This project is part of an ongoing program by the principal investigator revolving about problems dealing with the control of nonlinear systems under imperfect or partial observations. Topics include: Adaptive Control, treated as a Bayesian Problem, large time behavior of the filtering diffusion, asymptotic behavior of exit distributions of the filtering diffusion, regularity of the value function in Partially Observed Control, stability under small perturbations, and uniqueness of viscosity solutions of Bellman equations. This research helps lay the groundwork for the automatic control of vehicles or processes when measurements of the current state and the environment are uncertain due to random effects or noise. One is interested in separating the noise from the true measurements and also designing a control procedure which is somewhat insensitive to random fluctuations, as one typically finds in most physical systems.
