General necessary conditions for optimal control of stochastic systems

1976 ◽  
pp. 30-48 ◽  
Author(s):  
U. G. Haussmann
Keyword(s):  
Optimal Control ◽  
Stochastic Systems ◽  
Necessary Conditions

scholarly journals Necessary Conditions for Optimal Control of Forward-Backward Stochastic Systems with Random Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-50 ◽  
Author(s):  
Jingtao Shi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Systems ◽  
Necessary Conditions ◽  
Control Variable ◽  
Optimal Controls ◽  
Linear Quadratic ◽  
Forward Equation ◽  
Random Jumps

This paper deals with the general optimal control problem for fully coupled forward-backward stochastic differential equations with random jumps (FBSDEJs). The control domain is not assumed to be convex, and the control variable appears in both diffusion and jump coefficients of the forward equation. Necessary conditions of Pontraygin's type for the optimal controls are derived by means of spike variation technique and Ekeland variational principle. A linear quadratic stochastic optimal control problem is discussed as an illustrating example.

scholarly journals An existence theorem for optimal stochastic programming

1968 ◽  
Vol 8 (1) ◽  
pp. 114-118 ◽  
Author(s):  
A. W. J. Stoddart
Keyword(s):  
Optimal Control ◽  
Stochastic Programming ◽  
Existence Theorem ◽  
Stochastic Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Direct Methods ◽  
Optimal Program ◽  
Sufficient Conditions For Optimality ◽  
Theory Of Optimal Control

In [4], Hanson has obtained necessary conditions and sufficient conditions for optimality of a program in stochastic systems. However, in many cases, especially in a general treatment, a program satisfying these conditions cannot be determined explicitly, so that the question of existence of an optimal program in such systems is significant. In this paper, we obtain conditions sufficient for existence of an optimal program by applying the direct methods of the calculus of variations [9], [6] and the theory of optimal control [7], [5].

Open-loop optimal control of a class of continuous-time stochastic systems—A simulation study†

1974 ◽  
Vol 19 (6) ◽  
pp. 1165-1175 ◽  
Author(s):  
EDGAR C. TACKER ◽  
THOMAS D. LINTON ◽  
CHARLES W. SANDERS
Keyword(s):  
Optimal Control ◽  
Simulation Study ◽  
Continuous Time ◽  
Stochastic Systems ◽  
Open Loop

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

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