Forward–backward linear quadratic stochastic optimal control problem with delay

2012 ◽  
Vol 61 (5) ◽  
pp. 623-630 ◽  
Author(s):  
Jianhui Huang ◽  
Xun Li ◽  
Jingtao Shi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Linear Quadratic ◽  
Stochastic Optimal Control Problem

Stochastic Optimal Control

2019 ◽  
pp. 333-350
Author(s):  
Tomas Björk
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Verification Theorem ◽  
Stochastic Optimal Control Problem ◽  
Hamilton Jacobi Bellman

We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.

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