Stages and main tasks of the century-long control theory and system identification development. Part X. Positional conflict-controlled processes

The paper concerns the conflict-controlled processes, described by the generalized quasi-linear systems of differential equations. We study the game problem of approaching the terminal set of a cylindrical form, under the positional information on the game state. It is assumed that, in the solution presentation (an analog of the Cauchy formula), the block of initial data is separated from the control block. Due to this, it becomes possible to consi­der the wide class of the game problems in a unique scheme. The research method is based on the extreme targeting rule. We study both the regular and the regularized cases. In so doing, the latter is formalized in the frames of differential inclusions. The general technique is applied to solving the game problems, in which the process dynamics is described by the integral, integral-differential equations. The theoretical results are illustrated by the model examples of game problems.