Vol 77, No 6 (2016)

Consideration was given to the problem of feedback control of a linear system. An algorithm to solve it was presented under the assumption that the linear combinations of the system phase states are measured with error at sufficiently frequent discrete time instants. The algorithm is stable to the information and computation errors.

Consideration was given to the systems of n quasilinear equations with first-order partial derivatives, two independent variables, and an arbitrary number of numerical control parameters. From the application standpoint, the independent variables play the part of time and space, and the parameters are replaced either by the control functions or the solutions of the inverse problem. The geometrical formalization ascending to Georg Friedrich Bernhard Riemann and enabling one to assign to a quasilinear system a field of linear operators on the corresponding vector bundle is applicable to the systems under consideration. The criterion for diagonalizability, that is, reduction to the Riemann invariants of quasilinear systems with control parameters by state transformations, was established in terms of this field.

In this paper, a stabilization problem of bilinear control systems is considered. Using the linear matrix inequality technique and quadratic Lyapunov functions, an approach is proposed to the construction of the so-called stabilizability ellipsoid such that the trajectories of the closed-loop system emanating from any point inside this ellipsoid asymptotically tend to the origin. The approach allows for an efficient construction of nonconvex approximations to stabilizability domains of bilinear systems.

The results are extended to robust formulations of the problem, where the system matrix is subjected to structured uncertainty.

Consideration was given to the problem of estimating the parameters of a trigonometric regression with the Gaussian Ornstein–Uhlenbeck noise. One-step sequential estimation procedure with a special stopping time defined by a sample Fischer information matrix was proposed. It ensures a given mean square accuracy of estimates uniformly over some parametric region. The results of Monte Carlo simulation of the sequential procedure were presented and compared with the maximum likelihood estimates.

We consider the estimation problem for the state vector of a linear stochastic discrete system some of whose components are constant parameters with Gaussian distribution and uncertain moments. Hypotheses regarding possible values of these moments are provided together with their prior probabilities. Instead of a classical multiple model solution that constructs Kalman filters for every hypothesis, we propose a less computationally intensive method that lets us compute posterior probabilities and estimate the state vector for individual hypotheses by the results of a single filter augmented with dummy measurements. The value and model of these measurements are defined by the possible values of the constant parameters’ moments. We give examples of rational definition of the dummy measurement model. We compare the computational costs of the proposed approach and the classical one.

Consideration was given to the possibility of applying the vector optimization methods and the optimal control theory to construction of the economy modes of maintaining the collective immunity to the infectious agent with allowance for the population psychology and medico-social effects of vaccination. Described was a population immunization model taking into account the natural immunization component. Cases of single and double vaccination with determination of their optimal modes were examined.

Consideration was given to the graph-theoretical model of self-diagnosis at the system level under multiple permanent faults. A group of testing models based on complete unreliable tests was analyzed. For the models of this group, the necessary and sufficient conditions for t-diagnosability without repair were established. A critical review of the results obtained in the publications of various authors was given, and the noticed errors concerning the proof of the conditions for t-diagnosability without repair were corrected.

We represent definitions of intellectualization as applied to industrial automation. Main characteristics of intelligent devices, intelligent algorithmic products and software for automation systems are briefly specified. We name peculiarities of intelligent branches: smart grid and intelligent buildings. A theory of self-replication is discussed in the sphere of intelligent robot industry.

The paper presents the mathematical model of automatic feed control in the power unit of a nuclear power plant (NPP). As initial data for model design, archival information about industrial process in the power unit is used. We obtain the transfer function of a shaping filter for random signal generation with a required autocovariance function. The results of simulation studies and optimization of automatic control system’s parameters using a genetic algorithm are produced.

The paper presents the methods and algorithms of automatic marking detection employed in the development of automatic marking identification system (AMIS) for billets movement tracking between warehouse and production facilities of JSC Vyksa Steel Works. The system enables automatic monitoring of metal-rolling products; its featured property is the capability of remote recognition over a 3–16 m distance.

Features of functional structure of the automated expert system of recognition of complex images are considered, approach to its design is offered. The scheme of the multistructural recognizer consisting of elementary neural network qualifiers is created.