Joint State and Fault Estimation for Networked Interconnected PDE Systems With Semi-Markov Fault Coefficient via Conjunct Measurement

Abstract

This paper interconnects N parabolic partial differential equations (PDEs) by a nonlinear coupling protocol to describe a class of large-scale distributed parameter systems, for which, based on the network communication, the issue of joint state and fault estimation is investigated. First, a generalized fault model, where the fault coefficient follows a semi-Markov switching law, is introduced into the system model. Then, to achieve joint state and fault estimation and ensure the estimation accuracy, a special augmented distributed estimator is designed with using associated information among subsystems. Note that the sampled-data and pointwise measurements are conjunctly employed, such that the network communication resources can be saved to a large extent. Moreover, based on the graph theory, a global Lyapunov-Krasovskii functional (LKF) is constructed to handle the nonlinear coupling function. As a result, an effective theorem is proposed to guarantee that both the state and fault estimation errors can converge to zero while satisfying a strictly (Ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,Ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,Ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> )-λ- dissipative index. Finally, a numerical example and an application study on chemical non-isothermal tubular reactors are provided to illustrate the feasibility and practicality of this paper.