On the controllability to the interval of the system governed by a hyperbolic equation
Abstract
Purpose
The purpose of this paper is to present the sufficient condition for the controllability to the interval of the system defined by a nonlinear hyperbolic equation.
Design/methodology/approach
The proof of the main theorem is based on the Miranda theorem which is a generalization of the Bolzano‐Weierstrass theorem.
Findings
In the course of the work, it was found that under some assumptions a system is controllable to the interval with the aid of controls from the oblique interval spanned by the given controls. In the end of the paper, an example illustrating the proposed method is derived.
Originality/value
This paper illustrates a procedure for finding a control which steers the system defined by a nonlinear hyperbolic equation to a given state.
Keywords
Citation
Bors, D. and Majewski, M. (2009), "On the controllability to the interval of the system governed by a hyperbolic equation", Kybernetes, Vol. 38 No. 7/8, pp. 1182-1190. https://doi.org/10.1108/03684920910976899
Publisher
:Emerald Group Publishing Limited
Copyright © 2009, Emerald Group Publishing Limited