A type of isomorphism between linear and nonlinear signature analyzers

It is proved that an automaton that is state and input isomorphic to a linear primitive automaton is only state isomorphic to the latter automaton. A criterion of state isomorphism between an irredundant signature analyzer (SA) and some linear SA with the zero initial state is found. This work was supported by the Russian Foundation for Basic Research under grant 98-01-00113. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 41–46, July–August, 2000.     

From Kalman—Mesarovic realization to a normal-hyperbolic linear model

The principles of the methodology are formulated, which underlie the procedures of the Kalman—Mesarovic realization for dynamic systems with state equations in the class of autonomous linear differential equations in the normalized Frechet space. In this connection, the key approaches to the solution of classical problems of realization theory regarding linear dissipation models of normal-hyperbolic type are interpreted. The study was sponsored by the Russian Fund for Basic Research (grant No. 05-01-00623), the “Integration” Russian Federal Target Program (grant No. B0077), and the Program for Basic Research of the Presidium of the Russian Academy of Sciences (program No. 19, project 2.5). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 137–157, November–December 2005.     

Kalman-Mesarovic nonstationary realization in terms of Rayleigh-Ritz operator

The paper outlines the methodology underlying the Kalman-Mesarovic realization for dynamic systems with equations of state in the class of linear nonstationary ordinary differential equations. In this sense, the key approaches to solving problems of realization theory in terms of the Rayleigh-Ritz operator are defined. The study was sponsored by the Russian Fund for Basic Research (Grant No. 05-01-00623), Program of Basic Research No. 22 of the Presidium of the Russian Academy of Science, the Grant of the President of the Russian Federation on the State Support of Scientific Schools of the Russian Federation (Grant No. NSh-9508.2006.1). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 82–90, January–February 2007.     

New Theory of Cooperative Games

The paper proposes a new theory of cooperative games based on the notions of conflict equilibrium alone. In this theory, the solution always exists, and it is often unique. The study was sponsored by the Russian Fund for Basic Research, Project No. 03-01-00329, and according to the OITVS Program of the Russian Academy of Sciences, Project No. 1–3. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 156–167, September–October 2005.     

Problems of discrete optimization: Challenges and main approaches to solve them

This paper briefly reviews the current state of the art in the field of discrete optimization problems. Emphasis is on the generalization of the experience gained at the V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine in research and development of solution methods and software for various classes of complicated discrete programming problems. The study was partially sponsored by the grant UKM2-2812-KV-06 (SRDF Cooperative Grants Program). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–25, July–August 2006.     

State estimation and filtering in stochastic systems using adequate simplification

The method of order reduction in solving stochastic problems of state estimation and filtering is considered. The method presented concerns the case where mathematical models of objects being studied are defined by systems of nonstationary differential equations. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 98–102, September–October, 1999.     

Interval Generalization of the Bayesian Model of Collective Decision-Making in Conflict Situations

A constructive interval model of making a collective decision by an independent group of experts is developed. The model is based on a priori information about the frequency of experts' errors in estimating a random state of an object using a finite sample. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 133–144, May–June 2005.     

Realization of a bounded feedback in a nonlinear control problem

We substantiate a method for design of a limited feedback to control a system whose mathematical model includes a nonlinear state function. Designing such a feedback is based on a positional solution of auxiliary optimal control problems which provides the transition from the vicinity of one equilibrium state to the vicinity of a new equilibrium state and stabilization of the system in the new state. Preassigned additional constrains on the trajectory of the control system are satisfied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 108–116, January–February 2009.     

Optimal Control of the Dynamic Viscoelastic Stress-Strain State of a Composite Body

New optimal control problems for the dynamic viscoelastic stress-strain state of a composite body with quadratic cost functionals are considered. Existence theorems for unique optimal controls are proved for all the cases considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 73–92, September–October 2005.     

Software tools for formation of state spaces of queuing systems with a common type buffer

Universal algorithms and software tools are developed for formation of discrete components of state spaces for queuing systems with a common type buffer. A statement on the parameters of such a buffer is proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 164–168, May–June 2007.     

Macroeconomic model of reproduction

A macroeconomic reproduction model consisting of commodities available in a state and population and of relations in commodity and population reproduction is defined, and structural laws of commodity reproduction are revealed. It is shown that the Ukrainian economy has a reduced reproduction characterized by net profit earned from reduction in depreciation costs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 101–116, November–December 2005.     

Stability of continuous hybrid systems

The stationary state of a continuous hybrid system is analyzed for stability using the method of Lyapunov functions. Sufficient conditions of stability and instability are established. These conditions are constructive and can easily be calculated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 123–128, March–April 2007.     

Balanced wage rate as a function of the capital endowment and market conjuncture

A balanced wage rate function is determined by the solution of a year balance equation with the coefficients of material consumption, capital amortization, labor use in the manufacturing sphere, and also with the income and payroll tax rates given by a statistics and a state budget. It is shown that the increase in the wage rate with respect to the balanced rate is possible only as a result of “eating up” the capital by the country population and state’s consumers demand. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 158–172, September–October 2008.     

Optimal linear extrapolation algorithm for realization of a vector random sequence observed without errors

A number of linear extrapolation algorithms for scalar random sequences have been proposed in [1-3]. However, as a rule, the state of real technical systems is characterized by more than one independent parameter. This leads to the vector optimal extrapolation problem considered in this article. The complexity of the problem is largely determined by the fact that, in general, we cannot make any simplifying assumptions about the vector sequence being investigated. As a rule, this is a nonstationary, nonmonotone, non-Markovian, and non-Gaussian sequence generated by a nonlinear system. It is in this highly general framework that we solve our problem. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 37–42, March–April, 1998.     

Influence of a uniform taxation and effects of monopolies on approaching equilibrium in an economic system

An open economic system with monopolies and a uniform taxation system is investigated. The technologies with regular expenditures are taken into account. Based on a model of the economic system with regular interests of consumers, an optimal equilibrium state of the economy being investigated is found. The levels of the monopoly taxation that correspond to the optimal equilibrium state of the economy are determined. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 152–164, July–August 2008.     

Optimal control of an elliptic system with a nonsymmetric state operator

New optimal control problems for elliptic systems with contact conditions and nonsymmetric state operators are considered. Existence theorems for optimal solutions are proved. High-accuracy schemes for approximating optimal controls are proposed for the case where the set of admissible controls coincides with a complete Hilbert space. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–85, November–December 2005.     

The concept of and search for the fair distribution in cooperative games

Well-known conflict equilibria are used to formulate the concept of fair distribution, and a technique is proposed to find it in an arbitrary cooperative game. Any cooperative game is shown to have only one fair distribution, which can always be found from the formulas of conflict equilibrium theory. The study was carried out in line with the OITVS RAN program (Project No. 1-3) and was sponsored by the Russian Foundation for Basic Research (Project No. 06-01-00821). Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 131–141, November–December 2008.     

On the theory of realization of quasilinear systems described by differential equations in a Hilbert space

We consider a system-theoretic methodology of mathematical modeling involved in the structural identification of continuous nonlinear dynamic systems with programmable position control. We present various functional-analytical modifications of a characteristic criterion for exogenous (“input-output”) behavior of these systems that permit, by virtue of this criterion, model realizations in the class of quasilinear nonstationary ordinary differential equations describing states in a separable Hilbert space. The study was sponsored by the Russian Foundation for Basic Research (Grant No. 05-01-00623), Basic Research Program No. 22 of the Presidium of the Russian Academy of Sciences, Grant of the President of the Russian Federation for the Governmental Support of Scientific Schools of the Russian Federation (No. NSh-1676.2008). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 82–95, September–October 2008.     

Formulation and analysis of problems for dynamic systems of inhomogeneous two-phase media

A mixed initial—boundary-value problem with a discontinuous solution for a system of dynamic equations of water-saturated soil consolidation is analyzed. The classical solution is proved to be unique. Error estimates are obtained for time-continuous and fully discrete approximate generalized solutions constructed by the finite-element method. The study was sponsored by the State Fund for Basic Research (GFFI), Grant No. F7/307-2001. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 85–100, November–December 2005.     

Passive-state generation mechanisms and stabilization of dynamic systems

Conclusion In the models of passive-state formation considered above we have assumed for simplicity constant control parameters. In reality, the control parameters are functions of time, environmental factors, and the values of the “active” variables [7, 8]. These functions are “reasonably” constructed: under “bad” conditions the variables shift to a passive state, and when “good” conditions are restored, the variables switch back to active state. It is relevant to develop and analyze the corresponding model circuits. Here we can expect to observe even stronger stabilization effects in the behavior of complex systems. In conclusion, I would like to thank an anonymous referee for useful comments. The study is financed by the Russian Foundation of Basic Research. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 103–112, November–December, 1995.