On the regularization error of state constrained Neumann control problems

• Autorzy: Krumbiegel K. , Rosch A.
• Języki publikacji: EN

Abstrakty

EN

A linear elliptic optimal control problem with point-wise state constraints in the interior of the domain is considered. Furthermore, the control is given on the boundary with associated constraints. An artificial distributed control is introduced in the cost functional, in the state equation and in the state constraints. Since there are no control constraints for the artificial control, efficient numerical methods can be easily established. Based on a possible violation of the pure pointwise state constraints, an error estimate for the regularization error is derived. The theoretical results are illustrated by numerical tests.

Słowa kluczowe

EN

optimal control; elliptic equation; state constraints; boundary control; regularization; virtual control

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 2
• Strony: 369--392
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Krumbiegel K.

autor

Rosch A.

• Universitat Duisburg-Essen, Department of Mathematics, Forsthausweg 2, D-47057 Duisburg,

Bibliografia

• BERGOUNIOUX, M., Fro, K. and KUNISCH, K. (1999) Primal-dual strategy for constrained optimal control problems. SIAM J. Control and Optimization 37, 1176-1194.
• BERGOUNIOUX, M. and KUNISCH, K. (2002) On the structure of the Lagrange multiplier for state-constrained optimal control problems. Systems and Control Letters 48, 169-176.
• CASAS, E. (1993) Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control and Optimization 31, 993-1006.
• GRISVARD, P. (1985) Elliptic Problems in Nonsmooth Domains. Pitman, Boston.
• HINTERMÜLLER, M., ITO, K. and KUNISCH, K. (2003) The primal-dual active set method as a semi-smooth Newton method. SIAM Journal Optimization 13, 865-888.
• HINTERMÜLLER, M. and KUNISCH, K. (2006) Feasible and non-interior path-following in constrained minimization with low multiplier regularity. SIAM J. Control Optim. 45(4), 1198-1221.
• HINTERMÜLLER, M. and KUNISCH, K. (2006) Path-following methods for a class of constrained minimization problems in function space. SIAM J. on Optimization 17(1), 159-187.
• KRUMBIEGEL, K, and RÖSCH, A. (2006) A virtual control concept for state constrained optimal control problems. COAP, accepted for publication.
• KUNISCH, K. and RÖSCH, A. (2002) Primal-dual active set strategy for a general class of constrained optimal control problems. SIAM Journal Optimization 13(2), 321-334.
• MATEOS, M. (2000) Problemas de control óptimo gobernados por ecuaciones semilineales con restricciones de tipo integral sobre el gradiente del estado. PhD thesis, University of Cantabria, Santander.
• MEYER, C., PRÜFERT, U. and TRÖLTZSCH, F. (2005) On two numerical methods for state-constrained elliptic control problems. Preprint 5-2005, Institute of Mathematics, Technische Universität Berlin.
• RÖSCH, A. and TRÖLTZSCH F. (2006) Existence of regular Lagrange multipliers for elliptic optimal control problem with pointwise control-state constraints. SIAM J. Control and Optimization 45(2), 548-564.
• RÖSCH, A. and WACHSMUTH, D. Semi-smooth newton method for an optimal control problem with control and mixed control-state constraints. Submitted.
• SCHIELA, A. and WEISER, M. (2004) Function space interior point methods for pde constrained optimization. PAMM 4, 43-46.
• TRÖLTZSCH, F. (2005) Optimale Steuerung partieller Differentialgleichungen-Theorie, Verfahren und Anwendungen. Vieweg, Wiesbaden.
• TRÖLTZSCH, F. and YOUSEPT, I. (2006) A regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraints. COAP, accepted for publication.