Ph.D. Thesis Defense by Dawn C. Foley
Friday, January 11, 2002

(Dr. Nader Sadegh, advisor)

"Short Horizon Optimal Control of Nonlinear Systems via Discrete State Space Realization"

Abstract

The complexity of nonlinear systems often require modelling techniques to be data driven.  Although this may yield an accurate model, if the model is not representable in state space form, it may not be suitable for system analysis and control.

We therefore examine data driven modelling procedures for creating a discrete-time input-output map that can be transformed into an observable state space form.  We first present previous results of a model form that guarantees the existence of an observable state space realization, as well as the state equations that can be implemented using that form.  We then examine the feasibility of NARMA models, feedforward neural networks, and nodal link perceptron networks with local basis functions in creating the model.

Once a system can be modelled in state space, a number of control options are available, although many of these are complex and restrictive.  Therefore, we will also present a novel controller for discrete nonlinear state space systems.  We have chosen a finite horizon optimal controller, designed to decrease computational expense in relation to more traditional optimal controllers. The controller will not require a solution to a dynamic programming problem, or approximate solutions via the Riccati equation.

Specifically, a nonlinear feedback control law will be designed, where a neural network in the feedback loop will be used to generate an optimal control input based on the current states and desired states. The generated input will be minimal with respect to a quadratic cost function with parameters governing the desired final states, and the magnitude and variation of the control input.  A local stability and robustness analysis of the controller is also presented.