Mathematical Sciences: Optimal Control Theory of            Input-Output Systems - Control Theory of Partial            Differential Equations
{'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 work will focus on the control theory of                           partial differential equations.  Two primary thrusts                            will be undertaken.                                                                     The first line of investigation deals with optimal                      control of input-output systems described by partial                            differential equations, functional differential                                 equations and associated applications.  This work will                          expand on recent work of the principal investigator                             which extended the classical Pontryagin maximum                                 principle to general nonlinear systems in infinite                              dimensions.  Applications of the resulting convergence                          principles have only been exploited in classical cases                          to date.  Work will now be directed to at least two new                         areas: functional differential equations and to shape                           optimization where the control is a time-dependent set.                         Here the general maximum principle is especially suited                         since the state equation is a partial differential                              equation in the variable domain and does not fit any of                         the available maximum principles.                                                       Work is also planned on the problem of                                  characterizing the set of attainable states for both the                        heat equation and the wave equation, primarily on                               special geometric domains at first.  In this active area                        of research, boundary conditions through which the                              control action is exercised are not specified.  These                           questions often reduce to problems in Fourier analysis                          in which estimates on the norms of sequences are                                required.  Fundamental questions focus on determining                           attainable states by means of boundary control, a state                         being represented by a function in the space variables                          which one wishes to reach in prescribed time from an                            initial shape.
{'FirstName': 'Hector', 'LastName': 'Fattorini', 'PI_MID_INIT': 'O', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Hector O Fattorini', 'EmailAddress': None, 'NSF_ID': '000109818', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Los Angeles', 'CityName': 'LOS ANGELES', 'ZipCode': '900244200', 'PhoneNumber': '3107940102', 'StreetAddress': '10889 WILSHIRE BLVD STE 700', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '36', 'CONGRESS_DISTRICT_ORG': 'CA36', 'ORG_UEI_NUM': 'RN64EPNH8JC6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, LOS ANGELES', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701877.xml'}