Input Delays: A challenge for control engineer

Abstract

Delays frequently occur at the input of systems in everyday life, technology, biology, and industry. In general, they substantially degrade the performance of these systems, making them a challenge for control specialists.

The main ideas of two approaches are presented for the simple case of linear systems:

·       The finite spectrum allocation method, which consists of using an exact prediction of the state one time step τ (corresponding to the input delay) ahead. For this purpose, Cauchy’s formula is used—an expression for the system’s solution containing an integral term that must be numerically approximated.

·       The observer-based prediction, which provides an approximate value of the state one time step τ ahead. A plant model is used for this purpose, which is fed with the control calculated at the present time. This strategy requires the use of sub-predictors to reduce the observation error.

The application of these input delay compensation strategies is illustrated through the control of a fleet of autonomous vehicles, a predictor of epidemic evolution, and the control of an inverted pendulum.

Finally, both approaches are compared, particularly regarding the complexity of the control law, its design and implementation, as well as the robustness properties of the resulting control scheme. These topics are analyzed for the cases that has delay on the states and systems with partial information of the state

Bio: 

Dr. Sabine Mondié holds a degree in industrial and systems engineering from the Monterrey Institute of Technology and Higher Education (ITESM) in Mexico (1981). She earned a Master of Science degree with a specialization in Automatic Control from the Center for Research and Advanced Studies (Cinvestav), Mexico (1983), and a Ph.D. in Science from Cinvestav and the Institut de Recherche en Communications et Cybernétique de Nantes (IRCyN), France (1996).

Since 1996, she has served as a 3F researcher in the Department of Automatic Control at Cinvestav, where she currently serves as department head. She has been a Level 3 member of the National System of Researchers since January 2026. She has directed or co-directed 22 doctoral theses and 25 master’s theses, and is the author or co-author of more than 90 articles published in scientific journals, as well as more than 150 papers presented at national and international conferences. In addition, she has delivered plenary lectures both in Mexico and abroad in the field of time-delay systems.

She has served as chair of the Education Committee and vice-chair of the “Linear Systems” Technical Committee of the International Federation of Automatic Control (IFAC), and currently serves on the IFAC Council for the 2023–2026 term. She has also served as an associate editor for various specialized journals in the field of control, including Systems & Control Letters, the European Journal of Control, and IEEE Transactions on Automatic Control.

His research focuses on the analysis and control of delayed systems, including applications in the technological and biological fields. His areas of interest include stability conditions, robust stability, control of systems with input delays, and the design of delay-based controllers. In his work, he employs tools from time-domain, frequency-domain, and graphical analysis.