Mathematical Sciences: Geometric and Computational          Foundations of Nonlinear Feedback Control
{'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}
Work underway on Control of air and spacecraft that have                   nonlinear dynamics suggests many new problems of geometric                      control theory.  In previous work, the PI has introduced the                    cauchy characteristic multifoliate structure associated with a                  control system.  It is a basic geometric invariant of the                       feedback structure, ultimately determining (both locally and                    globally) what can be accomplished by applying state-feedback                   control to the apparatus.  This proposed work will carry on the                 study of the cauchy characteristic structure both from the point                of view of traditional mathematics (e.g. to what extent does the                cauchy characteristic structure determine the control system up                 to feedback equivalent?)  and from the LISP/Symbolic computation                point of view.  In parallel, work will also continue on the Lie-                theoretic foundation of various numerical algorithms for dealing                with nonlinear differential equations.  For example, how can the                idea of the classical Runge-Kutta algorithm be implemented for                  differential equations which live on a differentiable manifold                  that carries a Lie group structure?  Many potential applications                are possible e.g. to the control of rotating and nonlinear                      mechanical systems, as encountered in the study of aircraft and                 Robotics.                                                                            This project falls into the broad area of control science,                 which is an interdisciplinary research activity involving both                  mathematics and engineering.
{'FirstName': 'Robert', 'LastName': 'Hermann', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Robert Hermann', 'EmailAddress': 'BLHermann@aol.com', 'NSF_ID': '000158328', 'StartDate': '02/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Association For Physical & Systems Mathematics', 'CityName': 'BROOKLINE', 'ZipCode': '024463907', 'PhoneNumber': None, 'StreetAddress': '200 IVY ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'MA04', 'ORG_UEI_NUM': 'CSJBJE6SEDG7', 'ORG_LGL_BUS_NAME': 'MAB COMMUNITY SERVICES, INC.', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1454', 'Text': 'SYSTEMS THEORY'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701195.xml'}