State constrained optimal control problems with states of low regularity

Please always quote using this URN: urn:nbn:de:0297-zib-509
  • We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.

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Author:Anton Schiela
Document Type:ZIB-Report
Tag:optimal control; optimality conditions; state constraints
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
Date of first Publication:2008/06/17
Series (Serial Number):ZIB-Report (08-24)
Published in:Appeared in: SIAM J. on Control and Optimization 48(4): 2407-2432 (2009)