Accession Number : AD0839963

Title :   A GENERALIZED STEEPEST DESCENT ALGORITHM FOR MULTISTAGE OPTIMIZATION PROCESSES,

Corporate Author : FRANK J SEILER RESEARCH LAB UNITED STATES AIR FORCE ACADEMY CO

Personal Author(s) : Vachino, Rinaldo F.

Report Date : 01 JUN 1968

Pagination or Media Count : 267

Abstract : The study analyzes two classes of multistage optimization processes, and presents computational algorithms for their solution. Two optimal control processes are considered. The first is characterized by a known ordering and number of stages, where the succession of the stages is dictated by the presence of staging conditions and jump discontinuity conditions on the state of the system. The second optimal control problem is characterized by an unspecified number and ordering of subarcs. Necessary conditions for these problems are given. Included is a generalized algorithm composed of two recursive relationships: The first is a generalization of the algorithm of steepest descent which can alter both the staging times and control during each stage; the second serves to introduce subarcs. Three examples are presented: (1) A control problem with two controls and with a two-sided inequality constraint on the control that appears linearly; (2) A single control problem which is linear in the state and control with an inequality constraint of the control; and (3) A control problem is linear in the scalar control and nonlinear in the state with an inequality constraint on the control. (Author)

Descriptors :   (*STEEPEST DESCENT METHOD, PROBLEM SOLVING), OPTIMIZATION, GAME THEORY, CALCULUS OF VARIATIONS, ITERATIONS, INEQUALITIES, GRAPHICS, LINEAR SYSTEMS, NONLINEAR SYSTEMS, FUEL CONSUMPTION, AIRCRAFT, FLIGHT PATHS, AERIAL TARGETS, ASTRONAUTS, GUIDED MISSILE TRAJECTORIES, SURFACE TO AIR MISSILES, SIMULATION, MOON, CONTROL, EVASION, ALGORITHMS.

Subject Categories : Theoretical Mathematics
      Unconventional Warfare

Distribution Statement : APPROVED FOR PUBLIC RELEASE