Том 77, № 2 (2016)

Interval state observers provide an estimate on the set of admissible values of the state vector at each instant of time. Ideally, the size of the evaluated set is proportional to the model uncertainty, thus interval observers generate the state estimates with estimation error bounds, similarly to Kalman filters, but in the deterministic framework. Main tools and techniques for design of interval observers are reviewed in this tutorial for continuous-time, discrete-time and time-delayed systems.

Some results obtained by the present author in the field of designing the finitedimensional root-mean-square filters for stochastic systems with polynomial equations of state and multiplicative noise from the linear observations were overviewed. A procedure to derive the finite-dimensional system of approximate filtering equations for a polynomial arbitrary-order equation of state was presented. The closed system of filtering equations for the root-mean-square estimate and covariance matrix error was deduced explicitly for special cases of linear and quadratic coefficients of drift and diffusion in the equation of state. For linear stochastic systems with unknown parameters, the problem of joint root-mean-square state filtering and identification of the parameters from linear observations was considered in the Appendix.

We show the solution to the optimal filtering problem for states of Markov jump processes by observations of multivariant point processes. A characteristic feature of observations is that their compensators are random linear functions of the system state, and the composite “state–observations” process does not possess the Markov property. The provided optimal filtering estimate is expressed via the solution of some recurrent system of linear differential equations and algebraic relations. We present examples of using theoretical results to construct typical models of real queueing networks. We establish the connections between our new optimal filtering algorithm and classical results of Kalman–Bucy and Wonham. We propose a solution for the problem of estimating the current state of a UDP connection given the observations of video stream.

We consider two approaches to the design and analysis of social networks, namely, macro- and microdescriptions. According to the former approach, the structure of relations in a social network is averaged, and agents’ behavior is studied “in the mean.” The latter approach takes into account the structural features of the influence graph of agents and their individual decision-making principles. The first and second approaches are compared using the threshold model of collective behavior with a common relative threshold.

This paper presents an intelligent management system realized on the basis of ontologies and formalized expert knowledge, mathematical models and numerical methods. We introduce a complex approach to the analysis of transport logistics systems using an original concept of multilevel modeling. The constructed mathematical models and software modules integrated in the system are described in brief. Modern intellectualization tools are applied for providing interaction among different modules and processing of incomplete statistical data. And finally, we consider some test and applied problems and their solution by the system.

This paper presents the model of Globus-M active spherical tokamak without plasma in the vacuum vessel. The tokamak passive structures are taken into account in the model. The authors develop the multivariable control system of poloidal magnetic fluxes in the tokamak vacuum vessel of the external cascade based on the internal current control cascade in the poloidal windings. The numerical simulation results of the control system in Matlab are given.