A Combined Newton-Raphson and Gradient Parameter Correction Technique for Solution of Optimal-control Problems PDF Download

Author: Ernest S. Armstrong
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 76

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Book Description
A parameter correction technique is developed to solve a boundary-value problem which frequently occurs in optimal-control theory. It is assumed that an indirect optimal-control method has been applied to a controllable dynamic system with a two-point boundary-value problem resulting such that the boundary conditions take the form of a set of unknown parameters to be determined to meet an equal number of terminal conditions. The optimal-control law is a piecewise continuous function with discontinuities occurring only at the zeros of certain continuous functions. A procedure is developed to improve upon an assumed set of parameters so that, by repetitive use of a correction formula, a monotonic decreasing sequence of values of a positive definitive function that measures the terminal errors is produced. The direction of the correction vector is found to lie between the directions given by the gradient and the Newton-Raphson procedures. Integral equations are derived for influence matrices that describe the effect of a change in the parameters on the terminal conditions. The procedure is successfully applied to the determination of both planar and nonplanar fuel-optimal trajectories for a space vehicle which is launched from the surface of the moon and required to rendezvous with a space vehicle in a circular orbit.