Estimation and analysis of nonlinear stochastic systems.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.Vita.Bibliography: leaves 147-157.Ph.D

Finite dimensional nonlinear estimation in continuous and discrete time

Bibliography: p. 19-20.Caption title. "October 2, 1978."Supported in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-77-C-0101 Air Force Office of Scientific Research Contract AFOSR 77-3281 National Science Foundation Grant ENG 76-11106Steven I. Marcus, Sanjoy K. Mitter, Daniel Ocone

Control for large scale and uncertain systems : (interim report)

Research supported by Air Force Office of Scientific Research (AFSC) Research Grant AF-AFOSR 72-2273. Report for 1975/76 distributed through Industrial Liaison Program.by Michael Athans and Sanjoy K. Mitter

Research on optimal control, stabilization and computational algorithms for aerospace applications

The research carried out in the areas of optimal control and estimation theory and its applications under this grant is reviewed. A listing of the 257 publications that document the research results is presented

Nonlinear estimation theory and phase-lock loops.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS.Vita.Bibliography : leaves 226-229.Ph.D

ESTIMATION AND ANALYSIS OF NONLINEAR STOCHASTIC SYSTEMS

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a solvable Lie group, necessary and sufficient conditions for stochastic stability are derived. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups are also discussed. The study of estimation problems involving bilinear systems is motivated by several practical applications involving rotational processes in three dimensions. Two classes of estimation problems are considered. First it is proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. Finally, the theory of harmonic analysis is used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces