| Summary: | 碩士 === 國立中央大學 === 數學研究所 === 100 === Trajectory optimization problem is concerned with the design of an optimal trajectory that maximizes or minimizes some measurement and satisfies prescribed conditions. Because of this characteristic, it is in general formulated as an optimal control problem and hence is related to the optimal control theory, a branch of mathematics as an application of the calculus of variations. Recently, with an improvement of computer powers, computational techniques become more widely used in solving optimal control problems. Two main approaches, namely direct and indirect methods, reformulated an optimal control problem as a boundary value problem and a nonlinear programming problem respectively and then numerical methods can be employed. In this work, we focus on a class of direct methods and purposed a full space Lagrange-Newton-Krylov algorithm for the nonlinear programming problems. This algorithm is based on the full space sequential quadratic programming framework and associated with particular globalization strategy and process to generate the initial guess. With the implementation of this algorithm, we try to solve several minimum time trajectory optimization problems and the numerical results exhibit the practicability and potentiality of this algorithm.
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