Joint State and Unknown Input Estimation for a Class of Artificial Neural Networks With Sensor Resolution: An Encoding–Decoding Mechanism

This article is concerned with the joint state and unknown input (SUI) estimation for a class of artificial neural networks (ANNs) with sensor resolution (SR) under the encoding–decoding mechanisms. The consideration of SR, which is an important specification of sensors in the real world, caters to engineering practice. Furthermore, the implementation of the encoding–decoding mechanism in the communication network aims to accommodate the limited bandwidth. The objective of this study is to propose a set-membership estimation algorithm that accurately estimates the state of the ANN without being influenced by the unknown input while accounting for the SR and the encoding–decoding mechanism. First, a sufficient condition is derived to ensure an ellipsoidal constraint on the estimation error. Then, by addressing an optimization problem, the design of the estimator gains is accomplished, and the minimal ellipsoidal constraint on the state estimation error is obtained. Finally, an example is provided to confirm the validity of the proposed joint SUI estimation scheme.

I. Introduction

ANNs have gained significant attention in recent years due to their remarkable performance in nonlinear function approximation and self-learning. ANNs have been widely applied in various fields such as signal processing [14], [29], [43], crack detection [8], [42], [51], and pattern recognition [16], [17]. In certain applications involving ANNs, there is a necessity to accurately ascertain the state of key neurons. However, acquiring such precise information directly is frequently challenging, where the difficulty stems primarily from the large scale of ANNs and the limited availability of observational resources. As a result, one often has access only to partial state information through sensor observations. Recently, research efforts have been focused on state estimation for ANNs, where the goal is to accurately estimate the unavailable state information by utilizing measurements from deployed sensors [3], [9], [27], [39], [40].