×

On pseudoparabolic optimal control problems. (English) Zbl 0810.49005

This paper discusses the following optimal control problem \[ J(u)= \min_{u\in U_{ad}} J(u)= \min_{u\in U_{ad}} \{\| Dy(T,u)- z_ d\|^ 2_ X+ j(u)\}, \] subject to the pseudoparabolic equations \[ A_ 1(t,u) y_ t(t,u)+ A_ 0(t,u) y(t,u)= f(t),\;A_ 1(0,u) y_ t(0,u)= f_ 0, \] where \(A_ 1(\cdot,\cdot)\), \(A_ 0(\cdot,\cdot)\), \(f(\cdot)\), \(j(\cdot)\) satisfy certain conditions. An existence theorem, conditions for the uniqueness and sensitivity analysis are presented.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[1] I. Bock, J. Lovíšek: Optimal control of a viscoelastic plate bending. Math. Nachr. 125 (1968), 135-151. · Zbl 0606.73104
[2] I. Bock, J. Lovíšek: An optimal control problem for a pseudoparabolic variational inequality. Appl. Math. 31 (1992), 1, 62-80. · Zbl 0772.49008
[3] H. Gajewski K. Gröger, K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin 1974. · Zbl 0289.47029
[4] J. Sokolowski: Differential stability of solutions to constrained optimal control problems. Appl. Math. Optim. 13 (1985), 97-115.
[5] J. Sokolowski: Sensitivity analysis of control constrained optimal control problems for distributed parameter systems. SIAM J. Control Optim. 25 (1987), 1542-1556. · Zbl 0647.49019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.