Modeling and Control of Nonlinear Systems.

Abstract

Abstract : We have conducted research on the modeling and control of nonlinear systems. Our efforts have been directed toward understanding the control of truly nonlinear behavior as well as the synthesis of control laws for systems that can be nearly transformed into linear systems (via approximate feedback linearization). We have introduced a new framework for understanding and analyzing the stability and control of nonlinear maneuvering systems. This approach is based on the concept of transverse dynamics. We have demonstrated the usefulness of this approach in the control of the swinging energy of the pendulum for an experimental cart and pendulum system. On the theoretical side, we have provided a new method for the construction of converse Lyapunov functions for exponentially stable periodic orbits. New techniques for the approximate feedback linearization of nonlinear systems have been developed. In order to construct a feedback linearizing coordinate transformation, a class of optimization problems has been formulated for finding approximate solutions to an appropriate system of partial differential equations. In contrast to previous results, this approach does not require differentiation of the data describing the system and is therefore applicable to systems with, for example, tabular data. Nonlinear control.