Accession Number : AD0718347

Title :   The Absolute Maximum Payoff in Differential Games and Optiman Control.

Descriptive Note : Technical memo.,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Cunningham,E. P.

Report Date : APR 1970

Pagination or Media Count : 60

Abstract : The report deals with a differential game or optimal control problem, in which the payoff is the maximum (or minimum) during play of some scalar function K of the state x. This unconventional payoff has many practical applications in pursuit-evasion and control problems. By defining certain auxiliary games for a significant class of problems, it is shown how to solve the general case where more than one maximum of k(t) = K(x(t)) occurs under optimal play. For a subclass of such problems, it is found that closed optimal solutions can exist on certain surfaces in the playing space. As the playing interval becomes indefinitely long, the open optimal trajectories converge to (or diverge from) such surfaces. In particular, for two-dimensional problems of this subclass, the closed optimal trajectories are periodic and are called periodic barriers. They are analogous to limit cycles in uncontrolled nonlinear systems. (Author)

Descriptors :   (*GAME THEORY, OPTIMIZATION), (*CONTROL SYSTEMS, MATHEMATICAL MODELS), DIFFERENTIAL EQUATIONS, SET THEORY, MINIMAX TECHNIQUE, INEQUALITIES, INTEGRALS

Subject Categories : Theoretical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE