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40 results on '"SKLYAR, G. M."'

2. On exact controllability of neutral type time-delay systems

Author

Rabah, R., Sklyar, G. M., and Barkhayev, P. Yu.

Subjects
Mathematics - Optimization and Control, Mathematics - Dynamical Systems
Abstract

The paper is devoted to the problem of global exact controllability for a wide class of neutral and mixed time-delay systems. We consider an equivalent operator model in Hilbert space and formulate steering conditions of controllable states as a vector moment problem. The existence of a basis of eigenvectors of system operator allows to simplify substantially the form of the moment problem. A change of control by a feedback law allows to modify the system structure to guarantee the existence of a basis of eigenvectors of the corresponding operator. We prove a criterion of exact controllability and ascertain the precise critical time of controllability.

Published
2015

3. On estimation of solutions of neutral type systems on nonclosed sets

Author

Sklyar, G. M. and Polak, P.

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider a differential system of neutral type with distributed delay. We obtain a precise norm estimation of solutions of the system in question on some nonclosed set. Our result is based on a spectral analysis of the operator and Riesz basis theory. We also discuss the stability properties of corresponding solutions.

Published
2013

4. Linearizability of Multi-Control Systems of the Class C 1 by Additive Change of Controls

Author

Sklyar, K. V., Sklyar, G. M., Ignatovich, S. Yu., Gohberg, Israel, Founded by, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, André, Carlos, editor, Bastos, M. Amélia, editor, Karlovich, Alexei Yu., editor, Silbermann, Bernd, editor, and Zaballa, Ion, editor

Published
2018
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21. Notes on the Asymptotic Properties of Some Class of Unbounded Strongly Continuous Semigroups.

Author

Sklyar, G. M. and Polak, P.

Subjects
LINEAR differential equations, SEMIGROUP algebras, BANACH spaces, MATHEMATICS theorems, HILBERT space
Abstract

Copyright of Journal of Mathematical Physics, Analysis, Geometry (18129471) is the property of B Verkin Institute for Low Temperature Physics & Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Published
2019
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24. Solving of the polynomial systems arising in the linear time-optimal control problem

Author

Korobov, V. I., Sklyar, G. M., and Ignatovich, S. Yu.

Subjects
Hankel determinant, 49N05, Rational function, Markov moment min-problem, 49M30, Linear time optimality
Abstract

The analytic solution of the time-optimal control problem for the system $\dot x_1=u$, $\dot x_k=x_{k-1}$, $k=2,\ldots,n$, $|u|\le1$, for arbitrary $n$ is given. The paper relies on the approach originated in V.I.Korobov, G.M.Sklyar, Mat. Sb. (N.S.) 134(176) (1987), pp 186-206 which proved to be closely connected with ideas from Markov moment problem theory. We give the explicit form of a polynomial $P_n(x,\theta)$ such that for any initial point $x^0$ the optimal time $\theta_0$ coincides with the maximal real root of the equation $P_n(x^0,\theta)=0$. When $\theta_0$ is known, the switching times of the optimal control are found as the roots of a single polynomial. The approach leads to the transparent and easy algorithm for solving of the time-optimal control problem mentioned above. We present two programs using Maple and discuss several examples.

Published
2011

29. OPTIMAL CONTROL WITH BUDGET CONSTRAINTS AND RESETS.

Author

SKLYAR, K. V., RABAH, R., and SKLYAR, G. M.

Subjects
CONTROLLABILITY in systems engineering, EIGENVALUES, MOMENT problems (Mathematics), EIGENVECTORS, SPECTRUM analysis
Abstract

We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider deterministic shortest path problems on graphs with a full budget reset in all preferred nodes. In the continuous case, we derive augmented PDEs of optimal control, which are then solved numerically on the extended state space with a full/instantaneous budget reset on the preferred subset. We introduce an iterative algorithm for solving these problems efficiently. The method's performance is demonstrated on a range of computational examples, including optimal path planning with constraints on prolonged visibility by a static enemy observer. [ABSTRACT FROM AUTHOR]

Published
2015
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34. ON THE EXACT CONTROLLABILITY AND OBSERVABILITY OF NEUTRAL TYPE SYSTEMS.

Author

RABAH, R., SKLYAR, G. M., and BARKHAYEV, P. Yu.

Subjects
*MOMENT problems (Mathematics), *RIESZ spaces, *HILBERT space, *EIGENVECTORS, *MOMENTS method (Statistics)
Abstract

Neutral type systems considered in infinite-dimensional Hilbert space are analyzed for exact controllability characterization. The approach is based on the problem of moments using a Riesz basis of eigenvectors. The duality with observability is investigated. A criterion of exact observability is deduced. [ABSTRACT FROM AUTHOR]

Published
2014

36. ON BANG-BANG CONTROLS FOR SOME NONLINEAR SYSTEMS.

Author

SKLYAR, K. V., SKLYAR, G. M., and KARLOVICH, YU. I.

Subjects
*FEEDBACK control systems, *NONLINEAR systems, *SET theory, *DIMENSIONAL analysis, *MATHEMATICAL mappings, *ALGORITHMS, *MATHEMATICAL variables
Abstract

In the paper we consider the class of nonlinear n-dimensional control systems that can be mapped to linear ones by change of variables and an additive change of control (A-linearizable systems). We show that for suiciently small initial points the transferring to the origin is possible by means of bang-bang controls with no more than n-1 points of switching. Moreover in some cases such a transferring is extremal in the sense of time optimality. These results are based on technique of the power Markov min-problem. An algorithm of searching the mentioned above bang-bang controls is also given. [ABSTRACT FROM AUTHOR]

Published
2013

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