Stochastic Control and Nonlinear Estimation

In stochastic control, a major focus of this research was numerical methods for finding approximately optimal control laws. Dynamic programming and Monte Carlo optimization algorithms were followed. Both probabilistic methods, based on weak convergence ideas, and analytical methods were used to prove convergence of algorithms. The latter were based on viscosity solution methods for nonlinear partial differential equations. In nonlinear estimation, low dimensional approximate nonlinear filters were found for cases when a piecewise one-to-one function of a system state plus low intensity observation noise was observed.