Simultaneous State and Fault Estimation over Bandwidth-Constrained Networks: A Relay-Aided Binary Encoding Strategy

Abstract

This paper is concerned with the joint state and fault estimation problem for a class of discrete-time systems over a bandwidth-constrained network subject to actuator and sensor faults. The signal attenuation is resisted by locating the amplify-and-forward relay between the sensor and the estimator. In the sensor-to-relay channel, a binary encoding mechanism is employed to encode the measurement signal into a series of binary numbers. The random bit error, governed by a series of Bernoulli distributed random variables, is considered due to long-distance transmission and channel noise. The objective of the problem addressed in this paper is to design a joint state and fault estimator by augmenting the system state and the sensor fault into a descriptor system model. Sufficient conditions are established to ensure that the joint estimation error is exponentially bounded in the mean-square sense. The desired joint estimator gain is parameterized based on the solution of certain matrix inequalities. Finally, a numerical simulation is provided to validate the effectiveness of the proposed joint estimator design method.