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Results for “differential game, game theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Colonel Blotto Games and Lancaster's Equations: A Novel Military Modeling Combination

Military strategists face a difficult task when engaged in a battle against an adversarial force. They have to predict both what tactics their opponent will employ and the outcomes of any resultant conflicts in order to make the best decision about their actions. Game theory has been the dominant technique used by analysts to investigate the possible actions that an enemy will employ. Traditional game theory can be augmented by use of Lanchester equations, a set of differential equations used to determine the outcome of a conflict. This paper demonstrates a novel combination of game theory and Lanchester equations using Colonel Blotto games. Colonel Blotto games, which are one of the oldest applications of game theory to the military domain, look at the allocation of troops and resources when fighting across multiple areas of operation. This paper demonstrates that employing Lanchester equations within a game overcomes some of practical problems faced when applying game theory.

Collins, Andrew J.↗
NASA NTRS1990

Optimal helicopter trajectory planning for terrain following flight

Helicopters operating in high threat areas have to fly close to the earth surface to minimize the risk of being detected by the adversaries. Techniques are presented for low altitude helicopter trajectory planning. These methods are based on optimal control theory and appear to be implementable onboard in realtime. Second order necessary conditions are obtained to provide a criterion for finding the optimal trajectory when more than one extremal passes through a given point. A second trajectory planning method incorporating a quadratic performance index is also discussed. Trajectory planning problem is formulated as a differential game. The objective is to synthesize optimal trajectories in the presence of an actively maneuvering adversary. Numerical methods for obtaining solutions to these problems are outlined. As an alternative to numerical method, feedback linearizing transformations are combined with the linear quadratic game results to synthesize explicit nonlinear feedback strategies for helicopter pursuit-evasion. Some of the trajectories generated from this research are evaluated on a six-degree-of-freedom helicopter simulation incorporating an advanced autopilot. The optimal trajectory planning methods presented are also useful for autonomous land vehicle guidance.

Menon, P. K. A.↗
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.↗