On numerical solution of singularly perturbed optimal control problems
type: Item
instance of: scholarly article
title: On numerical solution of singularly perturbed optimal control problems
zbMATH Open document ID: 1391.49004
author: V. Gaitsgory
author: Matthias Gerdts
published in: Journal of Optimization Theory and Applications
publication date: 2017-10-27T00:00:00Z
review text: Singularly perturbed (SP) optimal control problems in which optimal controls may take the form of rapidly oscillating functions, i. e., problems with fast and slow dynamics depending on a parameter \(\varepsilon\), are considered. It is demonstrated that a straightforward application of standard optimal control methods is computationally infeasible for small values of \(\varepsilon\). To overcome this difficulty, an averaged optimal control problem and a ``discrete-time'' version of it are considered. A convergence result establishing that a near-optimal solution of the SP problem can be constructed on the basis of an optimal solution of the time-discrete version of the averaged problem is provided. An iterative algorithm for finding numerical solutions of the time-discrete version of the averaged optimal control problem, in which the equations describing the fast dynamics are independent of the slow state variables, is proposed. The algorithm is based on a fixed-point iteration scheme using a forward and a backward sweep for the adjoints, where periodic optimal control problems have to be solved during the forward sweep. Finally, the numerical results are presented.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 6800882
zbMATH Keywords: fixed-point iteration
zbMATH Keywords: optimal control
zbMATH Keywords: singularly perturbed systems
zbMATH Keywords: time averaging
describes a project that uses: Ipopt
MaRDI profile type: Publication
full work available at URL: s10957-017-1138-8
OpenAlex ID: W2734572742
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DOI: 10.1007/S10957-017-1138-8
description: scientific article; zbMATH DE number 6800882