Accession Number : AD0486916

Title :   PERTURBED OPTIMAL CONTROL PROBLEMS.

Descriptive Note : Technical rept.,

Corporate Author : CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS

Personal Author(s) : Korsak, Andrew J.

Report Date : JUN 1966

Pagination or Media Count : 76

Abstract : The effects of perturbations of an 6ptimal control problem upon its optimal control are studied for two classes of optimal control problems. The first class consists of fixed-time, fixed-initial-point, free-terminal-point optimal control problems. The second class consists of certain calculus-of-variations problems interpreted as optimal control problems. The principal results of this study are that an optimal control depends continuously upon the optimal control problem, with respect to certain natural topologies, provided this optimal control is essentially unique, and that an essentially unique optimal control exists for an optimal control problem in the classes studied here, under certain additional assumptions. Some auxiliary results in the calculus of variations are derived to obtain the above conclusions for the second class of problems studied. Among these are an implicit function theorem for absolutely continuous functions and the proof of existence of a field of extremals for certain calculus-of-variations problems. (Author)

Descriptors :   *PERTURBATION THEORY), (*CONTROL SYSTEMS, CALCULUS OF VARIATIONS, TOPOLOGY, OPTIMIZATION, FUNCTIONS(MATHEMATICS), MATRICES(MATHEMATICS), DIFFERENTIAL EQUATIONS, TRANSIENTS, STABILITY, BOUNDARY VALUE PROBLEMS, CONTROL SEQUENCES, SET THEORY.

Subject Categories : Theoretical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE