We consider a time-optimal control problem for a hybrid system of variable dimension. Continuous motion of the system alternates with discrete variations (switchings) at which the dimension of the state space changes. The change of the space of states of the system can occur if the number of control objects changes, which is typical, for example, for the control problems for groups of a variable number of aircrafts. We obtain sufficient conditions for the time-optimal achievement of all purposes by a group of control objects. The application of optimality conditions is demonstrated by academic examples. Bibliography: 18 titles. Illustrations: 3 figures.

The article describes a new method for contextual resolution of homonymy based on a centroid-context model (CCM). The proposed method of detecting cases of homonymy in the corpus of texts and its resolution using the CCM model is based on the theoretical concept of phraseological conceptual analysis of texts (FCAT) and unique machine grammar, which is based on a system of inflective classes of russian words. The rigid conformity between the form of presentation of words and their grammatical information laid down in the theoretical concept of inflective classes of words of the Russian language made it possible to create on this basis new classes - classes of words that have the same sets of grammatical features, conforming to their forms of representation in similar contextual environments. When developing this model, the authors proceeded from the following hypothesis: the same sequences of generalized characters of word classes (generalized syntagms) should correspond to the same syntactic structures of various fragments of texts. At the same time, it was assumed that such a hypothesis is true for any syntactic models and can be useful in solving both global and particular problems of text analysis. Using this method, a new solution to the problem of resolving homonymy based on the proposed CCM model was proposed.

The article describes a new method for contextual resolution of homonymy based on a centroid-context model (CCM). The proposed method of detecting cases of homonymy in the corpus of texts and its resolution using the CCM model is based on the theoretical concept of phraseological conceptual analysis of texts (FCAT) and unique machine grammar, which is based on a system of inflective classes of russian words. The rigid conformity between the form of presentation of words and their grammatical information laid down in the theoretical concept of inflective classes of words of the Russian language made it possible to create on this basis new classes - classes of words that have the same sets of grammatical features, conforming to their forms of representation in similar contextual environments. When developing this model, the authors proceeded from the following hypothesis: the same sequences of generalized characters of word classes (generalized syntagms) should correspond to the same syntactic structures of various fragments of texts. At the same time, it was assumed that such a hypothesis is true for any syntactic models and can be useful in solving both global and particular problems of text analysis. Using this method, a new solution to the problem of resolving homonymy based on the proposed CCM model was proposed.

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The article deals with the problem of time-optimal control of a hybrid system of variable dimension. The problem of synthesis of optimal hybrid systems of variable dimension is of theoretical interest, since the problems under consideration differ from the classical problems of optimal control of deterministic systems, and methods for their solution have not been developed. The need for research is determined by modern problems of designing complex aviation and rocket and space systems, and the results obtained have a practical orientation and can be used in the creation of automatic control systems.