Singular stratified manifolds of involutive controlled systems
type: Item
instance of: scholarly article
title: Singular stratified manifolds of involutive controlled systems
zbMATH Open document ID: 1039.49031
DOI: 10.1023/A:1012561426661
author: L. F. Zelikina
author: M. I. Zelikin
author: K. V. Khlyustov
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: Using the rather abstract setting of differential 1-forms, the authors obtain in Theorem 6 some characterizations of the optimal feedback control (``synthesis'', in their terminology) of the minimal-time problem for systems of the form: \[ \dot x=\sum_1^nu^i(t)\varphi_i(x), \;x(0)=a\in \mathbb R^n, \;x(T)=b\in W_{1\dots n}, \] \[ u(t)\in U:=\left\{u\in \mathbb R^n; \;\sum_1^n u^i=1, \;u^i\geq 0\right\}, \;t\in [0,T], \] in the case the set of smooth vector fields \(\{\varphi_1(\cdot),\dots ,\varphi_n(\cdot) \}\) is such that ``the distribution induced by any of its subsets'' is integrable. The authors are using, rather loosely, a large number of their previous concepts and results on this topic.
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1915925
zbMATH Keywords: optimal control
zbMATH Keywords: minimal-time problem
zbMATH Keywords: optimal feedback synthesis
zbMATH Keywords: singular control
zbMATH Keywords: singular manifold
zbMATH Keywords: differential form
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
Recommended article: Q4762747
Recommended article: Q4861694
Recommended article: Singular manifolds in optimal control problems
Recommended article: Topological aspects of controllability and observability on the manifold of singular and regular systems
Recommended article: Integral manifolds, singular perturbations and optimal control
Recommended article: Q3127844
Recommended article: Q3768741
Recommended article: Q5443670
Recommended article: Singular Control-Invariance PDEs for Nonlinear Systems
Recommended article: Singular Trajectories of Control-Affine Systems
description: scientific article; zbMATH DE number 1915925