Vol 79, No 4 (2018)

The method of diagonal domination that has been suggested by the present author was extended to the control-unstable plants.

The paper was devoted to analysis of the test Volterra equations of the first kind enabling one to study the specificity of important classes of integral equations in the mathematical models of developing system. Along with theoretical results, presented were numerical calculations for the model examples.

We consider a system of two conditionally independent alternating renewal processes with restructuring and with a general form of the distribution densities of interval lengths. The system models the operation of two units taking into account operation and repair intervals. The restructuring time is associated with the instant when the two-dimensional process first reaches a state where both components are operational. For a process as a whole, each such time corresponds to the system’s Markov regeneration when it begins working anew, from another initial state. Time intervals between restructurings depend on the so-called fixed guaranteed service times. We use the evolution property of the two-dimensional process between Markov regeneration times, which transforms such an evolution into a breaking second-order semi-Markov process. We derive integral equations for the expectations of system efficiency over the time interval from zero to the time of restructuring.

We consider the problem of two-phase filtering (oil and water) in a horizontal layer of an oil deposit. We propose an asymptotic method for calculating both the filtering process and related optimal control problems, namely the problems of choosing optimal control actions to achieve maximum oil production at a given level of water resource consumption or a minimum water flow rate that provides the level of oil production required by the plan.

Developed were new sum codes detecting efficiently twofold errors in the data vectors. A method of constructing concurrent error-detection systems of the logical combination devices with detection of all single malfunctions based on decomposing the outputs into individual groups and checking them with the use of new sum codes was proposed.

We derive analytic formulas for the prices of financial instruments in foreign currency within the framework of a stochastic model defined as the sum of a variance gamma and a Poisson process. We obtain our results for various types of dependencies in the model. The resulting formulas contain values of hypergeometric functions. Practical applications of our results include control over the activity of investors in financial markets.

We consider a stimulation model with Markov dynamics and discounted optimality criteria in case of discrete time and infinite planning horizon. In this model, the regulator has an economic impact on the executor, choosing a stimulating function that depends on the system state and the actions of the executor, who employs positional control strategies. System dynamics, revenues of the regulator and costs of the executor depend on the system state and the executor’s actions. We show that finding an approximate solution of the (inverse) Stackelberg game reduces to solving the optimal control problem with criterion equal to the difference between the revenue of the regulator and the costs of the executor. Here the ε-optimal strategy of the regulator is to economically motivate the executor to follow this optimal control strategy.

This paper considers a computer network with an extended functionality. The network is fully connected but only the currently necessary links are formed. The links are fast reconfigured, which allows for a repeated change of their structure subject to a solved problem. As shown below, such an approach significantly simplifies and accelerates the execution of massive operations with a simultaneous participation of many system devices. Using network resources only, it is possible to perform some types of distributed computing over data directly in the course of their transfer in the network. The examples of network usage and technical implementation of its basic components are given.

Within the model of social dynamics determined by collective decisions in a stochastic environment (ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents (or homines economici, or egoists). We present expressions for the optimal majority threshold and the maximum expected capital increment as functions of the parameters of the environment. An estimate of the rate of change of the optimal threshold at zero is given, which is an absolute constant: \(\left( {\sqrt {2/\pi } - \sqrt {\pi /2} } \right)/2\) .

This paper considers a market where two large companies provide services to the population through “cloud” virtual operators buying companies’ services and reselling them to clients. Each large company assigns a price for selling its services to virtual operators. Also the number of its clients and its resource (a characteristic of company’s attractiveness for clients) are known. The game process is a repetition of two-step games where virtual operators choose companies and prices for their services. Each virtual operator needs to choose a company whose services he is going to sell and also to define a price for the services to be sold to clients. Each virtual operator establishes the probability to choose the company and the price for services, taking into account that the partition of company’s clients choosing a given operator is defined by the Hotelling specification. At each step, each virtual operator seeks to maximize his payoff. We find the optimal strategies of the virtual operators and also explore the following question. Does the system achieve some stationary state in this repeated two-step game or a repeating cycle of states is formed instead?

A mathematical model of a control system for the hydraulic transmission of a transportation robot is developed. Position control for the pump rate regulator is implemented using a traverse speed-feedback loop. An operation algorithm of the automatic control mechanism for the hydraulic transmission of a transportation robot based on SF programming is suggested. Finally, the simulation results of automatic mechanism operation under nonlinear motion characteristics are presented.