Vol 79, No 9 (2018)

Consideration was given to the indeterminate nth order system with l observed coordinates and l controls l < n. With the use of a backstepping-based construction of the observer and quadratic Lyapunov function, designed were continuous or pulse controls under which the system becomes globally asymptotically stable.

We propose a method for generating random independent vectors that have a given continuous distribution density with compact support. The main advantage of the proposed method are guaranteed estimates of the error in the generation of random vectors. We show an illustrative experimental comparison of the proposed method with the Metropolis-Hastings algorithm.

Consideration is given to the Markov inventory control system of a discrete product of maximum volume S under the strategies (s,Q) and (s, S) with a positive service time. Upon arrival, the order is queued if the inventory level is positive or, otherwise, leaves the system unserviced. One server handles the queued orders one-by-one in the sequence of their arrival. If the inventory level exceeds s, then the service time has the exponential distribution of intensity μ; otherwise, of intensity αμ, 0 < α ⩽ 1. The product in the inventory is consumed only at the instant when the service (of the order) ends. Inventory deficit is not allowed. When the inventory is empty new orders are not admitted into the system, and the service process of the queued orders (if any) is stopped. The lead time is assumed to be exponentially distributed. Analytical relations are established for the basic stationary performance characteristics of the system.

We propose a new structure of a self-checking combinational device where, based on the properties of parity and Berger codes, as well as a code with the detection of all double errors in information vectors, the problem of detecting all single faults of logical elements can be solved without transforming the structure of the source device. The properties of binary codes with the detection of all double errors that can be used in constructing the proposed structure are considered. We give an example of constructing a new structure.

We consider the solution of boundary value problems of mathematical physics with neural networks of a special form, namely radial basis function networks. This approach does not require one to construct a difference grid and allows to obtain an approximate analytic solution at an arbitrary point of the solution domain. We analyze learning algorithms for such networks. We propose an algorithm for learning neural networks based on the method of trust region. The algorithm allows to significantly reduce the learning time of the network.

With the example of boundary control for the rod heating process, we study the synthesis problem for controlling boundary conditions in systems with distributed parameters. Feedback is provided by measuring the state of the process at internal points whose values are used to construct the control. We propose a formulation of the synthesis problem where both measurement points and the time of measurements are optimized. To solve the problem, we derive formulas necessary to apply efficient first order numerical optimization methods. We show the results of numerical experiments.

The problem is considered of output controllers design for linear multivariable systems with deviating in prescribed bounds physical parameters of the plant, and subjected to the influence of unknown polyharmonic external disturbances, limited only in power. The controller is built so that to provide the prescribed bounds of mean-square values of controlled variables in addition to the robust stability of the closed-loop system. The problem solution is reduced to the H_∞-optimization procedure produced in some specific way. The solution of the well-known “benchmark” problem is considered.

One of the approaches to mathematical programming problems solving by means of R-functional modeling is considered. Some functional voxel method tools are presented for the wide class of optimization problems computer solution using voxel algorithm of gradient descent. The illustrative examples of the computer calculations in comparison to non-computer solutions are given.

In this paper, we develop and study a game-theoretic model of mutual choice with two types of agents (groups) as follows. Each agent wants to make a couple with another agent from the opposite group. In contrast to classical best-choice models, two agents make a couple only by mutual agreement. We consider two setups, namely, natural mating (each agent acts in accordance with personal interests) and artificial selection (forced mating to maximize the average quality of couples). In the first case, the Nash equilibrium is determined; in the second case, an optimal selection procedure is designed. We analyze some modifications of the problem with different payoff functions and incomplete information.

The article reviews the options for the degree of detailing of the refining operations for optimization of production on the planned horizon in the LP-model. The author formulates a selection criterion, which takes into account the execution of the planning regulations, where the revision of the LP-model, search for an optimum production plan, interpretation of the decision and submission of the plan for execution should be carried out within the deadlines set by the refinery. The article also provides estimations of the efficiency of the LP-model detailing and practical recommendations on how to achieve them.