SYSTEM OPTIMIZATION WITH FIXED CONTROL STRUCTURE

摘要

The implementation difficulties associated with most conventional formulations of the optimal control problem are eliminated by intro¬ducing structural specifications on the control as constraints. Necessary conditions, in the form of a nonlinear two-point boundary value problem, are obtained from the calculus of variations. An algorithm for obtaining numerical solutions to a class of problems in which the initial conditions are a priori known, is presented. It is applied to the problem of optimal submarine diving, and the performances for various control configurations are compared. Another procedure, which permits the minimization of statistical functions of the per¬formance index, when the probability distribution of initial conditions is known, is also presented. This procedure, which is especially useful when the terminal time is infinite, is obtained from ordinary calculus procedures.