The Absolute Maximum Payoff in Differential Games and Optiman Control.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1970
- Accession Number
- AD0718347
Entities
People
- E. P. Cunningham
Organizations
- Johns Hopkins University Applied Physics Laboratory