In the past three decades, numerous methods have been proposed to transcribe optimal control problems (OCP) into nonlinear programming problems (NLP). In this dissertation work, a unifying weighted residual framework is developed under which most of the existing transcription methods can be derived by judiciously choosing test and trial functions. This greatly simplifies the derivation of optimality conditions and costate estimation results for direct transcription methods. Under the same framework, three new transcription methods are devised which are particularly suitable for implementation in an adaptive refinement setting. The method of Hilbert space projection, the least square method for optimal control and generalized moment method for optimal control are developed and their optimality conditions are derived. It is shown that under a set of equivalence conditions, costates can be estimated from the Lagrange multipliers of the associated NLP for all three methods. Numerical implementation of these methods is described using B-Splines and global interpolating polynomials as approximating functions. It is shown that the existing pseudospectral methods for optimal control can be formulated and analyzed under the proposed weighted residual framework. Performance of Legendre, Gauss and Radau pseudospectral methods is compared with the methods proposed in this research. Based on the variational analysis of first-order optimality conditions for the optimal control problem, an posteriori error estimation procedure is developed. Using these error estimates, an h-adaptive scheme is outlined for the implementation of least square method in an adaptive manner. A time-scaling technique is described to handle problems with discontinuous control or multiple phases. Several real-life examples were solved to show the efficacy of the h-adaptive and time-scaling algorithm.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 225-232). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 225-232). Also available on the Internet.

Thesis (M.S.)--Brigham Young University. Dept. of Electrical and Computer Engineering, 2004. / Includes bibliographical references (p. 75-79).

Thesis (Ph. D.)--Harvard University, 1968. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 1-5 (last group)).

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Thesis (Ph. D.)--Harvard University, 1968. / Typescript. Includes bibliographical references (leaves 1-5 (last group)). Also issued in print.

Thesis (Ph.D.)--University of Central Florida, 2008. / Adviser: Zhihua Qu. Includes bibliographical references (p. 117-121).

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1996. / Vita. Abstract. Includes bibliographical references (leaves 90-92). Also available via the Internet.