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Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions
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DOI：10.1515/anona-2016-0096.png)
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Abstract
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We consider a nonlinear optimal control problem governed by a nonlinear evolution inclusion and depending on a parameter lambda. First we examine the dynamics of the problem and establish the nonemptiness of the solution set and produce continuous selections of the solution multifunction xi Bar right arrow S(xi)(xi being the initial condition). These results are proved in a very general framework and are of independent interest as results about evolution inclusions. Thenwe use them to study the sensitivity properties of the optimal control problem. We show that we have Hadamard well-posedness (continuity of the value function), and we establish the continuity properties of the optimal multifunction. Finally, we present an application on a nonlinear parabolic distributed parameter system.
Keywords:
Evolution triple
evolution inclusion
PG and G convergence
compact embedding
Hadamard well-posedness
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