Abstract
A sequence of optimal control problems for systems described by nonlinear parabolic equations is considered. It is proved that, under the Γ-convergence of objective functionals, the parabolicG-convergence of operators in the state equations, and the Kuratowski convergence of control constraint sets, a convergent sequence of optimal pairs has a limit which is an optimal pair for the limit control problem. The convergence of minimal values is also obtained.
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Communicated by R. Conti
This research was supported in part by the Istituto Nazionale di Alta Matematica F. Severi, Rome, Italy. Part of this research was carried out while the author was visiting the Scuola Normale Superiore, Pisa, Italy.
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Migórski, S. Sensitivity analysis of distributed-parameter optimal control problems for nonlinear parabolic equations. J Optim Theory Appl 87, 595–613 (1995). https://doi.org/10.1007/BF02192136
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DOI: https://doi.org/10.1007/BF02192136