Vol 77, No 5 (2016)

This paper considers a control problem for a linear singularly perturbed system with minimum energy. The terminal state of the system and the transition time are given. We construct asymptotic approximations of optimal programmed control and optimal feedback control in the problem. A main advantage of the proposed algorithms is decomposing the initial optimal control problem into two unperturbed problems of smaller dimension.

The stability of the trivial solution for a class of difference systems with switching and sector-type nonlinearities is studied. Different approaches to common Lyapunov function design for the family of subsystems corresponding to the considered switched system are proposed. Sufficient conditions making the trivial solution asymptotically stable for any switching law are determined. In the case when common Lyapunov function design fails, multiple Lyapunov functions are used to obtain the restrictions on the switching law guaranteeing the asymptotic stability of the trivial solution.

Consideration was given to the two-server queuing system with resequencing buffer and customer resequencing to which a Markov customer flow arrives. The resequencing buffer has also an infinite capacity. The time of customer servicing by each server has the same phasetype distribution. A recurrent algorithm was proposed for calculation of the joint stationary distribution of the numbers of customers in the buffer and resequencing buffer. The stationary distributions of the customer sojourn time in the system and resequencing buffer were obtained in terms of the Laplace–Stieltjes transform in the form of infinite sums. Examples of calculations of the established relations were given.

We consider the minimax estimation problem in the linear regression model under elementwise constraints imposed on the covariance matrix of the random parameters vector. Minimax estimates are designed using several approaches to the numerical solution of the dual problem, namely, the semidefinite programming method, the conditional gradient method and its modification with the Lagrange multipliers and regularization. The efficiency of the suggested methods is illustrated by the example of path restoration for a maneuvering target with a statistically uncertain acceleration.

This paper considers Pontryagin’s generalized nonstationary example [1, p. 478] with several participants under equal dynamic and inertia capabilities of the players. Multiple capture occurs when a given number of pursuers catch one evader. We obtain sufficient conditions for the multiple capture of the evader by a group of pursuers.

We propose an approach for estimating the efficiency of biological systems and mechanisms in vivo. We compare two mechanisms for chemical transport: diffusion and endosome transport with a cargo along a system of microtubules. Our efficiency evaluation is based on a comparison of the organism’s energy expenditure for cell house-keeping and the transport system’s operation with the speed of cargo delivery. We study the relation between transport efficiency and adaptability of the transport network. Our approach can be used to study models of live systems and solve problems of artificial life design.

Ethernet evolution history and data packet assembly in the OSI model are discussed. Limitations impeding Ethernet application in industrial automation are formulated. The paper notes that real-time Ethernet operation requires additional mechanisms which allow to avoid collisions. The mechanisms in Ethernet-compatible real-time protocols such as EtherNet/IP, PROFINET, EtherCAT, Powerlink, Modbus TCP, Foundation Fieldbus HSE, and SERCOS III are analyzed. The IEEE1588 standard enabling high-precision synchronization of network users’ clocks is examined. Characteristics and application fields of wireless Ethernet networks are listed. Ethernet redundancy mechanisms such as STP, MSTP, MRP, Link Aggregation, PRP, and HSR are considered. Innovative solutions such as powering over Ethernet and embedded Ethernet switches are described.

This paper explores the following model of agents’ threshold behavior. Making binary decisions (choosing between “activity” and “passivity”), agents consider the choice of other members in a group. We formulate and solve an associated control problem, i.e., the random choice problem for the initial states of some agents in order to vary the number of agents preferring “passivity” in an equilibrium.