Second Order Necessary Conditions for Optimal Control Problems of Stochastic Evolution Equations

2021 ◽  
Vol 59 (4) ◽  
pp. 2924-2954
Author(s):  
Qi Lü ◽  
Haisen Zhang ◽  
Xu Zhang
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Second Order ◽  
Control Problems ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Second Order Necessary Conditions

scholarly journals Second order necessary conditions for optimal control problems of evolution equations  involving final point equality constraints 

2021 ◽  
Author(s):  
Helene Frankowska ◽  
Qi Lu
Keyword(s):  
Optimal Control ◽  
Variational Principle ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Second Order ◽  
Equality Constraints ◽  
Control Problems ◽  
Final Point ◽  
Second Order Necessary Conditions

We establish some second order necessary conditions for optimal control problems of evolution equations involving final point equality and inequality constraints. Compared with the existing works, the main difference is due to the presence of end-point equality constraints. With such constraints, we cannot simply use the variational techniques since perturbations of a given control may be no longer admissible. We also cannot use the Ekeland's variational principle, which is a first order variational principle, to obtain second order necessary conditions. Instead, we combine some inverse mapping theorems on metric spaces and second order linearization of data to obtain our results.

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