Vol 79, No 1 (2018)

We consider, in chronological order, the main results that have defined the concept of conditionally minimax nonlinear filtering. This would let us to follow all the evolution stages of this universal method, from a particular application, through basic mathematical concepts, to an advanced theory able to solve a wide class of robust estimation problems in linear and nonlinear stochastic systems.

Consideration was given to the multicriterial approach to the problems of estimation, filtration, and control; among them under uncertainty in regard to the covariance of random factors. The Pareto-optimal estimates, filters, and controllers in the problems where the data can arrive from any of the more than one data sources with various statistical characteristics, as well as in the dual problems where it is required to minimize the rms deviations of more than one objective output, were designed on the basis of the Germeier convolution and the apparatus of linear matrix inequalities.

We consider a known bench calibration scheme for a strapdown inertial navigation system (SDINS) that consists of sequential rotations of the SDINS on the bench. We propose a mathematical formalization of this calibration scheme that lets us embed the calibration problem to stochastic Kalman setting of the estimation problem.

A minimization problem for mathematical expectation of a convex loss function over given convex compact X ∈ R^N is treated. It is assumed that the oracle sequentially returns stochastic subgradients for loss function at current points with uniformly bounded second moment. The aim consists in modification of well-known mirror descent method proposed by A.S. Nemirovsky and D.B. Yudin in 1979 and having extended the standard gradient method. In the beginning, the idea of a new so-called method of Inertial Mirror Descent (IMD) on example of a deterministic optimization problem in R^N with continuous time is demonstrated. Particularly, in Euclidean case the method of heavy ball is realized; it is noted that the new method no use additional point averaging. Further on, a discrete IMD algorithm is described; the upper bound on error over objective function (i.e., of the difference between current mean losses and their minimum) is proved.

The sufficient ε-optimality conditions for the control of the nonlinear continuous stochastic systems with incomplete feedback were formulated and proved. They enabled one to estimate the precision of approximate control as compared with the value-optimal performance functional. Relations were established to determine the ε-optimal control, and a strategy was worked out to determine its use in minimizing the total mismatch of the resulting relations.

This paper briefly considers solutions of primary statements of problem of anisotropic analysis of time-invariant systems and problems of synthesis of suboptimal and γ-optimal anisotropic controllers and filters for the time-invariant systems. Numerical procedures for finding the respective solutions are described. To demonstrate the efficiency of the proposed algorithms, illustrative numerical examples are given.

This paper considers the calculation problem of the heart rate-normalized electrocardiographic interval—an important indicator of cardiac performance—for removing its correlation with cardiac cycle length (or heart rate). We suggest a regularized least-squares procedure to calculate the normative interval under a heart rate of 60 bpm. This procedure is applied to recalculate the electrocardiographic interval into the corrected electrocardiographic interval. We demonstrate that the correlation coefficient between the resulting corrected electrocardiographic interval and cardiac cycle length is smaller than in the case of recalculations based on all well-known formulas. Our suggested method of electrocardiographic interval estimation is almost heart rate independent and therefore can be recommended for clinical practice.

This paper considers a problem of fractional-order PID controller tuning to optimize it in average over a set of initial states of the plant–controller closed system and over a set of typical input signals. The problem is reduced to a multidimensional optimization problem. We suggest an approach to the solution, implementing it algorithmically. The approach is illustrated by a parametric design of an optimal in average fractional-order PID controller for pitch control of an aircraft.

A spatial odor distribution in an environment can be used for navigation, goal search, localization and mapping, like by video, ultrasonic, temperature and other sensors. Modern e-noses can perform the selective detection of different gases with an extremely low concentration but the source localization algorithms of a selected gas against the background of other odors are still underinvestigated. This paper studies an odor field representation in terms of an e-nose based on an array of low-selective sensors. Using a simulation model, we show how the vector measurements of a field of several odor sources can be processed to navigate for reaching a selected odor source. In addition, we demonstrate that the source having a high level of odor intensity can interfere with the search of another odor source of a low intensity. The well-known class of matching receivers does not solve this problem. However, a solution can be obtained by distributed measurements. As shown below, the spatial structure of an odor field allows to implement vector selection. Using deep learning machines, we may reach a high resolution of odor sources in the space. Our future research will be focused on augmented odor reality and autonomous mobile e-nose (e-dog) design.

The problem of comprehensive assessment of available enterprise management systems from implementation and application viewpoint is discussed. The degree of information system’s synergetic openness, which described system’s ability to respond to external users’ requests by means of built-in self-organization mechanisms and tools, is offered as an integrated quality index. This complex index depends of partial factors, describing system’s adaptability and integrability. With the help of comprehensive assessment the available ERP systems are compared, and the need in taking into account industrial user’s specific features during system selection is demonstrated.