Sensitivity Analaysis for Parametric Optimal Control of Semilinear Parabolic Equations
نویسنده
چکیده
Parametric optimal control problems for semilinear parabolic equations are considered. Using recent Lipschitz stability results for solutions of such problems, it is shown that, under standard coercivity conditions, the solutions are Bouligand differentiable (in L, p < ∞) functions of the parameter. The differentials are characterized as the solutions of accessory linear-quadratic problems. A uniform second order expansion of the optimal value function is obtained, as a corollary.
منابع مشابه
VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کاملLipschitz Stability of Solutions Toparametric Optimal Control
A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...
متن کاملLipschitz Stability of Solutions Toparametric Optimal
A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...
متن کاملOptimal Control Problems Governed by Semilinear Parabolic Equations with Low Regularity Data
We study the existence of optimal controls for problems governed by semilinear parabolic equations. The nonlinearities in the state equation need not be monotone and the data need not be regular. In particular, the control may be any bounded Radon measure. Our examples include problems with nonlinear boundary conditions and parabolic systems.
متن کاملLipschitz Stability of Solutions
A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...
متن کامل