Robust \(L_2\)-gain control for nonlinear systems with projection dynamics and input constraints: An example from traffic control
type: Item
instance of: scholarly article
title: Robust \(L_2\)-gain control for nonlinear systems with projection dynamics and input constraints: An example from traffic control
zbMATH Open document ID: 0946.93015
DOI: 10.1016/S0005-1098(98)00164-2
author: Joseph A. Ball
author: Martin V. Day
author: Tungsheng Yu
author: Pushkin Kachroo
published in: Automatica
publication date: 2000-10-17T00:00:00Z
review text: The main aim of this paper consists in solving a Hamilton-Jacobi equation related to an \(\mathbb{L}_2\)-gain control problem through construction of a stable ``invariant manifold'' for the Hamiltonian flow. Because in general this ``invariant manifold'' is not regular the stability has to be understood in the sense of Filippov's solutions to ODEs. Another difficulty in this topic is the presence of constraints. So the original dynamics of the system is replaced by a ``projected'' one on the set of constraints (assumed to be convex). This method presents the state of the new dynamics to escape the constraint set. This idea is, in general, of great use in viability theory and is also related to Krasovski solutions of a dynamical system with disturbance. This method of projection together with the Hamilton-Jacobi equation allows to define a set-valued feedback attenuating the \(\mathbb{L}^2\)-gain. Also a construction of a storage function derived from the Hamiltonian system (the solutions of which are taken in Filippov's sense) is given. One main motivation of this very interesting paper is a traffic signal control problem the solution of which is discussed in this work.
reviewed by: Marc Quincampoix
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 1331887
zbMATH Keywords: \(H^\infty\)-control
zbMATH Keywords: invariant manifold
zbMATH Keywords: \(\mathbb{L}_2\)-gain control problem
zbMATH Keywords: Filippov's solutions
zbMATH Keywords: constraints
zbMATH Keywords: method of projection
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: set-valued feedback
zbMATH Keywords: storage function
zbMATH Keywords: traffic signal control problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1331887