O jednom důkazu principu duality v lineárním programování
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Libuše Grygarová (1985)
Časopis pro pěstování matematiky
Fabio Bagagiolo, Dario Bauso (2011)
ESAIM: Control, Optimisation and Calculus of Variations
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
Fabio Bagagiolo, Dario Bauso (2011)
ESAIM: Control, Optimisation and Calculus of Variations
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
Michael Bildhauer, Martin Fuchs (2021)
Commentationes Mathematicae Universitatis Carolinae
We discuss variational problems on two-dimensional domains with energy densities of linear growth and with radially symmetric data. The smoothness of generalized minimizers is established under rather weak ellipticity assumptions. Further results concern the radial symmetry of solutions as well as a precise description of their behavior near the boundary.
Fabbri, R., Impram, S.T., Johnson, R. (2003)
International Journal of Mathematics and Mathematical Sciences
Jan Kučera (1970)
Czechoslovak Mathematical Journal
Adam Czornik, Andrzej Świernik (2005)
International Journal of Applied Mathematics and Computer Science
In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated...
K. Maciej Przyłuski (2014)
International Journal of Applied Mathematics and Computer Science
In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.
M. Motta, C. Sartori (2014)
ESAIM: Control, Optimisation and Calculus of Variations
The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem....
Boltyanski, V.G., Marti Vazques, J. (1995)
Journal of Applied Analysis
Ira Neitzel, Fredi Tröltzsch (2008)
Control and Cybernetics
Piernicola Bettiol (2005)
ESAIM: Control, Optimisation and Calculus of Variations
We study the asymptotic behavior of as , where is the viscosity solution of the following Hamilton-Jacobi-Isaacs equation (infinite horizon case)withWe discuss the cases in which the state of the system is required to stay in an -dimensional torus, called periodic boundary conditions, or in the closure of a bounded connected domain with sufficiently smooth boundary. As far as the latter is concerned, we treat both the case of the Neumann boundary conditions (reflection on the boundary)...
Piernicola Bettiol (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We study the asymptotic behavior of as , where is the viscosity solution of the following Hamilton-Jacobi-Isaacs equation (infinite horizon case) with We discuss the cases in which the state of the system is required to stay in an n-dimensional torus, called periodic boundary conditions, or in the closure of a bounded connected domain with sufficiently smooth boundary. As far as the latter is concerned, we treat both the case of the Neumann boundary conditions (reflection on the...
Pavel Drábek (2002)
Mathematica Bohemica
We study the Dirichlet boundary value problem for the -Laplacian of the form where is a bounded domain with smooth boundary , , , and is the first eigenvalue of . We study the geometry of the energy functional and show the difference between the case and the case . We also give the characterization of the right hand sides for which the above Dirichlet problem is solvable and has multiple solutions.
Drábek, Pavel (2002)
Proceedings of Equadiff 10
Jan Chleboun (2003)
Applications of Mathematics
In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by and maximizes a functional criterion reflecting a particular feature of the state solution, as local stress, displacement, or temperature, for instance. An increase in the criterion value indicates a deterioration in the featured quantity....
Tomáš Roubíček (1999)
Kybernetika
Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for...
Tvrdý, Milan (1986)
Equadiff 6
Azé, Dominique, Rahmouni, Abdelouahed (1996)
Journal of Convex Analysis
Alexander Ioffe (2007)
Control and Cybernetics
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