KOETC: Koopman Operator-Based Event-Triggered Control from Data

Zeyad M. Manaa1, Ayman M. Abdallah1, Mohamed Ismail1, Sami El-Ferik2,
1IRC-ASE, and the AE Department, KFUPM, 31261, Saudi Arabia. 2IRC for Smart Mobility and Logistics, and the CIE Department, KFUPM, 31261, Saudi Arabia.

This work was supported by the IRC-ASE at KFUPM under research project/grant INAE2401.

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KOETC enables advanced control from data-driven models.

Abstract

We present a new method for dealing with nonlinear systems Event-triggered control (ETC) design from data using Koopman operator theory. We reduce communication overhead by 40% for digital nonlinear systems using data-driven event-triggered control, requiring no system knowledge, while maintaining excellent performance and control costs compared to time triggered methods!

ETC presents a promising paradigm for efficient resource usage in networked and embedded control systems by reducing communication instances compared to traditional time-triggered strategies. This work introduces a novel approach to ETC for discrete-time nonlinear systems using a data-driven framework. By leveraging Koopman operator theory, the nonlinear system dynamics are globally linearized (approximately in practical settings) in a higher-dimensional space. We design a state-feedback controller and an event-triggering policy directly from data, ensuring exponential stability in Lyapunov sense. The proposed KOETC method is validated through extensive simulation experiments, demonstrating significant resource savings.

We show that KOETC can enable advanced control from data-driven models, allowing for precise and efficient event-triggered control strategies. We evaluate our method by conducting extensive simulations and real-world experiments, demonstrating its effectiveness in various scenarios.

Related work

There is a substantial body of work related to event-triggered control and data-driven methods, upon which our approach builds.

A Simple Event-Based PID Controller by K.-E. Årzén introduced one of the earliest event-triggered control strategies.

The formalization of event-triggered control in real-time systems is presented in Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks by P. Tabuada.

Data-driven control techniques have been explored in works like Data-Driven LQR Control Design by G. R. G. da Silva et al., and Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness by C. De Persis and P. Tesi, which have influenced our method.

For data-driven event-triggered control, recent works such as Data-Driven Event-Triggered Control for Discrete-Time LTI Systems by V. Digge and R. Pasumarthy offer insights into event-based control without explicit models.

The use of the Koopman operator in control is explored in Linear Predictors for Nonlinear Dynamical Systems: Koopman Operator Meets Model Predictive Control by M. Korda and I. Mezić, which inspired our Koopman-based approach.

For a comprehensive overview of the Koopman operator theory and its applications, consider Applied Koopmanism by M. Budišić, R. Mohr, and I. Mezić.

BibTeX

@article{manaa2024KOETC,
  author    = {Manaa, Zeyad M. and Abdallah, Ayman M. and Ismail, Mohamed and El-Ferik, Sami},
  title     = {KOETC: Koopman Operator-Based  Event-Triggered Control from Data},
  journal   = {Submitted to European Journal of Control},
  year      = {2024},
}