We study the long term asymptotic behavior of attainable sets and their shapes of linear time-invariant impulse controlsystems. We give an exhaustive description of attractors arising and the related dynamics. The re...
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We study the long term asymptotic behavior of attainable sets and their shapes of linear time-invariant impulse controlsystems. We give an exhaustive description of attractors arising and the related dynamics. The results are compared with [4], [3].
In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. Alo...
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In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. Along with the original inclusion, we consider a sequence of approximating evolution inclusions with the same perturbation and the evolution operators that are subdifferentials of the Moreau-Yosida regularizations of the original function. We show that the attainable set of the original inclusion, regarded as a multivalued function of time, is the uniform (in time) limit in the Hausdorff metric of the sequence of attainable sets of the approximating inclusions. As an application we consider an example of a controlsystem with discontinuous nonlinearity.
We prove invariance of the fast diffusion equation in the two-dimensional coordinate space and give its reduction to a one-dimensional analog in the space variable. Using these results, we construct new exact multidim...
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We prove invariance of the fast diffusion equation in the two-dimensional coordinate space and give its reduction to a one-dimensional analog in the space variable. Using these results, we construct new exact multidimensional solutions which depend on arbitrary harmonic functions. As a consequence, we obtain new exact solutions to the well-known Liouville equation, the stationary analog of the fast diffusion equation with a linear source. We consider some generalizations to the case of systems of quasilinear parabolic equations.
In this paper some class of nonlinear differential-algebraic equations of high index is considered. For the numerical solution of this problem the family of multistep, multistage difference schemes of high order is pr...
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New logical apparatus for intelligent control is proposed. The problem of temporal reasoning on the basis of this apparatus with application to mobile objects is considered.
New logical apparatus for intelligent control is proposed. The problem of temporal reasoning on the basis of this apparatus with application to mobile objects is considered.
Given a digraph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a simple heuristic for large scale instances,...
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We continue the research of the first part of the article. We mainly study codensity for the set of admissible "trajectory-control" pairs of a system with nonconvex constraints in the set of admissible "...
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We continue the research of the first part of the article. We mainly study codensity for the set of admissible "trajectory-control" pairs of a system with nonconvex constraints in the set of admissible "trajectory-control" pairs of the system with convexified constraints. We state necessary and sufficient conditions for the set of admissible "trajectory-control" pairs of a system with nonconvex constraints to be closed in the corresponding function spaces. Using an example of a control hyperbolic system, we give an interpretation of the abstract results obtained. As application we consider the minimization problem for an integral functional on solutions of a controlsystem.
We consider a controlsystem described by a nonlinear second order evolution equation defined on an evolution triple of Banach spaces (Gelfand triple) with a mixed multivalued control constraint whose values are nonco...
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We consider a controlsystem described by a nonlinear second order evolution equation defined on an evolution triple of Banach spaces (Gelfand triple) with a mixed multivalued control constraint whose values are nonconvex closed sets. Alongside the original system we consider a system with the following control constraints: a constraint whose values are the closed convex hull of the values of the original constraint and a constraint whose values are extreme points of the constraint which belong simultaneously to the original constraint. By a solution to the system we mean an admissible "trajectory-control" pair. In this part of the article we study existence questions for solutions to the controlsystem with various constraints and density of the solution set with nonconvex constraints in the solution set with convexified constraints.
We study the possibility of constructing a Sobolev-Schwartz generalized solution to the problem A(t)x'(t) + B(t)x(t) = f(t), t G T = [0, + infinity), x(0) = a, whose coefficient (n x n)-matrix of derivatives is de...
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We study the possibility of constructing a Sobolev-Schwartz generalized solution to the problem A(t)x'(t) + B(t)x(t) = f(t), t G T = [0, + infinity), x(0) = a, whose coefficient (n x n)-matrix of derivatives is degenerate for every t is an element of T in the situation when there is no classical solution x(t) is an element of C-1(T) (the initial data do not satisfy the agreement conditions and the right-hand side is not a sufficiently smooth vector-function). We prove that the generalized solution is the limit of a sequence of classical solutions of the Cauchy problem for a system with constant coefficients, obtained by the perturbation method.
Examples of problems of motion stability solved with the help of computer algebra systems (CAS) are presented. The authors have experience in developing and applying problem-oriented systems of symbolic computations a...
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