Event-triggered control cannot improve the $\ell_2$ gain of $h_\infty$ optimal periodic control and transmit at a smaller average rate
Abstract
We consider a standard discrete-time event-triggered control setting by which a scheduler collocated with the plant's sensors decides when to transmit sensor data to a remote controller collocated with the plant's actuators. When the scheduler transmits periodically with period larger than or equal to one, the optimal controller guarantees an optimal attenuation bound ( gain) from any square-summable disturbance input to a plant's output. We show that, under mild assumptions, there does not exist a controller and scheduler pair that strictly improves the optimal attenuation bound of periodic control with a smaller average transmission rate. Equivalently, given any controller and scheduler pair, there exists a square-summable disturbance such that either the attenuation bound or the average transmission rate are larger than or equal to those of optimal periodic control.
Keywords
Cite
@article{arxiv.2310.17033,
title = {Event-triggered control cannot improve the $\ell_2$ gain of $h_\infty$ optimal periodic control and transmit at a smaller average rate},
author = {Duarte J. Antunes and J. P. Hespanha},
journal= {arXiv preprint arXiv:2310.17033},
year = {2023}
}