Conditionally Gaussian processes in stochastic control theory Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6d570069f

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  • An application of the theory of conditionally Gaussian random processes to filtering and stochastic control problems is presented here. The results due to Liptser and Shiryayev are proved to hold in the multidimensional case under somewhat relaxed conditions, when compared to the original ones. Such a generalization is required from the point of view of modelling real engineering systems. The concept of a weak solution to the stochastic differential equations involved in the problem formulation is used. A detailed filter derivation for conditionally Gaussian multidimensional processes is presented. In this derivation both conditionally Gaussian processes and nonlinear filtering theories are used. A finite dimensional, recursive formula (filter) for calculating the optimal mean-square estimate of the unobservable part of the process is obtained. An application of the derived filter to an optimal stochastic control problem is presented. The class of systems under consideration includes linear, partially observable control systems with quadratic criteria, that have random coefficients which are certain functionals of a Wiener process. All stochastic processes involved in the problem formulation are assumed to be strong solutions to the corresponding stochastic differential equations. Separation of filtering and control is shown to hold, and the optimal regulator is a function of both the observable part and the estimate of the unobservable part of the process. Sufficient conditions for an optimal control to exist are expressed through the existence of a solution to a certain Cauchy problem of the parabolic type partial differential equation. The existence and uniqueness of a solution to the above mentioned partial differential equation is studied. The references to the results used in the text are given. A simple simulation example, which gives an illustration of the obtained results, is also presented.
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