Steering control of singularly perturbed systems: A composite control approach
type: Item
instance of: scholarly article
title: Steering control of singularly perturbed systems: A composite control approach
zbMATH Open document ID: 0673.93029
DOI: 10.1016/0005-1098(89)90120-9
author: S. H. Smith
published in: Automatica
publication date: 1989-01-01T00:00:00Z
review text: For the problem \[ I(u)=\int^{T}_{0}L(x,z,u,\epsilon,t)dt\to \min_{u}, \] \[ \dot x=f(x,z,u,\epsilon,t),\quad x(0)=x^ 0,\quad x\in {\mathbb{R}}^ n,\quad u\in {\mathbb{R}}^{\ell},\quad 0<\epsilon \ll 1, \] \[ \epsilon \dot z=a(x,u,\epsilon,t)+A(x,\epsilon,t)z+B(x,\epsilon,t)u+\epsilon g_ 1(x,z,u,\epsilon,t),\quad z(0)=z^ 0,\quad z\in {\mathbb{R}}^ m \] the authors consider the construction of zero-order composite closed-loop and open-loop controls on the basis of degenerated problem solution and two (left and right) boundary-layer stabilizing controls. The asymptotic validity of the composite controls is established.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 49K99
zbMATH DE Number: 4102909
zbMATH Keywords: singular perturbations
zbMATH Keywords: zero-order composite closed-loop and open-loop controls
zbMATH Keywords: boundary-layer stabilizing controls
MaRDI profile type: Publication
full work available at URL: 0005-1098(89)90120-9
OpenAlex ID: W2068058564
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description: scientific article; zbMATH DE number 4102909