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

TL;DR

The effectiveness of the proposed ETL methods is demonstrated using the application example of wireless real-time pitch angle measurements of a human foot in a feedback-controlled neuroprosthesis, which shows that communication load can be reduced by 70% while the root-mean-square error between measured and received angle is less than 1°.

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°.

Figures (5)

• Figure 1: Event-triggered learning in a two-agents network. If the measured signal (e.g., a human foot angle) can be described by a cyclically excited system model, the model is shared with the receiver and the communication is reduced to those samples that cannot be predicted using the model and previously transmitted data. Inaccuracy of the model (e.g., due to change in walking pattern) is detected and a new model is identified and shared.
• Figure 2: One sending and one receiving agent with the typical event-triggered state estimation architecture in black and event-triggered learning in blue (extended from c4). The process provides the measured state $x[k]$ at every sampling instant $k$. At the same time, the state is estimated by the prediction blocks of the sender and the receiver using the previous estimate $\hat{x}\left[k-1\right]$ and a trajectory model of the excitation $\hat{\boldsymbol{u}}$. If the prediction differs significantly from the measured state, then a state update is triggered, and the internal states of both prediction blocks are set to the measured state. Too frequent state updates indicate poor model quality and, therefore, trigger model learning. This can either lead to only an adjustment of certain parameters $\vartheta$ of the current model trajectory or to a completely new excitation trajectory $\hat{\boldsymbol{u}}$. In any case, the new model information is shared between sender and receiver.
• Figure 3: Number of transferred values $V$ with respect to full communication $V_{\text{full}}$ (left) and resulting RMSE (right). We compare full communication (full), decimation with factor 2 (decim), event-triggered state estimation (ETSE), and two parametrizations of event-triggered learning (ETL$_\text{h}$ / ETL$_\text{o}$) for about 0.5 h of highly variable gait. The results show that ETL reduces the communication significantly without changing the accurancy of the transferred signal in comparison to ETSE.
• Figure 4: Small model update ($\gamma _{\text{learn}}[k]=1\wedge \gamma _{\text{full}}[k]=0$) triggered at 98.9 s due to a change of cycle length (gait velocity). (A) measured and estimated state; (B) error $\left|x\left[k\right]-\hat{x}\left[k\right]\right|$ and state-update trigger threshold $\delta$; (C) probability $p\left[k\right]$ of the KS-test \ref{['eq:l-trigger']} and significance level $\eta$. Model learning is triggered because too many state updates ($\gamma _{\text{state}}[k]=1)$ occur and $p\left[k\right]$ falls below $\eta$ for the minimum holding time $t_{\text{min}}$.
• Figure 5: Full model update ($\gamma _{\text{learn}}[k]=1\wedge \gamma _{\text{full}}[k]=1$) triggered at 91.8 s due to a change of trajectory shape (walking style). Plotted signals and quantities are the same as in Fig. \ref{['fig:small']}.