybypiecewise-constantcontrols^1055Reachabilitybysmoothcontrols1106Recurrentdriftsandcontrolofarigidbody1127Compac

7、tconstraintsandtheclosureofthereachablesets1178Non-holonomicaspectsofcontroltheory121Notesandsources1245Linearandpolynomialcontrolsystems:1251Feedback,controllability,andthestructureoflinearsystems1261.1Controllabilityindicesandthefeedback-decompositiontheorem1291.2Controllab

8、ilityandthespectrum1332Boundedcontrolsandthebang-bangprinciple1343Co