MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB
This thesis investigates the adaptive stochastic control of linear dynamic systems with purely random parameters. Hence there is no posterior learning about the system parameters. The control law is non-dual still it has the qualitative properties of an adaptive control law. In the perfect measurement case, the control law is modulated by the priori level of uncertainty of the system parameters. Optimal stochastic control of dynamic systems with uncertain parameters has certain limitations. For the linear-quadratic optimal problem, the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold. By considering the discounted cost problem, we have obtained some results on optimality versus stability for this class of stochastic control problems. For the noisy sensor measurement case the optimal fixed structure estimator-controller is obtained. The control law requires the solution of a coupled nonlinear two-point boundary value problem. Computer simulations of the forward and backward difference equations provided some insight into the uncertainty threshold for the closed loop system.