Abstract: We study solvability questions for the problem on realization of operator functions foran invariant polylinear regulator of a higher-order differential system in an infinite-dimensionalseparable Hilbert spac...
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For a time-dependent controlsystem we consider a “reversed” minimum time problem, which consists in finding the minimum time needed by the system, whose state is initially located in a given set, to reach a given p...
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One of the challenges for the popularization of knowledge-based systems (KBS) is to be more user-friendly and involved in solving everyday tasks. A way to encourage users to apply KBSs more actively is the use of up-t...
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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.
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 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.
In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and the evolution operators that are the compositions of a linear operator and the subdifferentials of a time-dependent p...
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In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and the evolution operators that are the compositions of a linear operator and the subdifferentials of a time-dependent proper convex lower semicontinuous function. Alongside the initial inclusion, we consider a sequence of approximating evolution inclusions with the same perturbation and the evolution operators that are the compositions of the same linear operator and the subdifferentials of the Moreau-Yosida regularizations of the initial function. We demonstrate that the attainable set of the initial inclusion as a multivalued function of time is the time uniform limit of a sequence of the attainable sets of the approximating inclusions in the Hausdorff metric. We obtain similar results for evolution controlsystems of subdifferential type with mixed constraints on control. As application we consider an example of a controlsystem with discontinuous nonlinearities containing some linear functions of the state variables of the system.
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.
This paper is concerned with an optimal impulsive control problem under intermediate state constraints. The controlsystem of this problem is bilinear with respect to states of bounded variation and impulsive controls...
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