Guaranteed Miss Distance in Guidance Systems with Bounded Controls and Bounded Noise

A conflict between two players is naturally described by a differential game. There are basically two approaches: stochastic or deterministic.Mixed cases, where strategies are deterministic but some inputs such as noise in guidance systems are stochastic, are discussed in the present paper. It suggests the use of a deterministic differential gamewith bounded noise, driving an observer. In this way, the discussion is entirely deterministic, and a guaranteed cost (miss distance) is obtained in a closed form and can be calculated in a single run. Moreover, one is able to perform a parameter study at a preliminary design stage. According to the game theoretic approach, the guaranteed miss distance in the case of ideal players is proportional to the square of some uncertainty measure and is inversely proportional to the difference between missile and target maneuver bounds.