An Operator Theory Approach to Nonlinear Controller Design

• Main Author: Economou, Constantin George
• Format: Others
• Language: en
• Published: 1986
• Online Access: https://thesis.library.caltech.edu/1009/1/Economou_cg_1986.pdf; Economou, Constantin George (1986) An Operator Theory Approach to Nonlinear Controller Design. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2ewe-dp19. https://resolver.caltech.edu/CaltechETD:etd-03192008-083200 <https://resolver.caltech.edu/CaltechETD:etd-03192008-083200>

<p>Strong similarities between control theory and the theory on the solution of operator equations have been observed and basic results in control theory have been derived from operator theory arguments. The purpose of this work is to investigate the theory of controller design as an application of basic operator theory principles and to establish a unified framework in which control theory can benefit from a "rich" operator theory. The major impact is anticipated in nonlinear feedback control theory: controller design can be formulated as selection of an iterative algorithm to solve a nonlinear operator equation corresponding to the control objective. As an example, controllers induced by the method of successive substitution and the Newton method are introduced and the corresponding analysis and synthesis issues are studied. Applied to linear systems, the proposed concepts have a straightforward interpretation in terms of familiar notions in linear controller design theory. Applications are presented and extensions of the current results are suggested to conclude the thesis.</p>