Everyday life is full of processes that happen simultaneously, often unnoticed. A cup of coffee slowly cools down, a car gradually accelerates, and the room dims as evening falls. This fluid evolution of physical reality is what we call the continuous world.
Today, however, more processes rely on digital systems that gather data and make decisions at specific intervals. Take modern vehicles: onboard sensors constantly evaluate metrics like speed and distance to determine precisely when to accelerate, brake, or adjust course.
The core challenge is that while a system processes data, the physical world keeps moving. Because modern automotive components, electrical grids, and industrial systems are increasingly digital, researchers must develop innovative mathematical tools and algorithms. These solutions ensure safe and reliable control—even when information arrives with delays, disruptions, or irregular intervals.
To address this challenge, Dr. Karina Barbosa, a researcher in the Faculty of Engineering at Usach, is leading a Fondecyt Regular 2026 project. Her team is developing advanced control mechanisms to ensure these critical systems respond safely and reliably, even under adverse or unpredictable conditions.
“Our goal is for different types of systems—whether electrical, mechanical, or biological—to operate satisfactorily. Using mathematics, we want to design control mechanisms that are as simple as possible while still ensuring a stable response,” said the USACH researcher.
In this context, the research examines sampled-data systems—networks where multiple sensors collect information at fixed intervals and feed it to a digital processor. The core vulnerability of this setup lies in timing: while the controller waits for the next data update, the physical process continues to move forward. As a result, even minor delays or irregular sampling rates can cause the system to react using outdated information.
“The information reaching the system is neither continuous nor exact; rather, it arrives at different points in time. Furthermore, during communication, there may be information loss, noise, or latency. Therefore, the challenge is to design a control system that is as simple as possible and that, even with all these real-world factors, yields a satisfactory response,” added the researcher.
Designed to anticipate the challenges of digital transformation, this four-year initiative unfolds in two distinct phases. The first phase focuses on establishing the theoretical framework and mathematical tools necessary to design these advanced control mechanisms.
In the second phase, the team will test these theoretical models using Hardware-in-the-Loop (HIL) testing. This real-time simulation methodology evaluates how the controller responds under realistic operating conditions. Ultimately, this approach lays the foundation for transforming academic research into practical applications—and potentially commercial products—for industry.
“Someone began thinking about this problem, and another person decided to study it. Thus, each piece of research adds a small grain of sand to the next, until, at some point, that knowledge can be transformed into a concrete technological solution. That is why science requires time and a great deal of collaboration,” concluded Dr. Barbosa.