Optimal control of nonlinear hereditary systems
type: Item
instance of: scholarly article
title: Optimal control of nonlinear hereditary systems
zbMATH Open document ID: 0617.34072
DOI: 10.1016/0022-0396(87)90184-7
author: Douglas C. Reber
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: In this paper a functional space \(\Lambda\) is introduced in order to study hereditary control systems of the form \[ (*)\quad x(t)=\phi (0)+\int^{t}_{a}f(s,x_ s,u_ s)ds,\quad t\in [a,b] \] with the initial condition \(x_ a=\phi\) (here, if x is a function defined in [a,b] and \(s\in [a,b]\), then \(x_ s(\theta)=x(s+\theta)\), for \(\theta\in [-r,0])\). The space \(\Lambda\) is isometrically isomorphic to \(L_{\infty}([-r,0])\times {\mathbb{R}}\). It allows us to consider discontinuous controls; moreover, the point evaluation of functions is continuous in \(\Lambda\). Under suitable assumptions, existence, uniqueness and continuous dependence results for solutions of (*) are obtained. An optimization problem is also considered.
reviewed by: Andrea Bacciotti
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4000468
zbMATH Keywords: hereditary control systems
zbMATH Keywords: discontinuous controls
zbMATH Keywords: optimization problem
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90184-7
OpenAlex ID: W1975490056
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description: scientific article; zbMATH DE number 4000468