Mathematical Sciences: The Structure of the Small-Time      Reachable Set and Regularity Properties of Optimal          Trajectories for Control- Linear Systems
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
This project addresses the qualitative structure of                        small-time reachable sets and piecewise regularity properties                   of optimal controls for nonlinear systems.  For single-input                    systems it is known that optimal trajectories can exhibit                       undesirable features such as chattering bang-bang arcs if the                   dimension of the system becomes too large.  This may be due to                  a lack of possibility to influence the system via the control                   vector field.  To explore that scenario this project seeks to                   analyze the local structure of small-time reachable sets in                     dimension n for increasing values of n, in particular, to                       develop tests for optimality of complex concatenations of bang                  and singular arcs, and ii) to investigate multi-input systems                   using higher-order approximating cones which take into account                  specific structures of trajectories under consideration.  The                   underlying technical framework is provided by                                   differential-geometric descriptions and Lie-algebraic                           computational techniques.                                                            The long term aim of this work is to achieve a qualitative                 understanding of the local behavior of nonlinear control                        systems.  Aside from its evident theoretical relevance, such a                  knowledge might also be practically of interest for any                         possible future approach to design involving nonlinear                          components.
{'FirstName': 'Heinz', 'LastName': 'Schaettler', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Heinz M Schaettler', 'EmailAddress': 'hms@wustl.edu', 'NSF_ID': '000194452', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Washington University', 'CityName': 'SAINT LOUIS', 'ZipCode': '63110', 'PhoneNumber': '3147474134', 'StreetAddress': 'ONE BROOKINGS DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Missouri', 'StateCode': 'MO', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'MO01', 'ORG_UEI_NUM': 'L6NFUM28LQM5', 'ORG_LGL_BUS_NAME': 'WASHINGTON UNIVERSITY, THE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8820413.xml'}