Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Abstract

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

A Two-Filter Approach for State Estimation Utilizing Quantized Output Data

“…p(y t:N |x t ) = p(y t |x t )p(y t+1:N |x t ), (18) where p(y t+1:N |x t ) and p(y t:N |x t ) are the backward prediction and the backwardmeasurement-update equations, respectively, and (ii) the second formula, given by: p(x t |y 1:N ) = 17) and (18). Due to the non-Gaussianity of p(y t |x t ), the integrals in both the filtering and backwardfiltering algorithms in (15) and (17), respectively, are difficult to compute or intractable. Widely used methods to deal with these integrals are Monte-Carlo-based algorithms, such as particle filtering and smoothing; see, e.g., [31,66].…”

“…This procedure results in a GMM form. Hence, the integrals in both the filtering and backward filtering in (15) and (17), respectively, can be computed in closed form.…”

“…First, it is verified that it holds for t = N − 1, then it is assumed to be true for t = s + 1, and finally, it is verified that it holds for t = s. Notice that the recursion starts in t = N with p(y N:N |x N ) = p(y N |x N ), which is defined in (39). From (17), at time t = N − 1, the backward-prediction step is defined as:…”

“…State estimation is a scientific discipline that studies methodologies and algorithms for estimating the state of dynamical systems from input-output measurements [2,3]. There are a variety of applications that use state estimation, such as control [4][5][6][7], parameter identification [8][9][10], power systems [11,12], fault detection [13][14][15][16][17], prognosis [18,19], cyber-physical systems [20], hydrologic and geophysical data assimilation [21,22], maritime tracking [23], consensusbased state estimation using wireless sensor networks [24][25][26], navigation systems [27], and transportation and highway traffic management [28][29][30], to mention a few. Depending on the measurements that are used, two algorithms of state estimation can be distinguished: filtering and smoothing.…”

Adaptive event-triggered distributed recursive filtering with stochastic parameters and faults

“…Observers have been designed (Huong et al, 2020b) for nonlinear systems. Recalling these achievements, the adopted thresholds possess various forms, such as a fixed one unrelated to measurement outputs or states (named absolute ETCMs), a fixed one dependent on measurement outputs or states (called static ETCMs), a time-varying one with an additional internal variable having a predetermined dynamic (named dynamic ETCMs) (Ge et al, 2017(Ge et al, , 2019Huang et al, 2021) and an adaptive one (regarded as adaptive ETCMs) (Zhang et al, 2019). It is worth pointing out that the last two strategies have the capability of adjusting communication requirements dynamically according to the system's dynamic behaviour, and hence receive an even-increasing research concern.…”