Abstract
This paper aims to develop a continuous-discrete finite memory observer (CD-FMO) for a class of nonlinear dynamical systems modeled by ordinary differential equations (ODEs) with discrete measurements. The nonlinear systems under consideration are at least locally Lipschitz, which guarantees the existence and uniqueness of solution at each time instant. The proposed nonlinear observer uses a finite number of collected measurements to estimate the system state in the presence of measurement noise. Besides, a one-step prediction algorithm incorporated with an iterative-update scheme is performed to solve the integral problem caused by system nonlinearity, and an analysis of the numerical integration approximation error is given. The properties of estimation performance have been further proved in deterministic case and been analyzed by Monte Carlo simulation in stochastic cases. It is worth noting that the presented method has a finite-time convergence, while most nonlinear observers are usually asymptotically convergent. Another advantage of CD-FMO is that it has no initial value problem. For the application purpose, residuals are generated to implement fault detection cooperated with Cumulative Sum (CUSUM) control charts, while a bank of CD-FMOs is adopted to realize fault isolation for different sensor and actuator faults of the considered nonlinear robotic arm. The robustness and effectiveness of the proposed approach are illustrated via the simulation results.
Highlights
Over past decades, it was noticed that state estimation, especially observer, plays an important role in the modern control theory and practice [1,2,3]
We are going to present a nonlinear observer design where the estimation instant is synchronized with the measurements instant since it is exactly what is needed under the background of diagnosis. e proposed continuous-discrete finite memory observer (CD-Finite memory observer (FMO)) will be detailed
A nonlinear observer has been proposed to perform state estimation and fault diagnosis for a class of continuous-discrete nonlinear dynamical systems. e performance of state estimation is great and can be significantly improved by choosing a larger window length
Summary
It was noticed that state estimation, especially observer, plays an important role in the modern control theory and practice [1,2,3]. Observations are usually taken at discrete time instants when using digital sensors For this reason, there is a significant amount of observer designs that has been investigated in the literature based on continuous-discrete modeling [3, 8, 11, 12]. Finite memory observer (FMO) was first proposed by Medvedev [20] for linear system in the deterministic framework, which indicates that this observer is extremely efficient for state estimation. Kratz et al have synthesized this observer in fault diagnosis of linear system [22] and hybrid system [23] All these previous researches reveal that finite memory observer provides a great potential in state estimation as well as in fault diagnosis.
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