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Matviychuk O.G.,RAS Institute of Mathematics and Mechanics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

The problem of estimating reachable sets of linear impulsive dynamical control systems with uncertainty in initial data is considered. It is assumed that the impulsive controls in the dynamical system belong to the intersection of a special cone with a generalized ellipsoid both taken in the space of functions of bounded variation. The algorithms for constructing the ellipsoidal estimates of reachable sets for such control systems are given. Numerical simulation results relating to the proposed procedures are also given. © 2014 Springer-Verlag. Source


Vasin V.V.,RAS Institute of Mathematics and Mechanics
Automation and Remote Control | Year: 2012

An ill-posed problem is considered in the form of a nonlinear operator equation with a discontinuous inverse operator. It is known that in investigating a high convergence of the methods of the type of Levenberg-Marquardt (LM) method, one is forced to impose very severe constraints on the problem operator. In the suggested article the LM method convergence is set up not for the initial problem, but for the Tikhonov-regularized equation. This makes it possible to construct a stable Fejer algorithm for approximation of the solution of the initial irregular problem at the conventional, comparatively nonburdensome conditions on the operator. The developed method is tested on the solution of an inverse problem of geophysics. © 2012 Pleiades Publishing, Ltd. Source


Chentsov A.G.,RAS Institute of Mathematics and Mechanics
Automation and Remote Control | Year: 2012

Consideration was given to a scheme for solving the extremal routing problem constrained by the precedence conditions and based on a modification of the dynamic programming method. Attention was focused on an issue related with parallelization of the procedure of constructing the Bellman function layers. A hypothetical construction for distribution of the space of positions between the processors such that they can run without any data exchange until the final stage of computations was proposed. © 2012 Pleiades Publishing, Ltd. Source


Gusev M.I.,RAS Institute of Mathematics and Mechanics
Automation and Remote Control | Year: 2012

Consideration was given to formation of the external estimates of the reachability sets of the nonlinear controlled systems in the form of the level sets of the functions satisfying the differential Hamilton-Jacobi inequalities. The trajectories of the nonlinear system are estimated by modifying the estimates of its linear part. The constructions proposed are based on comparing the systems of differential inequalities. Applications of the reachability sets of the multivariable controlled systems with nonlinear cross connections to the ellipsoidal estimates were examined. © 2012 Pleiades Publishing, Ltd. Source


Slunyaev A.,Keele University | Didenkulova I.,RAS Institute of Mathematics and Mechanics | Pelinovsky E.,RAS Institute of Applied Physics
Contemporary Physics | Year: 2011

In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for sailing and sea use. A number of huge wave accidents, resulting in damages, ship losses and people injuries and deaths, are known. Now marine researchers do believe that these waves belong to a specific kind of sea wave, not taken into account by conventional models for sea wind waves. This paper addresses the nature of the rogue wave problem from a general viewpoint based on wave process ideas. We start by introducing some primitive elements of sea wave physics with the purpose of paving the way for further discussion. We discuss linear physical mechanisms which are responsible for high wave formation, at first. Then, we proceed with a description of different sea conditions, starting from the open deep sea, and approaching the sea coast. Nonlinear effects which are able to cause rogue waves are emphasised. In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear optics. © 2011 Taylor and Francis Group, LLC. Source

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