We develop in this thesis four sufficiency criteria for the generalized problem of Bolza. These results represent a unification, in the sense that they can be applied to both the calculus of variations and to optimal control problems, as well as to problems with nonsmooth data. The first criterion, "point convexity", extends the convexity approach of Rockafellar. However, we derive a "Hamiltonian-Jacobi" approach which can be applied when the point convexity assumption fails to be satisfied. The method employed for this criterion brings to light a new point of view concerning the Jacobi condition in the classical calculus of variations. The latter can be considered as a condition which guarantees the existence of a canonical transformation transforming the original Hamiltonian to a locally concave-convex Hamiltonian. The third sufficiency criterion is an extension of the Hamilton-Jacobi approach from optimal control to the generalized problem of Bolza. This result gives rise to another sufficiency criterion in terms of a certain inequality. Our theorems on sufficient conditions are closely related. We prove that under certain assumptions the last three approaches can be unified. By this we mean that their hypotheses are equivalent. However, the point convexity, and hence the convexity, criterion turns out to have the most restrictive hypotheses of the four. The generality of the theorems proven stems to a great extent from the fact that not only non-differentiable but even infinite- valued functions are allowed in the treatment. The utility of using such functions appears when we apply these theorems to optimal control problems. / Science, Faculty of / Mathematics, Department of / Graduate

Consider the following nonlinear system [Formula Omitted] where ϰ ∈ Rⁿ, f, ℊ₁,…,ℊｍ are C∞ function in Rⁿ and ℎ is a C∞ function in R⍴, all defined on a neighborhood of 0. The problem of finding a necessary and sufficient condition such that system (1) can be transformed to a linear controllable system by a state coordinate change and feedback has been studied quite well. In this thesis, we first discuss a few different approaches to this problem and eventually we will show that the slightly different versions of the necessary and sufficient condition discovered are equivalent. Next we consider system (1) with all սi,= 0 together with system (2), and study the dual problem of transforming it to a linear observable system by a state and output coordinate change. Finally, we consider briefly system (l) and (2) with nonzero սi and study the problem of transforming it to a linear system that is both completely controllable and observable. Examples are given and applications to local stabilization and estimation are discussed. / Science, Faculty of / Mathematics, Department of / Graduate

Note:

by Michael Athans. / Bibliography: leaves 33-36. / Prepared under ONR Contract N00014-76-C-0346.

Thesis (Ph. D.)--Lehigh University, 2003. / Includes vita. Includes bibliographical references (leaves 155-163).

Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: control system design; flexible structures; piezoelectric. Includes bibliographical references (p. 35-36).

Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 23).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 164-168).

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