Internal layer solution of singularly perturbed optimal control problem with integral boundary condition
type: Item
instance of: scholarly article
title: Internal layer solution of singularly perturbed optimal control problem with integral boundary condition
zbMATH Open document ID: 1394.34114
published in: Qualitative Theory of Dynamical Systems
publication date: 2018-06-20T00:00:00Z
review text: The paper deals with the optimal control problem for linear singularly perturbed first-order ordinary differential equations with an integral boundary condition of the form \[ J[u]=\int_0^T f(y,u,t)dt\rightarrow \min_u, \] \[ \mu\frac{dy}{dt}=a(t)y+b(t)u, \] \[ y(0,\mu)=y^0,\;y(T,\mu)=\int_0^T g(s)y(s)ds, \] where the state variable \(y\in\mathbb{R},\) control input \(u\in\mathbb{R}\) and \(\mu\) is a small positive parameter; the functions \(f(y,u,t),\) \(a(t),\) \(b(t)\) and \(g(t)\) are sufficiently smooth, moreover, \(b\) is positive and \(f\) is convex as function of the variable \(u\) for every \(t\in[0,T]\) and \(|y|< A,\) where \(A\) is some constant. By using the \(k+\sigma\) Exchange Lemma the authors proved the existence of optimal solution with an internal layer, and consequently, the boundary function method and asymptotic expansion techniques are applied to construct the formal asymptotic solution and to determine the location of the internal transition point \(t^*\).
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 6891596
zbMATH Keywords: singular perturbation
zbMATH Keywords: internal layer solution
zbMATH Keywords: optimal control
author: Limeng Wu
author: Mingkang Ni
author: Haibo Lu
MaRDI profile type: Publication
full work available at URL: s12346-017-0261-0
OpenAlex ID: W2774364213
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DOI: 10.1007/S12346-017-0261-0
description: scientific article; zbMATH DE number 6891596