A fixed-point iteration method for optimal control problems governed by parabolic equations

2020 ◽  
Author(s):  
Stefania Ragni
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Parabolic Equations ◽  
Iteration Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fixed Point Iteration

Solving optimal control problems using the Picard’s iteration method

2020 ◽  
Vol 54 (5) ◽  
pp. 1419-1435
Author(s):  
Abderrahmane Akkouche ◽  
Mohamed Aidene
Keyword(s):  
Optimal Control ◽  
Iteration Method ◽  
Optimal Trajectory ◽  
Optimal Control Problems ◽  
Approximate Analytical Solution ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Control Law ◽  
Control Problems ◽  
Objective Functional

In this paper, the Picard’s iteration method is proposed to obtain an approximate analytical solution for linear and nonlinear optimal control problems with quadratic objective functional. It consists in deriving the necessary optimality conditions using the minimum principle of Pontryagin, which result in a two-point-boundary-value-problem (TPBVP). By applying the Picard’s iteration method to the resulting TPBVP, the optimal control law and the optimal trajectory are obtained in the form of a truncated series. The efficiency of the proposed technique for handling optimal control problems is illustrated by four numerical examples, and comparison with other methods is made.

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