Accession Number : AD0717174

Title :   Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraint,

Corporate Author : CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE

Personal Author(s) : Fong,Thomas S. ; Leondes,C. T.

Report Date : NOV 1970

Pagination or Media Count : 35

Abstract : The method of conjugate gradients is used in solving state variable constraint optimal control problems. The search directions generated in the iteration process are locally conjugate with respect to the Hessian of the performance functional. The convergence is along the expanding sequence of sets, the intersections of the linear spaces spanned by the search directions and the set of admissible controls. The computational problems associated with this class of control problems are discussed. The discussion is limited to the cases in which the optimal trajectory enters the constraining surface at most once. This computational technique is applied to a state variable constraint problem in which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraint directly. For this same problem, the method of steepest descent is also studied. The results showed that the method of conjugate gradients provided a higher rate of convergence in comparison with the method of steepest descent, but the difference in the rate of convergence is less pronounced for this constraint problem as compared with the cases of unconstrained problem reported by other investigators. (Author)

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), PARTIAL DIFFERENTIAL EQUATIONS, CONVEX SETS, MATRICES(MATHEMATICS), PERTURBATION THEORY, HAMILTONIAN, STEEPEST DESCENT METHOD, ITERATIONS, MATHEMATICAL PROGRAMMING, OPTIMIZATION

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE