Aiming control: (D,T)-stability and residence probability controllers

This dissertation is devoted to formulation and analysis in the notion of the first passage time of a linear stochastic system driven by white noise, which is described by an ITO stochastic differential equation. In general, it is possible that one of trajectories governed by an ITO stochastic differential equation will exit a given domain irrespective of the intensity of white noise. In other word, the probability of the first passage time being finite is not zero independent of the system's stability in case without white noise.;It was shown the mean first passage time can be represented as the solution of a certain boundary value problem, however this problem is very difficult to solve. When the noise intensity is sufficiently small, the approximation techniques of large deviation theory can be utilized. In this dissertation the probability of the first passage time less than a given finite time T in a given finite open domain D is approximately characterized by large deviation theory and is considered as a measure of system's stability as residence probability in a domain.;Given this residence probability, (D,T) stability problem and residence probability controllability problem are formulated. Strong and weak residence probability controllability problem are also introduced and designed to find a controller and an initial domain D. These controllers are also compared with covariance, H_2 and H_infinity optimal controllers. Finally time varying residence probability controllers for time invariant linear plants are also introduced and analyzed.