Article

Game Problems for Systems with Variable Delay

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Abstract

Game problem of approach of trajectory of quasilinear conflict-controlled process with cylindrical terminal set under the presence of variable delay is considered. Sufficient conditions of approach in the class of quasi- and stroboscopic strategies were obtained by the method of resolving functions. Example of the pursuit problem with quasilinear delay in dynamics of evader is given.

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Chapter
The paper is devoted to investigation of game problems on bringing a trajectory of dynamic system to a cylindrical terminal set. We proceed with representation of a trajectory of dynamic system in the form, in which the block of initial data is separated from the control block. This makes it feasible to consider a wide spectrum of functional-differential systems. The method of resolving functions, based on use of the inverse Minkovski functionals, serves as ideological tool for study. Attention is focused on the case when Pontryagin’s condition does not hold. In this case the upper and lower resolving functions of two types are introduced. With their help sufficient conditions of approach a terminal set in a finite time are deduced. Various method schemes are provided and comparison with Pontryagin’s first direct method is given. Efficiency of suggested mathematical scheme is illustrated with a model example.