Finite-Dimensional Approximations of State-Constrained Continuous Optimal Control Problems

1972 ◽  
Vol 10 (4) ◽  
pp. 649-670 ◽  
Author(s):  
Jane Cullum
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Finite Dimensional

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.

scholarly journals On the convergence of min/sup points in optimal control problems

2001 ◽  
Vol 6 (1) ◽  
pp. 35-52
Author(s):  
Adib Bagh
Keyword(s):  
Optimal Control ◽  
Large Class ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Finite Dimensional ◽  
Lopsided Convergence ◽  
Definition Of ◽  
Stability Results ◽  
Convex Control

We modify the definition of lopsided convergence of bivariate functionals to obtain stability results for the min/sup points of some control problems. In particular, we develop a scheme of finite dimensional approximations to a large class of non-convex control problems.

scholarly journals Mean-field sparse optimal control

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130400 ◽  
Author(s):  
Massimo Fornasier ◽  
Benedetto Piccoli ◽  
Francesco Rossi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Mean Field Theory ◽  
Mean Field ◽  
Control Problems ◽  
Mean Field Limit ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Leaders And Followers ◽  
Sparse Optimal Control

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory, one studies the behaviour of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper, we address instead the situation where the leaders are actually influenced also by an external policy maker , and we propagate its effect for the number N of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the Γ -limit of the finite dimensional sparse optimal control problems.

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