Geometric and Stochastic System Theory (REU Supplement)
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{'SignBlockName': 'Radhakisan Baheti', 'PO_EMAI': None, 'PO_PHON': None}
Recently the PI's have obtained some explicitly solvable stochastic             optimal control problems of diffusion type in noncompact, rank-one              symmetric spaces.  It is proposed to generalize these results to                noncompact symmetric spaces of rank greater than one, compact                   symmetric spaces, and homogeneous spaces.  Such manifolds provide               models for many physical phenomena, and relatively few examples of              solvable stochastic control problems are known.  It is proposed to              continue work in stochastic adaptive control by investigating the               asymptotic distribution and the rate of convergence of the average              costs or the estimators for continuous-time, linear stochastic systems          with and without time delays.  It is proposed to investigate some               specific models, and to expand work on the adaptive control of                  bilinear stochastic systems.  It is proposed to relate adaptive                 control to geometric control by investigating some stochastic adaptive          control problems in the aforementioned symmetric spaces.  The                   aggregation of an autoregressive process is often used in                       applications, and they propose to continue some of their previous               work.  Some estimation problems have been solved in compact Lie groups          and a symmetric space, and it is proposed to expand this work to other          Lie groups and symmetric spaces.  From these special estimation                 results and the relation between nonlinear filtering and stochastic             control, it is proposed to use the aforementioned estimation and                stochastic control results to solve some nonlinear filtering problems.
[{'FirstName': 'Tyrone', 'LastName': 'Duncan', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Tyrone E Duncan', 'EmailAddress': 'duncan@math.ku.edu', 'NSF_ID': '000472110', 'StartDate': '04/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Bozenna', 'LastName': 'Pasik-Duncan', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bozenna Pasik-Duncan', 'EmailAddress': 'bozenna@ku.edu', 'NSF_ID': '000409922', 'StartDate': '04/15/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1360', 'Text': 'EWFD-Eng Workforce Development'}, {'Code': '1454', 'Text': 'SYSTEMS THEORY'}, {'Code': '1518', 'Text': 'CONTROL, NETWORKS, & COMP INTE'}]
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