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Title:  Design of minimax controllers for nonlinear systems using costtocome methods 
Author(s):  Didinsky, Garry 
Doctoral Committee Chair(s):  Basar, Tamer 
Department / Program:  Engineering, Electronics and Electrical 
Discipline:  Engineering, Electronics and Electrical 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Engineering, Electronics and Electrical 
Abstract:  This thesis develops and utilizes the costtocome methodology for the construction of minimax controllers for nonlinear systems with partialstate information (PSI), which are subjected to deterministic uncertainty. It introduces the notion of a costtocome function and shows how it leads to necessary and sufficient conditions for the existence of a minimax controller. These conditions are the existence of the costtocome function and the existence of a solution to an auxiliary fullinformation (FI) minimax problem. It is also proven that a solution of the FI problem leads directly to a solution of the original PSI problem. The significance of this result is that the auxiliary FI problem can be solved using betterknown dynamic programming (DP) techniques. Generally, the auxiliary problem has an infinitedimensional state, which may make the costtocome methodology impractical. Toward resolving this impediment, the thesis first identifies two classes of problems for which costtocome methods offer significant insights: one, problems that satisfy a certaintyequivalence principle (which is attributed to the case when a minimax controller can be chosen to be a fullstate information (FSI) minimax controller with the state replaced by a "worstcase" value of the state), and two, problems for which the costtocome function can be characterized by a finite number of parameters (which is attributed to the case where the auxiliary FI problem has a finitedimensional state). Outside these two classes, bounding techniques can be used to reduce the problem complexity, at the expense of some possible performance degradation. By bounding the FSI costtogo function from above, the certaintyequivalence principle can be generalized to gain some insight into the structure of costbounding controllers, which may lead to alternative parameter design methods. Bounding the costtocome function by finitedimensional structured costtocome functions allows the construction of an auxiliary FI problem, which leads to a costbounding controller policy. As an application of the costtocome methodology, a class of affinequadratic (AQ) disturbance attenuation problems is considered in some detail. This class contains H$\sp\infty$optimal control and filtering problems, problems of parameter identification and nonlinear adaptive control, and memoryless control problems. For the former subclass, costtocome methods provide an alternative derivation of the wellknown necessary and sufficient conditions and of a minimax policy. For the latter three subclasses, new algorithms are developed that lead either directly or recursively to optimal solutions. Some numerical examples and simulation studies are provided to illustrate the theoretical results. 
Issue Date:  1995 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/23641 
Rights Information:  Copyright 1995 Didinsky, Garry 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9522104 
OCLC Identifier:  (UMI)AAI9522104 
This item appears in the following Collection(s)

Dissertations and Theses  Electrical and Computer Engineering
Dissertations and Theses in Electrical and Computer Engineering 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois