Accession Number : AD0650434

Title :   VARIATIONAL PROBLEMS WITH STATE VARIABLE INEQUALITY CONSTRAINTS.

Descriptive Note : Revised ed.,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Dreyfus,Stuart E.

Report Date : AUG 1963

Pagination or Media Count : 103

Abstract : The primary interest is the development of analytic and computational results applicable to the optimization of missile or airplane trajectories, the paper is restricted to problems involving one independent variable. The paper considers a problem requiring the determination of a control or decision function that, in conjunction with a set of differential equations of motion dependent upon the control, yields a maximal or minimal value of an objective function evaluated at an unspecified future time T, at which time certain specified final conditions are satisfied. This general problem is called the 'Problem of Mayer' and is one of three completely equivalent formulations of any one-dimensional variational problem. New results are derived concerning the characterization of the optimal solution of a variational problem in which the variables involved are restricted, by an inequality constraint, to lie only in a specified region of space. The computational aspects of this problem lead, in the concluding chapters, to a rather thorough investigation of techniques of numerical solution of unconstrained optimal trajectory problems. (Author)

Descriptors :   (*CALCULUS OF VARIATIONS, *EQUATIONS OF MOTION), (*TRAJECTORIES, OPTIMIZATION), DIFFERENTIAL EQUATIONS, DECISION THEORY, GUIDED MISSILE TRAJECTORIES, FLIGHT PATHS, NUMERICAL ANALYSIS, BOUNDARY VALUE PROBLEMS, DYNAMIC PROGRAMMING, FUNCTIONS(MATHEMATICS)

Subject Categories : Numerical Mathematics
      Guided Missile Traj, Accuracy and Ballistics

Distribution Statement : APPROVED FOR PUBLIC RELEASE