Bilinear Controllability of a Simple Reparable System

TL;DR

This paper investigates the controllability of a simple two-state reparable system modeled by coupled transport and integro-differential equations, aiming to improve system availability through bilinear control strategies.

Contribution

It establishes the bilinear controllability of a reparable system and develops theoretical control strategies to enhance system availability.

Findings

Proves bilinear controllability of the system

Develops control strategies based on the system's bilinear structure

Provides theoretical foundations for system availability enhancement

Abstract

Reparable systems are systems that are characterized by their ability to undergo maintenance actions when failures occur. These systems are often described by transport equations, all coupled through an integro-differential equation. In this paper, we address the understudied aspect of the controllability of reparable systems. In particular, we focus on a two-state reparable system and our goal is to design a control strategy that enhances the system availability -- the probability of being operational when needed. We establish bilinear controllability, demonstrating that appropriate control actions can manipulate system dynamics to achieve desired availability levels. We provide theoretical foundations and develop control strategies that leverage the bilinear structure of the equations.