# Theory and implementation of event-triggered stabilization over digital channels

## TL;DR

This paper presents a novel event-triggered control method that leverages timing information in digital channels to stabilize a system more efficiently, reducing data transmission rates compared to traditional methods.

## Contribution

It introduces an encoding-decoding scheme that exploits timing information for stabilization and demonstrates its effectiveness through experiments on an inverted pendulum.

## Key findings

- Higher communication delays require increased data payload rates.
- Timing information can reduce data transmission needs for stabilization.
- The method achieves input-to-state practical stability for nonlinear systems.

## Abstract

In the context of event-triggered control, the timing of the triggering events carries information about the state of the system that can be used for stabilization. At each triggering event, not only can information be transmitted by the message content (data payload) but also by its timing. We demonstrate this in the context of stabilization of a laboratory-scale inverted pendulum around its equilibrium point over a digital communication channel with bounded unknown delay. Our event-triggering control strategy encodes timing information by transmitting in a state-dependent fashion and can achieve stabilization using a data payload transmission rate lower than what the data-rate theorem prescribes for classical periodic control policies that do not exploit timing information. Through experimental results, we show that as the delay in the communication channel increases, a higher data payload transmission rate is required to fulfill the proposed event-triggering policy requirements. This confirms the theoretical intuition that a larger delay brings a larger uncertainty about the value of the state at the controller, as less timing information is carried in the communication. In addition, our results also provide a novel encoding-decoding scheme to achieve input-to-state practically stability (ISpS) for nonlinear continuous-time systems under appropriate assumptions.