The Bellman function and optimal synthesis in control problems with nonsmooth constraints
type: Item
instance of: scholarly article
title: The Bellman function and optimal synthesis in control problems with nonsmooth constraints
zbMATH Open document ID: 1075.49015
author: M. I. Zelikin
author: N. B. Melnikov
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-05-23T00:00:00Z
review text: The authors study the chattering solutions for the following nonsmooth control problem: find an optimal control \(\widehat{u}(t) \in L_{\infty}([0,\infty))\) and optimal trajectories \((\widehat{x}(t), \widehat{y}(t))\in W_{1}^{1}([0,\infty))\) that give a minimum value to the functional \[ \mathcal{ I}(u(\cdot)) = \int_{0}^{\infty}| x(t)| ^{r}dt \] on the solutions of the system \[ \dot{x} = y,\;\; \dot{y} = u| x| ^{s},\;\; u \in [-1,1], \] understood in the sense of Filipov with the initial conditions \(x(0) = x_{0}\), \(y(0) = y_{0} (0\leq s<1, 3s+1<2r).\)
reviewed by: Gheorghe Aniculăesei
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 2170244
zbMATH Keywords: non-smooth optimal control
zbMATH Keywords: chattering trajectories
zbMATH Keywords: Hamiltonian-Jacobi equation
MaRDI profile type: Publication
DOI: 10.1023/B:JOTH.0000023092.95301.6C
description: scientific article; zbMATH DE number 2170244