Accession Number : AD0704905

Title :   ADAPTATIONS OF THE CONJUGATE GRADIENT METHOD TO OPTIMAL CONTROL PROBLEMS WITH TERMINAL STATE CONSTRAINTS.

Descriptive Note : Technical rept.,

Corporate Author : IOWA STATE UNIV AMES ENGINEERING RESEARCH INST

Personal Author(s) : Willoughby,John K.

Report Date : FEB 1970

Pagination or Media Count : 128

Abstract : The method of conjugate gradients (CG) has been shown to be a rapidly converging and efficient means of solving unconstrained optimal control problems. This dissertation presents some theoretical and computational characteristics of three modifications to the CG algorithm which make it applicable to control problems with terminal state variable constraints. The penalty function method and the projection method have been used to adapt ordinary gradient methods to constrained problems. It is concluded here that the penalty function technique is no more or less advantageous with the CG method than with other gradient techniques. The projection method is shown to be theoretically less compatible with the CG algorithm than with other gradient methods. However, a stepsize adjustment policy is suggested that preserves the rapid convergence that is characteristic of the CG method. It is also shown that nonlinear instead of linear terminal constraints cause no additional theoretical of computational difficulty. A third adaptation of the CG method is given which is original to this study. The method, called the modified conjugate gradient method (MCG), is applied to constrained problems by using constant Lagrange multipliers which converge to their optimal values as the iteration proceeds. A unique feature of the MCG method is that each control iterate produced by the method causes the constraints to be satisfied exactly. Furthermore, the technique is equally applicable to nonlinear and linear terminal state constraints. (Author)

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*ITERATIONS, PROBLEM SOLVING), CALCULUS OF VARIATIONS, MATHEMATICAL PROGRAMMING, NUMERICAL ANALYSIS, ROCKET TRAJECTORIES, OPTIMIZATION, NAVIGATION, THESES

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE