Stages and main tasks of the century-long control theory and system identification development. Part IX. Countercontrol in game problems of dynamics

This paper considers the problem of bringing the trajectory of quasilinear conflict-controlled process to a given cylindrical 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.