Vol 79, No 5 (2018)

The problem of getting the given output vector-function by program control was solved for the uniform linear stationary dynamic system. Cascaded decomposition revealed the minimal amount of the components of the vector-function which suffices for solution of the formulated problem. The control and state functions were constructed. Solution of the problem without constructing the projectors and semi-inverse matrices was demonstrated by way of example.

We consider difference systems obtained by discretizing certain classes of differential systems. It is assumed that the system under consideration can operate in several modes. The problem is to establish conditions that guarantee the asymptotic stability of a given equilibrium position when switching regimes. We use the method of Lyapunov functions. We study the case when solutions of the system under various operating modes can have features of both linear and nonlinear behavior.

Consideration was given to the model of a queuing network with resource queuing systems—the multi-server systems with losses where servicing of the accepted customer occupies random volumes of resources with the given distribution function depending on the customer class and the type of required servicing. Customer servicing in a node can be interrupted by a signal arriving at an exponential time from the start of servicing, and during the time of customer sojourn in the network it may be interrupted more than once. Analytical formulas for calculation of the fundamental probability-time model characteristics—including the joint distribution functions of the number of customers in the nodes and the volumes of resources occupied by them—were proposed on the assumption of the Poisson flows incoming to the nodes and arbitrary servicing.

We consider the optimal control problem for a certain class of production systems operating under uncertainty. We construct a mathematical model, give the settings of optimization control problems, and propose efficient algorithms for their solution. We also give examples of applied problems formalized within the framework of the constructed mathematical model.

We consider the problem of finding equilibria in games with three agents on an oligopolic market with a linear demand function and nonlinear agent cost functions. Under strategic reflexion of the agents regarding the presence of a Stackelberg leader (leaders) of the first and second levels, we obtain expressions for information equilibria. Modeling real agent costs and demand functions of the Russian telecommunication market has allowed us to construct a set of information equilibria which we have compared with parameters of the real market and showed the presence of reflexion of the first and second ranks.

This work is devoted to the theoretical justification of a software and technological product that combines latest achievements in the field of mathematical computer modeling, sports physiology, and medicine. We present a review of theoretical foundations and practical solutions of the latest software and technological developments in the field of control over the training process in cyclic sports. We propose a new integrated approach to the training process planning, which combines known technology of the training impulse and a method for modeling individual physiological properties of the athlete’s body on the basis of the physiological avatar technology.

We consider the optimal control problem for a system defined by a one-dimensional diffusion equation with a fractional time derivative. We consider the case when the controls occur only in the boundary conditions. The optimal control problem is posed as the problem of transferring an object from the initial state to a given final state in minimal possible time with a restriction on the norm of the controls. We assume that admissible controls belong to the class of functions L_∞[0, T ]. The optimal control problem is reduced to an infinite-dimensional problem of moments. We also consider the approximation of the problem constructed on the basis of approximating the exact solution of the diffusion equation and leading to a finitedimensional problem of moments. We study an example of boundary control computation and dependencies of the control time and the form of how temporal dependencies in the control dependent on the fractional derivative index.

Modern methods of airborne magnetic field measurements are described. A stochastic algorithm to compensate the deviations between the indications of an aeromagnetometer and an aeromagnetic gradiometer is considered. An integration algorithm for the inertial and correlation-extremal navigation systems is briefly described. An advantage of using magnetic field gradient measurements as navigational data is justified. The performance of the integration algorithm is illustrated by numerical simulation.

The paper considers the iterative improvement algorithms, the efficiency of which substantially depends on the chosen parameters values. The problem of control of these parameters is formulated and discussed. We designed the modified algorithms where parameters are automatically adjusted at each iteration. The original and modified algorithms are applied to solve the problem of optimal control for the ecology-economic system.

A methodology for determining the optimal automation scheme ensuring minimum component manufacture cost subject to defective products probability is developed. The algorithm proposed eliminates the need in the exhaustive search of possible solutions.