Research in Differential Games
{'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}
The principal investigator intends to develop the theory of the            so-called differential games.  This term refers to problems described           by differential equations in which there are two or more different              equations in which there are two or more different control variables,           one for each decision maker or "player".  For instance, competition             games on stock markets or pursuit-evasion games (encountered in aerial          combat) can be mathematically analyzed by using the theory of                   differential games.  The latter represents a mixture of more                    traditional game theory, control and various recent mathematical                theories about partial differential equations.                                       The theory of differential games developed by the principal                investigator will be used to develop methods for approximating the              solutions of differential games to an arbitrary degree of accuracy.             The first method to be used is that of approximating the continuous             time game by a sequence of multimove infinite games corresponding to            the discretization of the time interval.  It will be shown that the             solutions of these infinite multimove games converge to the solutions           of the original game.  Estimates of the rates of convergence of the             values of the n-th stage games to the value of the differential game            will be obtained.  If the Isaacs condition does not hold then mixed             strategies will be used.  Methods for solving multimove infinite games          will also be investigated, as the solutions of such games is an                 essential part of the program.  For the multimove games, methods based          on necessary conditions and direct backward recursions will be                  investigated.  Another method that will be developed is one based on            the numerical solution of the Isaacs equation.  Since the value                 function is a viscosity solution of this equation, the adaptability to          out problem of numerical techniques proposed in the literature will be          investigated.  The preceding program will first be applied to games of          fixed duration and then extended to games of generalized pursuit and            evasion and to games of survival.                                                    A question that arises in pursuit and evasion problems that is             different from the two person zero-sum game is that of determining              those initial points from which capture can be assured and those                initial points from which evasion can be assured.  We shall                     investigate this problem when both pursuer and evader are permitted to          choose their actions at each instant time, knowing the previous                 actions of both players.  This is in contrast to previous Soviet and            other work in which only one of the antagonists is allowed to choose            his action as play evolves.                                                          Program Director for Applied Mathematics recommends a twenty-four          month award funded jointly with the Air Force Office of Scientific              Research.
{'FirstName': 'Leonard', 'LastName': 'Berkovitz', 'PI_MID_INIT': 'D', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Leonard D Berkovitz', 'EmailAddress': None, 'NSF_ID': '000307364', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Purdue Research Foundation', 'CityName': 'WEST LAFAYETTE', 'ZipCode': '479064353', 'PhoneNumber': '3174946200', 'StreetAddress': '1281 WIN HENTSCHEL BLVD STE 2500', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'IN04', 'ORG_UEI_NUM': 'C1G1LGYJF5G5', 'ORG_LGL_BUS_NAME': 'PURDUE RESEARCH FOUNDATION', 'ORG_PRNT_UEI_NUM': 'YRXVL4JYCEF5'}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '2330', 'Text': None}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8700813.xml'}