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The objects of the research are homogeneous bilinear control systems. The control synthesis problem of moving a bilinear system to the origin of coordinates in a finite time is considered. To solve this problem it is suggested to use an auxiliary linear system. It is known that the program control for the linear system that moves it to the origin can be represented in an equivalent form of positional...
The study of a deformation features of metal alloys with anisotropy of plastic properties under biaxial stress state is an important technical challenge in the design and creation of a new shipbuilding and aircraft constructions. The study of alloys which are sensitive to tension or compression loading is complicated nonlinear problem. To solve this problems, the Mises-Hill's theory of plasticity...
We consider nonlinear discrete-time control system with linearizable right-hand side and state and control constraints. The problem is to estimate the finite-time controllability region of the system, i. e., the set of initial states for which there is an admissible control sequence such that it moves the system from the initial point to the predefined terminal region in a given number of steps. An...
The problem of constructing a dual cone of a convex polyhedral cone arises in many mathematical and applied researches. In the paper the method of constructing the dual cone to the acute convex polyhedral cone in R3 is proposed. The Householder transformation, creating a convex hull on the plane and projecting the point lying on the z-axis onto a corresponding face are the basic operations which we...
Non-transferable utility game of oil market is considered. Special approach for defining solution is used. This approach enables to construct a real time models of conflicting processes. Connection between the solution in the game with moving information horizon and solutions on the truncated time intervals is shown.
The purpose of this research is to construct a solution of the boundary value problem for a system of nonlinear partial differential equations that simulates the quasi-geostrophic motion in the layer of an ideal incompressible electrically conductive fluid enclosed between space-changing and time-varying surfaces, taking into account inertial forces. Assuming that the Rossby numbers, which are a measure...
The propagation of applications the problem of optimal boundary control of a parabolic system with delay and distributed parameters on the graph. The necessary and sufficient conditions for the existence of an optimal control system using the dual state solved the problem of optimal control synthesis for the case of absence of restrictions on the control action and an analogue-known finite-dimensional...
It is shown that for some classes of functions all epiderivatives and subdifferentials of F. H. Clarke type and P. Michel J.-P. Penot type and others coincide. Several rules of calculation of subdifferentials for the difference of two convex functions are obtained. Some examples are considered.
Hydrodynamic models of the ocean can be very different. Assuming that the liquid is incompressible, it can be considered to be inhomogeneous. If we consider the planetary scales of the phenomenon, then it is necessary to take into account the rotation of the Earth. One of the characteristic models of ocean dynamics is the consideration of the irrotational motion of two layers of an ideal incompressible...
In this paper, the new model for dynamics of spreading of rumour in a continuous time is suggested. Model depends on a parameter representing the probability of the outcome of interaction between the two spreaders. The process of spreading rumors is described by a system of linear differential equations.
Nowadays the online learning area is actively developing as a part of machine learning. In this regard, there arises the problem of choosing an algorithm that solves the optimization problem with regard to online data processing. Since currently one of the active areas of online learning is ranking, the comparison of several state of art online optimization algorithms for the multi-armed bandit problem...
In the article the authors state and prove necessary and sufficient conditions for primitive one-variable functions to exist and the ways to find these functions.
Complex nonlinear control systems that are fundamentally non-linearizable (containing, for example, ambiguous nonlinearities), as a rule, can not be fully investigated analytically. On the other hand, the use of only computer technologies for their research often gives rise to doubts about the reliability of the results obtained. Therefore, methods based on the decomposition of the space of parameters...
We discuss the mathematical model of the structure and properties of matter in the Universe. The basis of all processes is the movement. The start can with the basic principles and laws of physics, statistical and thermodynamic equilibrium. We consider the collective movement of quasiparticle as wave function which satisfies the Schrodinger equation of quantum mechanics. The solution of this equation...
The problem of stabilization of the equilibrium position for the mechanical systems described by the Lagrange equations of the second kind with possible switching's of both a kinetic energy, and the forces field is investigated. The simple power law of a feed-back guaranteeing the transfer to equilibrium position for finite time from the small neighborhood with the subsequent retention for any admissible...
A problem of terminal control with linear dynamics on a finite time interval is considered. The right-hand end of trajectory is defined implicitly as a solution of boundary-value problem. The problem is reduced to finding a saddle point of the Lagrange function, and linear dynamics is regarded as an equality-type constraint. Dual extraproximal iterative method for solving the problem was proposed,...
In this paper we propose a new method of searching a Pareto optimal Nash Equilibrium in a bimatrix game. These method employ the Germeier convolutions of the payoff functions.
This paper deals with one of the canonical problems in networked systems — the resource allocation problem, that is based on user equilibrium principle. The user equilibrium principle was formulated in the middle of XX-th century by John Wardrop. Resource allocation problem has widespread applications. Urban road networks, financial networks, power grids and other systems could be modeled as network...
On the basis of the dynamic model combining a single vaccination with asymptomatic immunization, control problem consisting in seeking a vaccination regime providing a minimum negative effect at a given positive effect was formulated. The size of the negative effect consists of the cases of excessive and insufficient vaccination, and the size of the positive one the cases of normal vaccination. The...
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