Optimal Control Problems for the Nonlinear Heat Equation

2001 ◽  
pp. 173-183 ◽  
Author(s):  
Karsten Eppler ◽  
Fredi Tröltzsch
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Optimal Control Problems ◽  
Nonlinear Heat Equation ◽  
Control Problems

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Sweep Algorithm for Solving Discrete Optimal Control Problems with Three-point Boundary Conditions

2008 ◽  
Vol 40 (7) ◽  
pp. 48-58 ◽  
Author(s):  
Fikret Akhmed Ali Ogly Aliev ◽  
Rena Takhir kyzy Zulfugarova ◽  
Mutallim Mirzaakhmed ogly Mutallimov
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Point Boundary ◽  
Discrete Optimal Control ◽  
Sweep Algorithm
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