Search NASA⌕ Search

Engineering topics

Leitmann, G.

Publications and source records attributed to Leitmann, G..

9 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Qualitative differential games with two targets

So-called differential games of kind (qualitative games) were considered involving two or more players each of whom possesses a target toward which he wished to steer the response of a dynamical system that was under the control of all players. Sufficient conditions were derived, which assure termination on a particular player's target. In general, these conditions were constructive in that they permited construction of a winning (terminating) strategy for a player. The theory is illustrated by a pursuit-evasion problem.

Getz, W. M.↗
NASA NTRS1977

Evasion in the plane

Dynamic systems were considered subject to control by two agents, one of whom desires that no trajectory of the system emanating from outside a given set, intersects that set no matter what the admissible actions of the other agent. Constructive conditions sufficient to yield a feedback control for the agent seeking avoidance were employed to deduce an evader control for the planar pursuit-evasion problem with bounded normal accelerations.

Leitmann, G.↗
NASA NTRS1977

Avoidance control

Dynamical systems were considered, subject to control by two agents, one of whom desires that no trajectory of the system, emanating from outside a given set, intersects the set no matter what the admissible actions of the other agent. Conditions are given whose satisfaction assures that a given control results in avoidance. Furthermore, these conditions are constructive in that they yield an avoidance feedback control. Some examples are presented.

Leitmann, G.↗
NASA NTRS1976

Optimal strategies in the neighborhood of a collision course

We consider a simple differential game between pursuer P and evader E in the neighborhood of a nominal collision course. The payoff is the terminal lateral miss-distance. The control of each player is his acceleration normal to his velocity vector, and both players' controls are bounded. Saddlepoint strategies are deduced for three combinations of the acceleration bounds and are shown to be related to the sign of the derivative of the orientation of the line of sight (L.O.S.).

Gutman, S.↗
NASA NTRS1976

Stabilizing feedback control for dynamical systems with bounded uncertainty

The theories of differential games and generalized dynamic systems are used to deduce stabilizing controllers for quasi-linear systems. Attention is given to a class of dynamic systems subject to parameter and input uncertainty whose values range in a given compact set. Using a worst case design philosophy, a feedback control is derived that assures uniform asymptotic (Liapunov) stability of the origin under all admissible uncertainties.

Gutman, S.↗
NASA NTRS1970

Multiple-stage quantitative games

Multistage two player zero-sum games with state determined by difference equations, deriving optimal strategy pair satisfying saddle point condition

Blaquiere, A.↗
NASA NTRS1969

On a class of differential games.

Two player zero-sum differential games with emphasis on play with state determined by differential equations, noting optimal solutions

Leitmann, G.↗
NASA NTRS1968

A simple differential game.

Necessary and sufficient conditions for optimal strategies for differential /two person zero-sum/ game with sum determined by ordinary differential equations

Leitmann, G.↗