Treffer: INEXACT RESTORATION FOR RUNGE-KUTTA DISCRETIZATION OF OPTIMAL CONTROL PROBLEMS

Title:
INEXACT RESTORATION FOR RUNGE-KUTTA DISCRETIZATION OF OPTIMAL CONTROL PROBLEMS
Authors:
KAYA, Yalçin
Source:
SIAM journal on numerical analysis. 48(4):1492-1517
Publisher Information:
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2011.
Publication Year:
2011
Physical Description:
print, 44 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Algorithme, Algorithm, Algoritmo, Analyse numérique, Numerical analysis, Análisis numérico, Approximation, Aproximación, Calcul variationnel, Variational calculus, Cálculo de variaciones, Commande optimale, Optimal control, Control óptimo, Convergence, Convergencia, Multiplicateur Lagrange, Lagrange multiplier, Multiplicador Lagrange, Méthode Runge Kutta, Runge Kutta method, Método Runge Kutta, Méthode discrétisation, Discretization method, Método discretización, Méthode numérique, Numerical method, Método numérico, Méthode optimisation, Optimization method, Método optimización, Méthode stochastique, Stochastic method, Método estocástico, Partition, Partición, Programmation mathématique, Mathematical programming, Programación matemática, Système hamiltonien, Hamiltonian system, Sistema hamiltoniano, Temps continu, Continuous time, Tiempo continuo, 37Jxx, 49XX, 65C20, 65K10, 65K15, 65Kxx, 49K15, 49M05, 49M25, 65L06, Lagrange multiplier update, Runge-Kutta discretization, costate update, inexact restoration, optimal control, symplectic partitioned Runge-Kutta scheme, van der Pol system
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
School of Mathematics and Statistics, University of South Australia, Mawson Lakes, S.A. 5095, Australia
ISSN:
0036-1429
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=24069715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24069715
Database:
PASCAL Archive

Weitere Informationen

A numerical method is presented for Runge-Kutta discretization of unconstrained optimal control problems. First, general Runge-Kutta discretization is carried out to obtain a finite-dimensional approximation of the continous-time optimal control problem. Then a recent optimization technique, the inexact restoration (IR) method, due to Martinez and coworkers [E. G. Birgin and J. M. Martínez, J. Optim. Theory Appl., 127 (2005), pp. 229-247; J. M. Martinez and E. A. Pilotta, J. Optim. Theory Appl., 104 (2000), pp. 135-163; J. M. Martínez, J. Optim. Theory Appl., 111 (2001), pp. 39-58], is applied to the discretized problem to find an approximate solution. It is proved that, for optimal control problems, a key sufficiency condition for convergence of the IR method is readily satisfied. Under reasonable assumptions, the IR method for optimal control problems is shown to converge to a solution of the discretized problem. Convergence of a solution of the discretized problem to a solution of the continuous-time problem is also shown. It turns out that optimality phase equations of the IR method emanate from an associated Hamiltonian system, and so general Runge-Kutta discretization induces a symplectic partitioned Runge-Kutta scheme. A computational algorithm is described, and numerical experiments are made to demonstrate the working of the method for optimal control of the van der Pol system, employing the three-stage (order 6) Gauss-Legendre discretization.