Contributions to the Theory of Optimal Stochastic Controls

2020 ◽  
pp. 169-175
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Stochastic Controls

scholarly journals Conjugate duality in stochastic controls with delay

2017 ◽  
Vol 49 (4) ◽  
pp. 1011-1036
Author(s):  
Zimeng Wang ◽  
David J. Hodge ◽  
Huiling Le
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Maximum Principles ◽  
Conjugate Duality ◽  
Control Problems ◽  
Convex Problem ◽  
Stochastic Controls ◽  
The Relationship ◽  
Equations With Delay

AbstractIn this paper we use the method of conjugate duality to investigate a class of stochastic optimal control problems where state systems are described by stochastic differential equations with delay. For this, we first analyse a stochastic convex problem with delay and derive the expression for the corresponding dual problem. This enables us to obtain the relationship between the optimalities for the two problems. Then, by linking stochastic optimal control problems with delay with a particular type of stochastic convex problem, the result for the latter leads to sufficient maximum principles for the former.

A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations

2002 ◽  
Vol 124 (4) ◽  
pp. 561-565 ◽  
Author(s):  
O. Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Control Design ◽  
Stochastic Averaging ◽  
Moment Equation ◽  
Design Criteria ◽  
Numerical Examples ◽  
Rayleigh Approximation ◽  
Stochastic Controls ◽  
The Moment

This paper presents a method for designing and quantifying the performance of feedback stochastic controls for nonlinear systems. The design makes use of the method of stochastic averaging to reduce the dimension of the state space and to derive the Ito^ stochastic differential equation for the response amplitude process. The moment equation of the amplitude process closed by the Rayleigh approximation is used as a means to characterize the transient performance of the feedback control. The steady state and transient response of the amplitude process are used as the design criteria for choosing the feedback control gains. Numerical examples are studied to demonstrate the performance of the control.

scholarly journals Stochastic Controls with Terminal Contingent Conditions

1999 ◽  
Vol 238 (1) ◽  
pp. 143-165 ◽  
Author(s):  
Nikolai Dokuchaev ◽  
Xun Yu Zhou
Keyword(s):  
Stochastic Controls
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