Evaluating the Effects of Size and Precision of Training Data on ANN Training Performance for the Prediction of Chaotic Time Series Patterns

In this research, artificial neural networks (ANN) with various architectures are trained to generate the chaotic time series patterns of the Lorenz attractor. The ANN training performance is evaluated based on the size and precision of the training data. The nonlinear Auto-Regressive (NAR) model is trained in open loop mode first. The trained model is then used with closed loop feedback to predict the chaotic time series outputs. The research goal is to use the designed NAR ANN model for the simulation and analysis of Electroencephalogram (EEG) signals in order to study brain activities. A simple ANN topology with a single hidden layer of 3 to 16 neurons and 1 to 4 input delays is used. The training performance is measured by averaged mean square error. It is found that the training performance cannot be improved by solely increasing the training data size. However, the training performance can be improved by increasing the precision of the training data. This provides useful knowledge towards reducing the number of EEG data samples and corresponding acquisition time for prediction.

Guaranteed Cost Leaderless Consensus Protocol Design for Fractional-Order Uncertain Multi-Agent Systems with State and Input Delays

This paper addresses the guaranteed cost leaderless consensus of delayed fractional-order (FO) multi-agent systems (FOMASs) with nonlinearities and uncertainties. A guaranteed cost function for FOMAS is proposed to simultaneously consider consensus performance and energy consumption. By employing the linear matrix inequality approach and the FO Razumikhin theorem, a delay-dependent and order-dependent consensus protocol is formulated for FOMASs with input delay. The proposed protocol not only guarantees the robust stability of the closed-loop system error but also ensures that the performance degradation caused by the system uncertainty is lesser than that obtained with other approaches. Two numerical examples are provided in order to verify the effectiveness and accuracy of the proposed protocol.