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Duality theory for state-constrained control problems governed by a first order PDE system

100%

Pickenhain S.

Control and Cybernetics

2002

tom Vol. 31, no 3

833-845

In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem.

On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems

51%

Pickenhain S. , Lykina V. , Wagner M.

Control and Cybernetics

2008

tom Vol. 37, no 2

451-468

This paper deals with infinite horizon optimal control problems, which are formulated in weighted Sobolev spaces ... [wzór] and weighted Lp-spaces ... [wzór]. We ask for the consequences of the interpretation of the integral within the objective as a Lebesgue or an improper Riemann integral. In order to justify the use of both types of integrals, various applications of infinite horizon problems are presented. We provide examples showing that lower semicontinuity may fail for objectives involving Lebesgue as well as improper Riemann integrals. Further we prove a lower semicontinuity theorem for an objective with Lebesgue integral under more restrictive growth conditions on the integrand.