An algorithm for the method of successive approximations in optimal control problems

Abstract

SOME extensions and improvements to the method of successive approximations, and practical means for improving its convergence, are described. A procedure is given in ALGOL 60 for the algorithm of the method. A numerical method of successive approximations for solving optimal control problems was described in [1]. This method was subsequently used to solve a large number of concrete problems. Several types of standard program realizing the algorithm of the method were compiled. The present paper gives some extensions and improvements to the method of [1] and practical devices for improving its convergence. These modifications and devices have been tested and employed in computer evaluations based on the standard programs. The program here described amounts to a procedure written in ALGOL 60, realizing the method of successive approximations together with certain devices for improving its convergence. By using the program, the numerical solutions of quite a wide range of optimal control problems can be obtained automatically.