Numerical solution of positive control problem via linear programming
type: Item
instance of: scholarly article
title: Numerical solution of positive control problem via linear programming
zbMATH Open document ID: 0813.65096
DOI: 10.1007/BF02142690
author: Boris G. Zaslavsky
author: Alexander Moskvin
published in: Numerical Algorithms
publication date: 1995-05-28T00:00:00Z
review text: The following linear time-invariant control system \(x_{t+1} = Ax_ t + Bu_ t\), \(t = 0, 1, 2, \dots\), is considered, where \(x_ t \in \mathbb{R}^ m\), \(u_ t \in \mathbb{R}^ p_ +\) \((\mathbb{R}^ p_ +\) is the set of the vectors with nonnegative coordinates), and \(A\) and \(B\) are matrices of suitable dimensions. The reachability problem is to find a function \(u\) such that \(x_ 0 = 0\) and \(x_ t = x\). An iterative procedure (based on the simplex method) for determining the minimal number of time steps, assuring the reachability of the terminal point \(x\), is proposed. This procedure is used to obtain explicitly a corresponding control. The case of perturbations of the terminal point that leaves it inside the reachability cone is considered and two numerical examples are presented.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93B03
zbMATH DE Number: 720550
zbMATH Keywords: time optimal control
zbMATH Keywords: linear time-invariant control system
zbMATH Keywords: reachability
zbMATH Keywords: iterative procedure
zbMATH Keywords: simplex method
zbMATH Keywords: minimal number of time steps
zbMATH Keywords: reachability cone
zbMATH Keywords: numerical examples
zbMATH Keywords: time-invariant
reviewed by: Mikhail Krastanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 720550