Mathematical Sciences: Asymptotic Analysis for Some Stochastic Systems

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This project has three distinct parts: (1). A stopping rule for least squares identification is proposed. It is so designed that with any degree of accuracy, the recursive procedure will terminate if the iterates are inside a confidence ellipsoid with high probability. (2). The robustness problem of some stochastic approximation type algorithms will be investigated. The necessary and sufficient condition for convergence is expected to be derived. (3). The problem of open queueing network with parallel observers will be studied. Nearly optimal control and a suitable numerical algorithm are expected to be obtained. These represent areas in which mathematics may be used to solve problems related to the control of mechanical and electrical systems.