Optimal Estimation of Domains of Attraction for Nonlinear Dynamical Systems

Abstract

This thesis implements a recently proposed algebraic methodology for optimal domain of attraction estimation, and extends the method to include optimal estimation of the largest inscribed ball. In addition, a numerical optimal estimation methodology is proposed. The thesis addresses the important issues of Liapunov function construction and the optimal choice of parameters in the family of Liapunov functions. Several examples are included, including a detailed discussion of the classical inverted pendulum. Finally, the thesis addresses the importance of including a measure of the size of the domain of attraction as part of a generalized objective function in optimization-based controller design.