Vol 25, No 5 (2019)

Single-point boundary tasks are considered in part 1 for the fuzzy nonlinear differential equations like Rikkati and for the fuzzy linear differential equations. The fuzzy nonlinear differential equations arise at the solution of problems of synthesis of optimal linear regulators by method of dynamic programming. The fuzzy linear differential equations appear at synthesis of regulators by criterion of the generalized work. Three types of fuzzy optimization control problems are formulated. The first of these is the problem of synthesizing an optimal fuzzy regulator with full feedback. In the second task, the fuzzy functional of the generalized work is used as the optimality criterion. The third problem is formulated as a fuzzy optimization problem on the maximum principle and with a fuzzy right end. For the first fuzzy optimization problem solved by the dynamic programming method, Buckley-Feuring and Seikkala types of fuzzy optimal control are obtained. An example of optimal control of a DC motor with fuzzy dynamic parameters is considered, and conditions for the existence of Buckley-Feuring and Seikkala types of controls are formulated. For the second optimization problem, a fuzzy partial differential equation is solved, which leads to a fuzzy Cauchy problem for a linear differential equation. By the example of motor control with fuzzy parameters, the absence of a Buckley-Feuring optimal control is shown, however, an optimal Seikkala type controller with full feedback is obtained.

In article on the example of projection of matrix computing structures the synthesis algorithm of the simulativing Petri nets is offered. Approach to synthesis of new structures on the basis of use of vectors of a projection is described. It is shown that this approach doesn’t allow to receive all set of the possible Petri nets modeling realization of the function set on matrix structure. The original algorithm of projection of the complete set of the possible joint ventures models of matrix structures for the given function is described. The algorithm is based on use of a structure analysis and tensor methodology. Oscillation of programs of synthesis of structures of the joint venture models is result of work of an algorithm. It is shown that among the generated programs exist such which synthesize the equivalent joint ventures models. The properties revealing the "equivalent" programs are formulated. For the purpose of the quantitative and qualitative analysis of the constructed matrix structures criteria for evaluation of structural and dynamic properties of the synthesizable joint ventures models are injected. It is shown that owing to exponential body height of number of the synthesizable joint ventures models from dimension of an initial primitive system, searching of new receptions and approaches which would exclude from consideration of model is necessary, not meeting beforehand the given requirements.

Usage of the new or existing information systems is connected with need transfer of data acquisition about the incidents arising in them and also with transfer identification of the reasons of these incidents. If information systems have a set of hosts and also there are communications of information among them, then the logs accumulated for a small period can have a huge amount of records. It is natural that administrators of information systems are not able to carry out the full and detailed analysis of such information for a short period. In this paper architectures of multi-agent systems which are carrying out collection of data on incidents in information systems for the purpose of their further automatic analysis are considered.

Segmentation is usually understood as the task of separation an available time series into segments (periods) with different dynamics.

If we present the behavior of a complex system with an adequate model, then the transition process will correspond to the transition of model parameters in the state space from one stable phase trajectory to another.

In the case of a sufficiently large number of countdown in the sample and the number of realizations of the dynamic series, the procedure of segmentation of a signal into stationary fragments should give unambiguous results. If compare the distributions and dispersions in two successive fragments of a time series, then at the point of their junction, can state a violation of the stationarity of the process in the narrow sense.

Evaluation of the statistical properties of the physiological signal is possible, however, only on a certain finite time interval. At the same time, the estimated interval can be reduced by increasing the number of samples per unit of time due to the higher frequency of digitization of the studied continuous physiological process only up to a certain limit: until the moment when neighboring counts become strongly correlated. It is this circumstance that limits the possibility of distribution the theoretical definition of stationarity to real physical processes, therefore the concept of "quasi-stationarity" was introduced into practice, highlighting the understanding of stationarity in such a restrictively evaluative aspect.

Presence of self-similarity, i.e. scale invariance in relation to the main statistical characteristics leads to continuous repetition in the self-similarity interval of the properties of some components of the studied dynamic series, meaning that these components are not informative for assessing the changes.

The most free from various restrictions is the method of self-similarity assessment, based on discrete wavelet transform of the dynamic series in the framework of multiresolution analysis. Using the sum of the components of the original time series reconstructed from the wavelet decomposition, the fractal component is selected with the determination of the self-similarity depth of the random process under study and an estimate of its trend component is found.

Using the regression model of a time series with volatility represented by a dynamic series after rejection (removal) of its trend component, it is possible to determine change-points of volatility, which divide the initial series into quasistationary segments corresponding to the volatility function jumps. For this purpose, a special computational procedure is applied, which generalizes the iterative method of centered cumulative sums of squares.

In this paper we consider a problem of computer assisted language and pronunciation learning based on the deep neural networks and the information theory of speech perception. At first, a user learns the stable pronunciation of words. The best utterances from the user with high posterior probability estimated by the pre-trained convolutional neural network are added to the training set. Next, this training set is used to fine-tune this convolutional neural network. If new utterances are successfully recognized with the resulted neural network, it is concluded that pronunciation of all words is distinguishable. In this case in order to additionally verify the stability of pronunciation of each class (word), the closeness of the user pronunciations is estimated by computing the average Kullback-Leibler information discrimination between each signal and the centroid reference of the class. If this mean discrimination for particular word is greater than a certain threshold, then the training for this word should be repeated. The experimental results for learning of English words proved that the proposed approach is characterized by higher accuracy and speed for existing acoustic models when compared to conventional techniques.