scholarly journals A maximum principle for stochastic optimal control with terminal state constraints, and its applications

2006 ◽  
Vol 6 (4) ◽  
pp. 321-338 ◽  
Author(s):  
Shaolin Ji ◽  
Xun Yu Zhou
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Optimal Control ◽  
State Constraints ◽  
Terminal State

scholarly journals A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Shaolin Ji ◽  
Qingmeng Wei ◽  
Xiumin Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Differential Equation ◽  
State Constraints ◽  
Terminal State ◽  
Necessary Condition ◽  
Variation Principle ◽  
Linear Quadratic ◽  
Doubly Stochastic

We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.

scholarly journals Optimal control for quasilinear retarded parabolic systems

2001 ◽  
Vol 42 (4) ◽  
pp. 532-551 ◽  
Author(s):  
Liping Pan ◽  
Jiongmin Yong
Keyword(s):  
Optimal Control ◽  
Parabolic Equation ◽  
Maximum Principle ◽  
State Constraints ◽  
Quasilinear Parabolic Equation ◽  
Parabolic Systems ◽  
Terminal State ◽  
Spatial Derivative ◽  
The Cost ◽  
Quasilinear Parabolic

AbstractWe study an optimal control problem for a quasilinear parabolic equation which has delays in the highest order spatial derivative terms. The cost functional is Lagrange type and some terminal state constraints are presented. A Pontryagin-type maximum principle is derived.

scholarly journals Optimal Control of Diffusions with Hard Terminal State Restrictions

2012 ◽  
Vol 2012 ◽  
pp. 1-38
Author(s):  
Atle Seierstad
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Terminal State ◽  
The State ◽  
State Equations ◽  
Brownian Motions ◽  
Terminal Time ◽  
State Restrictions

A maximum principle is proved for certain problems of optimal control of diffusions where hard end constraints occur. The results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time.

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