scholarly journals Iterative Solution of Mesh Constrained Optimal Control Problems with Two-Level Mesh Approximations of Parabolic State Equation

2018 ◽  
Vol 06 (01) ◽  
pp. 58-68 ◽  
Author(s):  
A. Lapin ◽  
E. Laitinen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
State Equation ◽  
Control Problems ◽  
Constrained Optimal Control

On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems

2010 ◽  
Vol 10 (3) ◽  
pp. 283-301 ◽  
Author(s):  
E. Laitinen ◽  
A. Lapin ◽  
S. Lapin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Function ◽  
Elliptic Boundary ◽  
Iterative Algorithms ◽  
Iterative Solution ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Finite Dimensional ◽  
The Right

AbstractIterative methods for finite-dimensional inclusions which arise in applying a finite-element or a finite-difference method to approximate state-constrained optimal control problems have been investigated. Specifically, problems of control on the right- hand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergence for the iterative algorithms based on the finding of the control function or Lagrange multipliers are proved.

Explicit algorithms to solve a class of state constrained parabolic optimal control problems

2015 ◽  
Vol 30 (6) ◽  
Author(s):  
Alexander Lapin ◽  
Erkki Laitinen ◽  
Sergey Lapin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Time Derivative ◽  
Iterative Solution ◽  
State Equation ◽  
The State ◽  
Linear Parabolic Equation ◽  
Control Problems ◽  
State Function ◽  
Solution Methods

AbstractWe consider an optimal control problem of a system governed by a linear parabolic equation with the following features: control is distributed, observation is either distributed or final, there are constraints on the state function and on its time derivative. Iterative solution methods are proposed and investigated for the finite difference approximations of these optimal control problems. Due to explicit in time approximation of the state equation and the appropriate choice of the preconditioners in the iterative methods, the implementation of all constructed methods is carried out by explicit formulae. Computational experiments confirm the theoretical results.

scholarly journals Nonlinearly constrained optimal control problems

1992 ◽  
Vol 33 (4) ◽  
pp. 517-530 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong
Keyword(s):  
Optimal Control ◽  
General Class ◽  
State Constraints ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Continuous State ◽  
Constraint Transcription ◽  
Inequality Type

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

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