# Information technologies, systems analysis and control

# Simulation of Delay Effect on Pendulum Oscillations with Limited Excitation

We consider the non-ideal dynamical system “pendulum–electric motor” taking into account the delay effect of the electric motor impulse on the pendulum and delay of the medium reaction on the dynamical pendulum state. The system mathematical model is a system of ordinary differential equations with delay. We propose the approaches reducing the mathematical model of the system to a system of differential equations without delay. We investigate the influence of various factors of delay on steady-state regimes of the system “pendulum–electric motor”.

# Effective Implementation of the EM-algorithm using GPGPU

The problem of decreasing of running time for the data processing algorithms is very important especially when they are used in real time. For example, in real time image processing, process control systems, speech recognition, etc. The paper considers the possibility of decreasing running time of the expectation maximization (EM) algorithm using modern computing systems.

# Construction of Multidimensional Models Based on Kalman Filter and Analysis of Estimation Algorithms of its Parameters

In this paper, we construct the algorithms for estimating mathematical expectation of accelerating the values change of data sample. Simulation modeling is based on these algorithms for the random process. Based on its results, we analyze and choose best algorithms. We show that estimation of mathematical expectation of accelerating values change of data samples for constructed selective sequences of discrepancies does not show better results compared with its estimation based on a full sequence of discrepancies. Adaptive Kalman filter is constructed.

# Control of Periodic Action Apparatus

The article analyzes and studies features of constructing systems of dynamic control (SDC) of periodic action apparatus (PAA). Programming control and control with constraints are employed for PAA dynamic control. Technological requirements as well as solving the problem of dynamic optimization or heuristic method can be used to develop the program of transition functions from the initial to PAA final state. The choice of the control system depends on technological requirements, specificity of functioning and completeness of information on these objects.

# Component Model of the Automated Testing System with the Open form of the Test Task Presentation

In this paper we present state of the art for the automated testing systems that use an open form for the test task presentation. We have developed a numerical criterion for the comparison of the existing automated testing systems with the open form of the test task presentation. In the paper we also present a strategy for improving the efficiency of the automated testing systems with the open form of the test task presentation.

# The Cauchy Problem for Evolutionary Essentially Infinite-Dimensional Differential Equation

This paper presents the theoretical study of the infinite-dimensional analysis field. It is inspired by Paul Levy’s scientific works and grabbed the attention of many mathematicians. The Laplace–Levy operator has many very interesting properties and many applications for stochastic analysis. The essentially infinite-dimensional operator is a generalization of well-known Levy–Laplace operator. Specifically, the operator of the formally second order satisfies the Leibniz property.

# Application of Filters Theory for Analytical Description of Logical-Analytical Dependences

In this paper, we develop the approach combining local mathematical models into one comprehensive analytical mathematical model with its significant complications. Partial models are described using as simple analytical dependences as possible. The partial models obtained should be combined in one analytical model through multiplying them with the analytical ones in the whole range of weight functions of the object variables – equivalents of frequency filters. The single uniform analytical dependence is constructed by adding private models weighed by weight functions.

# Integro-Differential Riccati Equation in the Optimal Control Problem by the Process of Heat Conductivity

Riccati equations occur when solving the problems of dynamics of processes in continuous environments, problems of the theory of heat conductivity and diffusion, problems of the theory of optimal control. In case of systems with lumped parameters it is necessary to investigate the usual matrix differential Riccati equations. There are integro-differential Riccati equations for mathematical models of systems with the distributed parameters.

# Probabilistic Modeling of Operational Actuarial Risks

Insurance companies are functioning in conditions of uncertainties of various types and nature what results in respective financial risks. All these reasons lead to the problem of timely recognition and development of mechanisms for the risks management. To solve the problem appropriate mathematical models are developed to describe the risks, and methodologies proposed for their practical application. The sources of the insurance fraud are detected and respective risk classification is presented.

# A Scenario Approach to Modeling of the Pacific Trash Vortex

The study performed aimed at constructing and comparing scenarios of the solid waste treatment policy in different countries and their influence on variations of environmental dynamics changes in the area of ecological catastrophe – Pacific trash vortex. As input data for the scenario constructing and performing corresponding analysis the statistics for the solid waste processing in the USA, European Union and Singapore was used. The models were constructed for forecasting of the waste accumulated and the percentage of their processing.