Parametric synthesis of nonlinear controlled systems
type: Item
instance of: scholarly article
title: Parametric synthesis of nonlinear controlled systems
zbMATH Open document ID: 0827.93024
author: M. V. Trigub
published in: Automation and Remote Control
publication date: 1995-02-19T00:00:00Z
review text: The author studies a nonlinear -- but analytic -- control system: \(x'= f(t, x, \alpha, u)\) which depends on a parameter \(\alpha\). The control \(u\) is a discontinuous law of \((t, x, \alpha)\). The value of the problem is the infimum over \(\alpha\) of the supremum over initial conditions of some cost (a sum of an integral cost and an end point cost). It is well- known that this volume function is in general not differentiable. So it does not satisfy the Hamilton-Jacobi equation in the usual sense. Instead of studying nonsmooth solutions to this PDE (in a contingent or viscosity sense for example) the author studies suboptimal solutions to the problem and he gives an algorithm solving the suboptimal problem.
reviewed by: Marc Quincampoix
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93B12
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 710830
zbMATH Keywords: discontinuous control
zbMATH Keywords: nonlinear
zbMATH Keywords: suboptimal solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 710830