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On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints

Adel Mahmoud Gomaa (2012)

Czechoslovak Mathematical Journal

We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri...

On the best observation of wave and Schrödinger equations in quantum ergodic billiards

Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2012)

Journées Équations aux dérivées partielles

This paper is a proceedings version of the ongoing work [20], and has been the object of the talk of the second author at Journées EDP in 2012.In this work we investigate optimal observability properties for wave and Schrödinger equations considered in a bounded open set Ω n , with Dirichlet boundary conditions. The observation is done on a subset ω of Lebesgue measure | ω | = L | Ω | , where L ( 0 , 1 ) is fixed. We denote by 𝒰 L the class of all possible such subsets. Let T > 0 . We consider first the benchmark problem of maximizing...

Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics

Arturo Enrique Gil García, Vadim Azhmyakov, Michael V. Basin (2014)

Kybernetika

This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...

Optimality and sensitivity for semilinear bang-bang type optimal control problems

Ursula Felgenhauer (2004)

International Journal of Applied Mathematics and Computer Science

In optimal control problems with quadratic terminal cost functionals and systems dynamics linear with respect to control, the solution often has a bang-bang character. Our aim is to investigate structural solution stability when the problem data are subject to perturbations. Throughout the paper, we assume that the problem has a (possibly local) optimum such that the control is piecewise constant and almost everywhere takes extremal values. The points of discontinuity are the switching points. In...

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