Identification and Adaptive Control Methods for Some Stochastic Systems

This dissertation is focused on the identification and adaptive control of some stochastic systems. Initially a survey of some adaptive control problems for both discrete and continuous time stochastic systems is provided. Discrete time branching processes are described and some results on parameter estimation and adaptive control for these processes are reviewed. Then continuous time branching processes are introduced and the main results in this dissertation concerning estimation and adaptive control are given. The family of estimators is shown to be strongly consistent and the optimal rate of convergence of this family of estimators is obtained. Furthermore some other asymptotic properties of these estimators are verified. An adaptive control is given that posses self-tuning property. It is shown that it does not achieve the optimal asymptotic cost for the known system. Finally some computational methods and simulations are given for a variety of stochastic differential equations driven by a Brownian motion or an arbitrary fractional Brownian motion and computational properties of the parameter estimates for the branching processes are given