# Hierarchical Event-triggered Learning for Cyclically Excited Systems with Application to Wireless Sensor Networks

## TL;DR

This paper introduces a hierarchical event-triggered learning method for cyclically excited nonlinear systems, significantly reducing communication in wireless sensor networks while maintaining accurate state estimation.

## Contribution

It proposes an automatic cyclic pattern recognition and hierarchical model update approach for event-triggered learning in nonlinear systems with changing cyclic excitation.

## Key findings

- Communication load reduced by 70%.
- Root-mean-square error less than 1 degree.
- Effective in real-time neuroprosthesis applications.

## Abstract

Communication load is a limiting factor in many real-time systems. Event-triggered state estimation and event-triggered learning methods reduce network communication by sending information only when it cannot be adequately predicted based on previously transmitted data. This paper proposes an event-triggered learning approach for nonlinear discrete-time systems with cyclic excitation. The method automatically recognizes cyclic patterns in data - even when they change repeatedly - and reduces communication load whenever the current data can be accurately predicted from previous cycles. Nonetheless, a bounded error between original and received signal is guaranteed. The cyclic excitation model, which is used for predictions, is updated hierarchically, i.e., a full model update is only performed if updating a small number of model parameters is not sufficient. A nonparametric statistical test enforces that model updates happen only if the cyclic excitation changed with high probability. The effectiveness of the proposed methods is demonstrated using the application example of wireless real-time pitch angle measurements of a human foot in a feedback-controlled neuroprosthesis. The experimental results show that communication load can be reduced by 70 % while the root-mean-square error between measured and received angle is less than 1{\deg}.