Controllability of suspension bridge model proposed by Lazer and Mckenna under the influence of impulses, delays, and non-local conditions

TL;DR

This paper investigates the controllability of a suspension bridge model affected by impulses, delays, and non-local conditions, providing theoretical proofs for both approximate and exact controllability.

Contribution

It introduces a novel approach to analyze controllability of complex bridge models considering impulses, delays, and non-local effects, using fixed point techniques.

Findings

Proves approximate controllability of the model.

Establishes exact controllability using Banach Fixed Point Theorem.

Provides a mathematical framework for controlling complex suspension bridge models.

Abstract

The main purpose of this paper is to prove the controllability of the model proposed by Lazer and Mckenna under the influence of impulses, delay, and non-local conditions. First, we study approximate controllability by employing a technique that pulls back the control solution to a fixed curve in a short time interval. Subsequently, based on Banach Fixed Point Theorem we investigate the exact controllability.