Vol 22, No 1 (2017)

Control systems with implicit dynamics and endpoint constraints are considered. For these systems, sufficient solvability conditions are obtained in the terms of Lipschitz and covering mappings.

The method of dedetermination as a new method designed to solving problem of calculation of deterministic functions with the so-called singular points where the function does not take a certain value is proposed. The aim is to describe an approach that allows for division by zero and thus exclude singular points of such functions. The proposed method is to move from problematic (from point of view of calculating) exact function to the corresponding not determined (interval) function by replacing determined function parameters by corresponding interval parameters. Due to this change the values of the function at the singular points will be well-defined interval and values. Latter allows you to solve the problem of finding the function meaning. The solution to this problem is achieved by legalization of division by zero by intervalization of calculations. It uses the principle of cutting out a neighborhood of zero in the interval being denominator of the fraction representing studied function. For the simplified by cutting out interval function the effective formulas are derived based on the main provisions of interval mathematics and make it easy to calculate the value of this function. The proposed in the article approach to the problem of calculating functions with singular points is important for all classes of systems in which the problem really exists. It is about the systems which functions have any number of specific points. Such systems exist mostly in telemetry, reliability theory and practice, humanitarian and many others areas. Features of these areas is that they do not always apply the classical methods of deterministic mathematics. This leads to search for new approaches to solving problems that arise here.

The model of homogeneous artificial neural network (ANN) with a variable activation function of the neuron isstudied. The program is developed on Python 3. Numerical experiments for artificial neural network training using classical nonlinear programming methods (gradient, Monte Carlo, coordinate descent) on the basis of empirical data of blood tests showed that such approach can be used for the ANN-models implementation in various fields.