Risk sensitive optimal control and differential games

2007 ◽  
pp. 185-197 ◽  
Author(s):  
Wendell H. Fleming ◽  
William M. McEneaney
Keyword(s):  
Optimal Control ◽  
Differential Games ◽  
Risk Sensitive

scholarly journals A quantum Langevin formulation of risk-sensitive optimal control

2005 ◽  
Vol 7 (10) ◽  
pp. S198-S207 ◽  
Author(s):  
M R James
Keyword(s):  
Optimal Control ◽  
Risk Sensitive

Duality for differential games and optimal control

1974 ◽  
Vol 8 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Otomar Hájek
Keyword(s):  
Optimal Control ◽  
Differential Games

scholarly journals Risk-sensitive optimal control of queues

2017 ◽  
Author(s):  
Rahul Singh ◽  
Xueying Guo ◽  
Eytan Modiano
Keyword(s):  
Optimal Control ◽  
Control Of Queues ◽  
Risk Sensitive

scholarly journals An optimal control of a risk-sensitive problem for backward doubly stochastic differential equations with applications

2020 ◽  
Vol 28 (1) ◽  
pp. 1-18
Author(s):  
Dahbia Hafayed ◽  
Adel Chala
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Doubly Stochastic ◽  
Risk Sensitive ◽  
Performance Functional

AbstractIn this paper, we are concerned with an optimal control problem where the system is driven by a backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.

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