UC San Diego

In this dissertation, we study stochastic disturbance rejection, performance, and optimal control. This study is composed of three distinct investigations: an application, theory, and the development of an algorithm. The studies are linked by optimal control and its associated performance. In application, we study a disturbance rejection problem in a production pulsed light source to yield quantifiable and guaranteed improved performance over existing control techniques. We apply generalizations of continuous-discrete Kalman filter ideas for actuator and disturbance state estimation and prediction; following Harris, we analyze the variance light source output prediction errors in order to ascertain the theoretical lower bound for closed-loop control performance. We establish and solve a non-standard regularized minimum variance control problem, and use the derived control law in concert with the continuous-discrete estimator to construct a certainty-equivalence state-feedback controller. We demonstrate on a production light source that the estimator-controller yields closed-loop performance near the derived theoretical lower bound for the hardware. The theoretical framework is constructed around the application of Nonlinear Model Predictive Control (NMPC) schemes to discrete-time, nonlinear systems which are subject to persistent, stochastic disturbances. We pose a discounted-cost infinite-horizon optimal control problem and use its optimal value function as the performance benchmark to which all subsequent NMPC closed loops are compared. Following Jadbabaie, Hauser, Grüne, and Rantzer, who address performance and stability of NMPC in the undisturbed case, we employ monotonicity of finite- horizon optimal control value functions to establish an upper bound to NMPC loop performance. We highlight assumptions which are required to achieve this upper bound and offer insight as to how one might satisfy these assumptions. We tackle a third problem which is unrelated to performance of a closed-loop system, but which finds application in real-time MPC calculations. We consider the development of distributed algorithms which cooperating nodes can employ to solve a global optimization problem. The global solution constitutes the performance benchmark of interest and we seek distributed algorithms which nodes can employ in order to achieve this solution. Each node has access to local information which is suitable for solving a local optimization problem subject to local constraints; the nodes are coupled through a coupling constraint and through the structure of the global cost function. Our focus lies in understanding the required information content exchange between nodes to solve the global optimization problem. We show that the amount of information content is related to activity of both local constraints and coupled constraints at the global solution