scholarly journals First order necessary optimal conditions in Gursat-Darboux stochastic systems

2021 ◽  
Vol 21 (1) ◽  
pp. 89-104
Author(s):  
R.O. Mastaliyev ◽  
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Systems ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Optimal Conditions ◽  
First Order ◽  
System A ◽  
The Pontryagin Maximum Principle

For optimal control problems, described by the Gursat-Darboux stochastic system, a number of first-order necessary optimality conditions are formulated and proved, which are the stochastic analogue - the Pontryagin maximum principle, the linearized maximum principle and the Euler equation.

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

scholarly journals Stochastic maximum principle for optimal control problem of forward and backward system

1995 ◽  
Vol 37 (2) ◽  
pp. 172-185 ◽  
Author(s):  
Wensheng Xu
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Stochastic Systems ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Control Problems ◽  
State Variables ◽  
The Maximum Principle

AbstractThe maximum principle for optimal control problems of stochastic systems consisting of forward and backward state variables is proved, under the assumption that the diffusion coefficient does not contain the control variable, but the control domain need not be convex.

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