Shape optimization of control problems described by wave equations

• Autorzy: Nowakowski A.
• Języki publikacji: EN

Abstrakty

EN

The control problem with multidimensional integral functional under wave type constraints for control is considered. Next a type of deformation with control of the domain is described and then we define suitable shape functional. Having denned trajectory and control of deformation dual dynamic programming tools are applied to derive optimality condition for the shape functional with respect to that deformation.

Słowa kluczowe

EN

sufficient optimality conditions; control with wave equation; shape optimization; dual dynamic programming

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 4
• Strony: 1045--1055
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Nowakowski A.

• University of Lodz Banacha 22, 90-238 Lodz, Poland,

Bibliografia

• GALEWSKA, E. and NOWAKOWSKI, A. (2006) A dual dynamic programming for optimal multidimensional elliptic control problems. Numerical Functional Analysis and Optimization 27 (3-4), 279-289.
• GlLBARG, D. and TRUDINGER, N.S. (1983) Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin.
• LASIECKA, I., LIONS, J.L. and TRIGGIANI, R. (1986) Nonhomogeneous boundary value problems for second order hyperbolic operators. J. Math. Pures Appl. 65, 149-192.
• NAZAROV, S.A. and SOKOLOWSKI, J. (2003) Asymptotic analysis of shape functional. Journal de Mathematiques Pures et Appliquees 82, 125-196.
• NOWAKOWSKI, A. (2008) Sufficient optimality conditions for Dirichlet boundary control of wave equations. SI AM Journal on Control and Optimization 47 (1).
• NOWAKOWSKI, A. (1992) The dual dynamic programming. Proceedings of the American Mathematical Society 116 (4), 1089-1096.
• SOKOLOWSKI, J. and ZOLESIO, J.P. (1992) Introduction to Shape Optimisation. Springer - Verlag.
• SOKOLOWSKI, J. and ZOCHOWSKI, A. (1999a) Topological derivative for optimal control problem. Control and Cybernetics 28 (3), 611-625.
• SOKOLOWSKI, J. and ZOCHOWSKI, A. (1999b) Topological derivative for elliptic problems. Inverse problems 15 (1), 123-134.