A General Framework for the Control of Nonlinear Systems
Rios-Patron, Ernesto
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https://hdl.handle.net/2142/82478
Description
Title
A General Framework for the Control of Nonlinear Systems
Author(s)
Rios-Patron, Ernesto
Issue Date
2000
Doctoral Committee Chair(s)
Braatz, Richard D.
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
One of the main roadblocks in developing effective controller design techniques for nonlinear processes is the lack of a nonconservative framework for analyzing the closed loop stability and performance of generic nonlinear dynamical systems. Such a framework can be developed for systems consisting of interconnections of linear systems and bounded nonlinear operators. The use of the Standard Nonlinear Operator Form (SNOF) is proposed for the control of nonlinear systems. The SNOF is a linear system with a static diagonal nonlinear operator in feedback. It is shown that nonlinear systems written as SNOF's can approximate any nonlinear dynamical system to any degree of precision. This thesis focuses on a nonlinear stability analysis and performance framework designed around Dynamic Artificial Neural network (DANN) systems to produce computationally-feasible tools to analyze the stability and performance of these systems. The nonlinear stability analysis tools are formulated for discrete-time systems as feasibility problems over Linear Matrix Inequality (LMI) constraints. A Lur'e-Lyapunov function is used, and general properties of the nonlinear elements are exploited to reduce conservatism. The stability analysis conditions are extended to allow the quantification of the performance, measured in terms of a worst-case induced 2-norm. It is also described how the performance analysis condition can be used within an optimization-based formulation to design nonlinear optimal-feedback controllers.
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