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Correctness of a constrained control Mayer's problem for a class of singularly perturbed functional-differential systems

Glizer V. Y.

Control and Cybernetics

2008

Vol. 37, no 2

329-351

A Mayer's problem for a singularly perturbed controlled system with the general type of a small state delay is considered. The control is subject to geometrical constraints. The cost functional is a function of the terminal value of the slow state variable. A simpler parameter-free optimal control problem (the reduced problem) is associated with the original problem. A convergence of the optimal value of the cost functional in the original problem to the optimal value of the cost functional in the reduced problem, as a parameter of singular perturbation tends to zero, is established. An asymptotic suboptimality of the optimal control of the reduced problem in the original problem is shown. These results are extended to some more general optimal control problems. An illustrative example is presented.

Strong maximum principles for implicit parabolic problems together with nonstandard inequalities with integrals

Byszewski L.

Archiwum Odlewnictwa

2006

R. 6, nr 21/2

117-124

The aim of the paper is to give strong maximum principles for implicit parabolic problems together with nonstandard inequalities with integrals in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain. The results obtained can be applied in the theory of diffusion and in the theory of heat conduction.

Celem pracy są silne zasady maksimum dla uwikłanych zagadnień parabolicznych z niestandardowymi nierównościami z całkami we względnie dowolnych (n+1)-wymiarowych zbiorach czasoprzestrzennych bardziej ogólnych niż obszar walcowy. Otrzymane rezultaty mogą być stosowane w teorii dyfuzji i w teorii przewodnictwa cieplnego.