Citation
Tierno, Jorge E. (1996) A computational approach to nonlinear system analysis. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01072008082023
Abstract
Most practical control systems have significant nonlinear components. However, these systems are typically analyzed either through robustness analysis of their linearizations, or through extensive simulation of their nonlinear models. Other forms of analysis of nonlinear systems have not as yet led to computationally tractable solutions. The aim of this thesis is to extend the analysis methodology for linear systems given by the structured singular value framework to nonlinear systems. We study the question: Given an uncertain nonlinear system, driven by a nominal command signal over a finite time horizon, and subject to bounded noise, norm bounded feedback components, and uncertain parameters, how far from the nominal trajectory will the actual trajectory be? In order to inherit the properties of the structured singular value, we will use the 2norm as measure for noise signals and undermodeled feedback components. As is the case for robustness analysis of linear systems, we can only find efficient computation algorithms for upper and lower bounds to the answer to this question.
To compute the lower bound we develop a power algorithm similar to the one developed for the structured singular value. Since, as was the case for linear systems, the algorithm is not guaranteed to converge in general, its analysis has to be done empirically. We test this algorithm by applying it to simulations of real systems and show that it performs better than other available optimization methods. To develop an upper bound, we study a class of rational nonlinear systems. We show that for problems in this class, an uncertain, constrained linear system can be constructed that achieves the same performance level. Upper bounds on the performance of these systems can be computed by solving linear matrix inequalities. Finally, we study extensions that can be obtained to these analysis methods when the system is linear but time varying.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Electrical Engineering 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  20 November 1995 
Record Number:  CaltechETD:etd01072008082023 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01072008082023 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  54 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  24 Jan 2008 
Last Modified:  26 Dec 2012 02:27 
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