On the controllability to the interval of the system governed by a hyperbolic equation

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.

The proof of the main theorem is based on the Miranda theorem which is a generalization of the Bolzano‐Weierstrass theorem.

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.

This paper illustrates a procedure for finding a control which steers the system defined by a nonlinear hyperbolic equation to a given state.