Partial-Neurons-Based Proportional-Integral Observer Design for Artificial Neural Networks: A Multiple Description Encoding Scheme

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.