Combinatorial methods for constructing bipartite uniform minimal quasicomplete graphs (symmetrical block designs)

Consideration was given to a specific family of bipartite graphs consisting of two disjoint subsets X and Y of vertices and characterized by that each vertex in X (Y) is connected to each of the remaining vertices in X (Y) by a unique path of length two passing through some vertex in Y (X). The prefix “quasi” reflects the fact that complete connection of the vertices is realized by paths of length two rather than by edges. The problem of constructing uniform minimal graphs with identical cardinalities of the subsets X and Y which is of practical interest for complex communication networks was discussed. It belongs to the class of combinatorial problems of construction of the so-called symmetrical block designs.     

On one problem of integer optimization

A recognition problem of the following form is studied: to find put for the prescribed polyhedron whether the maximum of the linear objective function is achieved at its integral point. It is established that this problem is NP-hard in the general case and polynomially solvable in the class of rooted semimetric polyhedra.     

On absolute stability of discrete systems

Modernization is considered of the criterion of absolute stability of discrete systems [1, 2], which uses the method of quadratic transformation of the state vector. The modernization aim is to obtain the criterion form that does not explicitly depend on the notions of this method. The new formulation permits performing all calculations in the space of the initial dimension, which reduces the complexity of the problem solution. This work represents the development of the approach suggested in [3] for continuous systems.     

Randomized methods of stabilization of the discrete linear systems

Proposed was a new approach to system stabilization by low-order controllers based on generation of the stable random polynomials or matrices and their projection on the space of controller parameters.     

Decomposition of problems of optimal control and estimation for discrete systems with fast and slow variables

Consideration was given to the linear-quadratic problem of optimal control for the discrete linear system with fast and slow variables under incomplete information about system state. Decomposition of the discrete matrix Riccati equations was carried out. The proposed decomposition algorithm relies on a geometrical approach using the properties of the invariant manifolds of slow and fast motions of the nonlinear multirate discrete systems as basis. The splitting transformation was constructed in the form of asymptotic decomposition in the degrees of a small parameter.     

Estimation of non-stationary delay for a linear discrete dynamic plant

A nonlinear recurrent gradient-type algorithm is proposed for estimation of nonstationary delay arising in finite impulse response of a linear discrete dynamic plant. Convergence of the algorithm is investigated. Using linear matrix inequalities, its optimal functioning is investigated in order to provide for the maximal rate of convergence of the estimation error to zero.     

Petersen’s lemma on matrix uncertainty and its generalizations

Various generalizations and refinements are proposed for a well-known result on robust matrix sign-definiteness, which is extensively exploited in quadratic stability, design of robustly quadratically stabilizing controllers, robust LQR-problem, etc. The main emphasis is put on formulating the results in terms of linear matrix inequalities.     

Experience of multilevel parallelizing of the branch and bound method in discrete optimization problems

Various schemes are considered of the parallel implementation of the branch and bound method, as applied to multiprocessor computing systems (clusters) with the distributed memory. In the language of informal automata, questions are set out of the organization of the exchange of data and signals within the cluster, which afford the asynchronous operation of its processors. Common ideas are illustrated by the example of the classical traveling salesman problem and data of numerical experiments performed on the multiprocessor computing system-100 (MCS-100) are given.     

About a class of systems preserving the stability property at negative feedbacks

For linear and nonlinear systems are obtained tests for conserving the property of asymptotic stability at switching arbitrary coordinatewise negative feedbacks.     

Method for segregation of suspected logical malfunctions in combinatorial discrete devices

Consideration was given to the direct problem of technical diagnosis which lies in determining the technical state of a combinatorial discrete device from the results of testing. The graph and analytical models of behavior of the combinatorial discrete device allowing for the technical state of its elements were presented. A method of segregation of the suspected logical malfunctions under which observable behavior of the combinatorial discrete device is possible was proposed.     

Functional diagnosis of the nonlinear dynamic delay systems

Consideration was given to the problem of functional diagnosis of the nonlinear dynamic delay systems. Its solution implies design of redundancy relations whose verification underlies conclusions about system operability and the kind of system defect. For the systems obeying differential equations with a polynomial right-hand side, a method was proposed for designing the redundancy relations. It admits that some or all constant coefficients of the polynomials are unknown.     

Design of discrete control system of flexible spacecraft maintaining robust stability of elastic oscillations

For the flexible spacecraft with a nonlinear orientation control system using flywheel engines, an approach to making its elastic oscillations robust stable was considered. It relies on a purposeful variation of the boundaries of the stability domains in the parameter space of the spacecraft and controller with the aim of maximizing the number of robust stable elastic modes of the flexible spacecraft. To make its control stable in the large, consideration was given to the possibility of expanding the basic algorithm by adding the sum of the components using the estimated coordinates of the remaining series of low-frequency unstable modes. Presented was an example of mathematical modeling of the proposed spacecraft orientation system which corroborated operability of the approach making the multifrequency spacecraft stable to the elastic oscillations.     

On partial detectability of the nonlinear dynamic systems

Conditions were obtained under which the uniform stability (uniform asymptotic stability) in one part of the variables of the zero equilibrium position of the nonlinear nonstationary system of ordinary differential equations implies the uniform stability (uniform asymptotic stability) of this equilibrium position relative to another, larger part of variables. Conditions were also obtained under which the uniform stability (uniform asymptotic stability) in one part of variables of the “partial” (zero) equilibrium position of the nonlinear nonstationary system of ordinary differential equations implies the uniform stability (uniform asymptotic stability) of this equilibrium position. These conditions complement a number of the well-known results of the theory of partial stability and partial detectability of the nonlinear dynamic systems. Application of the results obtained to the problems of partial stabilization of the nonlinear control systems was considered.     

Supervisory control of the structured dynamic discrete-event systems

A new model is developed and studied in this paper—structured dynamic discrete event systems as a theoretical foundation for designing the supervisory control over the set of autonomous components. The composition of the model is defined and the question of a supervisor’s existence (the controllability of the given specification)is studied. Besides, there were stated the basic stages of the design technology in the framework of the introduced controllability analysis model and the supervisors synthesis method.     

Transformations of control systems for the investigation of pulse modes

It is considered a scheme of transformation of control system with unbounded velocity hodograph to a system of reduced order (called the derived system) via integral of the limit system which describes behavior of the original one under pulse (practically sufficiently large) control inputs. There are formulated the conditions (connected with controllability of the limit system on its integral manifold) when some solution of the derived system will be a generalized solution of the original one that is it can be approximated by a sequence of regular solutions. Methodical and applied examples are given.     

Estimation of the limit possibilities of vibration isolation systems

The limit possibilities of the vibration isolation systems damping the impact of dynamic actions at limited overall size are traditionally estimated by solving the corresponding optimal control problem. Its formulation was discussed, and an estimation method doing without direct determination of the optimal control was proposed.     

On instability of control systems for a certain class of objects and methods of its elimination

In practice of design of control systems, the cases occur when some of the roots of the transfer function of a controllable object are disposed on the imaginary axis of the complex plane. The optimal controller constructed for such objects, despite its realizability, will not afford the robustness properties in the system. The methods of removal of this phenomenon are given. The comparative estimate of the solution of this problem is provided both in the space of states and in the input-output relations (in the space of operators).     

Organization of the remote access to tomographic data through a slow communications link

Consideration is given to the problem of organization of the remote access to tomographic data obtained as a result of the investigation on the computerized tomograph through a slow communications link. The proposed access strategy together with the developed and realized method of tomographic data compression makes it possible to help users (physicians, scientists, and etc.) work with remote tomographic data, e.g., using the Internet. This, in its turn, opens up vast possibilities for using the data of tomographic investigations for conducting medical consultations “at a distance,” videoconferences, organizing network seminars for medical staff training, and etc.     

Development and application of the theory of parametric regulation of evolution of economic systems based on a neoclassical model of optimal growth

Presented were some results on roughness of the mathematical model of the neoclassical theory of optimal growth with and without parametric regulation, selection of the optimal law of parametric regulation, and the optimal law of parametric regulation vs. the uncontrollable parameters of this mathematical model based on the parametric regulation theory.     

To the optimal identification of multivariate systems under perturbations of unknown covariances

We consider the problem of parameter and covariance estimation for multivariate stochastic systems described by regression models with special structure perturbations of unknown covariance. Sufficient conditions of uniformly optimal estimations are obtained for system parameters and covariances. The observation vector distribution family is factorized, and the full sufficient statistics is found under those conditions. Equations for uniformely optimal unbiased estimates of covariance parameters are obtained.