Mathematical Sciences: Control Theory and Vector Field      Systems
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This project continues mathematical research into the                      modelling of physical systems by differential equations                         containing free functions, the controls.  One means of analyzing                such systems is the use of transforms, state feedback and                       coordinate change for example, to reduce the system to a linear                 one.  This amounts to determining when a local basis of vector                  fields can be chosen which, in proper local coordinates, is                     linear.  Although this can rarely be expected, the next most                    reasonable case would be bases which generate nilpotent or                      solvable Lie algebras.  The project will continue work towards                  this end.  Best results to date are possible when the free motion               or uncontrolled part of the system is not present.  Otherwise,                  major obstacles are presented due, primarily, to the large number               of (inequivalent) nilpotent systems present even in low                         dimensions.  Another, equally important, question is that of                    determining invariants of a system which will show whether or not               related nilpotent or solvable Lie algebras can be expected.                          A second line of investigation will focus on certain                       transformations called contact maps.  These are maps which are                  used to characterize jets and jet bundles of functions defined on               higher dimensional Euclidean spaces.  Differential operators may                be defined in terms of jets and contact transformations.  They                  provide a method for prolonging solutions.  The basic problems                  faced in the development of this theory are two:  a                             characterization of self-maps of jet bundles which are contact                  transformations and the construction of contact transformations                 which leave a given manifold invariant.  While there are several                fundamental results related to these questions due to Lie and                   Backlund, specific examples are needed.  In addition,                           constructive methods for obtaining contact tranformations need to               be developed.  A final direction this research will follow                      concerns control system linearization via an extended feedback                  group, specifically, canonical forms for control systems which                  can be obtained via the feedback group will be sought.
{'FirstName': 'Henry', 'LastName': 'Hermes', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Henry Hermes', 'EmailAddress': None, 'NSF_ID': '000198195', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Colorado at Boulder', 'CityName': 'Boulder', 'ZipCode': '803090001', 'PhoneNumber': '3034926221', 'StreetAddress': '3100 MARINE ST', 'StreetAddress2': 'STE 481 572 UCB', 'CountryName': 'United States', 'StateName': 'Colorado', 'StateCode': 'CO', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'CO02', 'ORG_UEI_NUM': 'SPVKK1RC2MZ3', 'ORG_LGL_BUS_NAME': 'THE REGENTS OF THE UNIVERSITY OF COLORADO', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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