Filtering Error System Research Articles

Asynchronous Fault Detection for Interval Type-2 Fuzzy Nonhomogeneous Higher Level Markov Jump Systems With Uncertain Transition Probabilities

Based on the interval type-2 fuzzy (IT2F) approach, this article investigates the fault detection filter design problem for a class of nonhomogeneous higher level Markov jump systems with uncertain transition probabilities. Considering that the mode information of the system cannot be obtained synchronously by the filter, the hidden Markov model can be seen as a detector to handle this asynchronous problem, and the parameter uncertainty can be processed by the IT2F approach with the lower and upper membership functions. Then, the asynchronous IT2F filter is designed to deal with the fault detection problem. Furthermore, the Gaussian transition probability density function is introduced to describe the uncertainty transition probabilities of the system and the filter. Based on the Lyapunov theory, the existence of the designed asynchronous IT2F filter and the dissipativity of the filter error system can be well ensured. In this article, the simulation study on a quarter-car suspension system verifies that the designed asynchronous IT2F filter can detect faults without error alarms.

Finite-time event-triggered filtering of the discrete-time switched linear systems with time delay

The finite-time event-triggered filtering of the discrete-time switched linear systems with time delay is addressed in the paper. The switched system and its filtering switched system are established as a filtering error system (FES) with augmented switching signal by the merging switching signal technique. The asynchronous switching phenomenon of switched system modes and filter modes occurs since a mode-dependent event-triggered transmission scheme (METS) which determines the system output and switching signal is addressed. Meanwhile, by the average dwell time (ADT) and multi-Lyapunov functional method, some sufficient conditions are given to make certain that the FES is finite-time bounded (FTB) and has a specified performance. Furthermore, the finite-time filter is designed by solving linear matrix inequalities. Ultimately, a numerical example is inspired to manifest the availability of the effects in the study.

Finite‐time [formula omitted] filtering for persistent dwell‐time switched piecewise‐affine systems against deception attacks

In this paper, the finite-time l2−l∞ filtering problem is investigated for discrete-time switched piecewise-affine systems against deception attacks, where switching signals are subject to the persistent dwell-time strategy. Considering the effect of deception attacks, a set of random variables obeying the Bernoulli distribution is used to describe the probability of false data injection between the plant and the filter. Based on the partition of state space with different operating regions, the objective of this paper is to design a mode-dependent and region-dependent filter such that the filtering error system is finite-time bounded and satisfies an l2−l∞ performance. By resorting to Lyapunov stability theory and finite-time analysis theory, some sufficient conditions are proposed to obtain such a desired filter. Finally, the availability of the proposed approach is demonstrated by two simulation examples.

Dissipative filtering for two-dimensional LPV systems: A hidden Markov model approach

In this article, the dissipative filtering problem is explored for two-dimensional (2-D) Markov jump linear parameter varying (MJLPV) systems. The underlying system is described based on the frequently-used Fornasini–Marchesini (FM) model with the measurement missing phenomenon. The hidden Markov model (HMM) is adopted to depict the partial accessibility between system and the designed filter modes. Based on this, a HMM-based filter is proposed, and sufficient conditions in the form of parameterized linear matrix inequalities (PLMIs) are established to guarantee that the filtering error system (FES) is asymptotically stable (AS) and strictly dissipative. Then, the corresponding filter synthesis problem is converted into a convex optimization problem. Ultimately, the simulation example is presented to demonstrate the utility of the obtained results.

Event‐triggered quantized L2−L∞$$ {\mathfrak{L}}_2-{\mathfrak{L}}_{\infty } $$ filtering for neural networks under denial‐of‐service attacks

AbstractThis article deals with the reliable event‐triggered quantized filtering issue for neural networks with exterior interference under denial‐of‐service attacks. In order to lighten the load of communication channels and save network resources, a resilient event‐triggered mechanism and a quantization scheme are employed, simultaneously. By applying a piecewise Lyapunov–Krasovskii functional method, sufficient conditions containing limitations of denial‐of‐service attacks are derived to guarantee that the filter error system is exponentially stable as well as possesses a prescribed disturbance attenuation performance. Then, a co‐design method of the desired quantized filtering gain matrix and event‐triggering parameter can be obtained provided that the linear matrix inequalities have a feasible solution. Finally, the usefulness of the proposed design method is demonstrated by a numerical example.

Distributed H∞ fuzzy filtering for nonlinear systems interconnected over graphs

SummaryThis article investigates the distributed fuzzy filtering problem for a class of Takagi–Sugeno (T‐S) fuzzy model‐based nonlinear systems interconnected over an undirected graph. The system we consider consists of numbers of heterogeneous nonlinear sub‐units interconnected over an undirected graph by sensing, computing, and communicating with each other. First, the system is represented by an undirected graph, a T‐S fuzzy model‐based state‐space equation of each subsystem and an interconnection condition. Based on this model, the concepts of the well‐posedness, stability, and contractiveness for the class of systems are introduced, and the distributed fuzzy filtering problem is established. By applying membership‐dependent multi‐Lyapunov functions, a sufficient condition on the well‐posedness, stability, and contractiveness of the open‐loop plant is then derived in terms of linear matrix inequalities (LMIs). And then, a distributed fuzzy filter inheriting the interconnected structure of the plant is designed such that the filtering error system is contractive, and a sufficient condition is correspondingly given to obtain the desired fuzzy filter parameters by solving a set of LMIs. Finally, a numerical simulation is exploited to show the validity of the proposed design method.

α− dissipative filtering for Singular Markov jump system with time delays

This paper considers the [Formula: see text] dissipative filtering problem for a class of Singular Markov jump systems (SMJSs) with distributed time delays and discrete time delays. First, using Lyapunov’s stability theory and combining delay partitioning technique, integral partitioning technique, and free weight matrix method, the sufficient conditions for stochastic admissibility and [Formula: see text] dissipation of system are studied. Then, a filtering design method based on linear matrix inequalities (LMIs) is given to make the filtering error system stochastically admissible and [Formula: see text] dissipative. Finally, numerical simulations verify the effectiveness of the resulting method.

Finite-time asynchronous control of discrete-time switched linear systems with event-triggered H∞ filtering

In this paper, the event-triggered H∞ filtering problem for discrete-time linear switched systems is investigated under asynchronous switching. Under the mode-dependent event-triggered transmission mechanism (METM), the switching signal and filtering signal are combined into an augmented switching signal by merging signal technology, and the switched system and filtering system are modeled as a filtering error system (FES). Because the switching signal of the filtering system is determined by METM, there will be an asynchronous switching phenomenon between the switched system and filtering system. The novel sufficient conditions are given to ensure that the FES is finite-time bounded (FTB) and has a specified H∞ performance by the average dwell time (ADT) and multi-Lyapunov functional method. And based on this, the design method of the H∞ filter is given. Ultimately, the numerical examples are inspired to manifest the availability of the effects in the study.

Asynchronously bounded filtering for discrete-time switched positive systems

In this paper, the asynchronous ℓ1 filtering issue is investigated for a class of discrete-time switched positive systems. An improved semi-time-dependent framework is established, which is compatible with the switching feature of asynchronously switched systems. First of all, the stability and ℓ1-gain analysis for switched positive linear systems are studied by using a semi-time-dependent multiple copositive Lyapunov function. On this foundation, both upper-bound and lower-bound positive filters are designed, which can ensure the positivity, stability and non-weighted ℓ1-gain of the corresponding filtering error systems. Moreover, the developed bounded filtering scheme is semi-time-dependent, which can achieve less conservative performance compared with the conventional time-independent methodology. Finally, an example is provided to demonstrate the potentials and merits of the proposed filtering scheme.

Dissipative Filter Design for Nonlinear Time-Varying-Delay Singular Systems against Deception Attacks

This paper applies a T-S fuzzy model to depict a class of nonlinear time-varying-delay singular systems and investigates the dissipative filtering problem for these systems under deception attacks. The measurement output is assumed to encounter random deception attacks during signal transmission, and a Bernoulli distribution is used to describe this random phenomena. In this case, the filtering error system modeled by a stochastic singular T-S fuzzy system is established and stochastic admissibility for this kind of system is defined firstly. Then, by combining some integral inequalities and using the Lyapunov–Krasovskii functional approach, sufficient delay-dependent conditions are presented based on linear matrix inequality techniques, where the system of filtering error can be stochastically admissible and strictly ℚ , S , ℝ -dissipative against randomly occurring deception attacks. Moreover, parameters of the desired filter can be obtained via the solutions of the established conditions. The validity of our work is illustrated through a mostly used example of the nonlinear system.

Asynchronous H∞ filtering for networked switched systems under effective DoS attacks

In this paper, the asynchronous filtering problem of discrete-time networked switched systems under effective DoS attacks is studied. DoS attacks launched by the opponent are not always successful, and effective DoS attacks refers to successful attacks. First, based on event-triggered communication mechanism (ETCM), combining multiple Lyapunov functions with the merging switching signal technique, sufficient conditions are given to make the filter error system mean square exponentially stable (MSES) and satisfy an performance. Then, switched filters and ETCM are co-designed by solving linear matrix inequalities. Furthermore, the relationship between the upper bound of attack duty cycle and the success rate of DoS attack is analysed. Finally, a practical example is given to illustrate the validity of the results.

Distributed Robust Filtering over Sensor Networks with Quantized Measurement and Switching Topologies

This paper aims at exploring the theoretical research and distributed filtering design of state estimation for sensor networked systems with quantized measurement and switching topologies. In a sensor network, each sensor node has an independent static logarithmic quantizer function, and the quantized measurement is transmitted to the filtering network via the wireless network. In the corresponding filtering network, each local estimator achieves distributed consistent state estimation of the plant based on the local measurement and the neighboring shared information. In particular, the design of the distributed filter fully takes into account the fact that the communication links between the nodes are not fixed. That is, the communication topology has random switching, and such random switching behavior is described using Markov chains with partially unknown transition probabilities. A set of linear matrix inequalities gives the sufficient conditions for the existence of the distributed filter, while ensuring that the filter error system has the desired H∞ performance. Finally, two numerical simulations show the effectiveness of the design method.

Dissipativity-based filter design for Markov jump systems with packet loss compensation

This paper is concerned with the dissipativity-based filtering problem for a class of discrete-time Markov jump systems with mode-dependent time-varying delays and random packet losses. The phenomenon of packet losses occurs between the plant and the filter, which is characterized by introducing a random variable. Based on the single exponential smoothing method, the prediction of the missing measurement is used as the packet loss compensation when a packet is lost. Then, a partially mode-dependent filter is established in view of the fact that the mode signals of the original system may not be completely accessible to the filter. By employing a mode-dependent Lyapunov-Krasovskii functional, some novel sufficient conditions are obtained and the filter parameters are derived to ensure that the filtering error system is stochastically stable with a strictly (U,V,W)-γ-dissipative performance. Finally, a numerical example is utilized to demonstrate the effectiveness of the proposed approach.

Integrated fault estimation and fault tolerant control for a class of uncertain Lipschitz systems with time-delays in finite frequency domain

This work describes an integrated fault estimation (FE) and fault tolerant control (FTC) strategy for a class of uncertain Lipschitz systems subject to time-delays in finite frequency domain. First, an FE filter is constructed by modeling the actuator faults and sensor faults as parameter changes. Second, an integral-type sliding mode FTC law based on the FE filter is developed, such that all states of the closed-loop system converge to the origin. By using the reconstructed Lipschitz property, the filter error system and the controlled system are rewritten as an augmented linear parameter varying (LPV) system. In addition, sufficient conditions for the augmented LPV system to have one full frequency and two finite frequency H∞ index bounds are converted to linear matrix inequalities. Finally, two examples are delivered to demonstrate the validity and benefits of the proposed method.

Reliable [formula omitted] filtering for the SP resonant ICPT system with stochastic multiple sensor faults

The inductively coupled power transfer (ICPT) system is one of the most important system in the wireless power transfer field. In this paper, the reliable H∞ filtering problem is considered for the ICPT system based on the series–parallel (SP) resonant compensation network. A more general SP resonant ICPT system model is proposed with considering external disturbances and multiple sensor faults. The sensor faults are assumed to happen in a random way, which are described by a set of stochastic variables satisfying certain statistical features. The main purpose of the addressed problem is to design an H∞ filtering scheme such that the filtering error dynamics are asymptotically mean-square stability (AMSS). For this purpose, a generalized state-space averaging (GSSA) model is built to characterize dynamical behaviors of the SP resonant ICPT system first. Then the filtering-error system with stochastic sensor faults is established via the GSSA model. By virtue of an extended Lyapunov function, a sufficient condition is given to achieve the AMSS of the system and H∞ performance requirement. Subsequently, the H∞ filtering gains are obtained by solving a set of linear matrix inequalities. Finally, a simulation example is provided to verify the availability and reliability of the proposed filtering scheme.

Fuzzy filtering based on decentralized adaptive event-triggered scheme for networked interconnected systems

This paper focuses on the problem of the fuzzy filtering for networked nonlinear interconnected systems based on decentralized adaptive event-triggered (AET) scheme. Firstly, a new decentralized AET scheme is proposed, and some unnecessary data packets are discarded through decentralized adaptive rule, thereby saving network communication resources. Secondly, the H∞ performance analysis of the filter error system is presented by using the fuzzy line-integral method, which does not need to give the time derivative upper bounds of the membership function in advance. Then, the combination of the Wirtinger-based inequality and the extended reciprocally convex matrix inequality is used to establish sufficient conditions for the filter error system to meet H∞ performance. Moreover, a method for jointly designing the distributed AET parameters and fuzzy filter parameters is proposed. Finally, two examples are given to verify the effectiveness of the proposed method.

Nonfragile Quantized $H_\infty$ Filtering for Discrete-Time Switched T–S Fuzzy Systems With Local Nonlinear Models

This article addresses the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of discrete-time nonlinear switched systems. Every subsystem of the considered nonlinear-switched systems is represented by the Takagi-Sugeno fuzzy systems with local nonlinear models. Signal quantization and filter parameter perturbation are considered simultaneously in the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter design. Both the measurement output signal and the performance output signal are quantized by two static quantizers, respectively, before they are transmitted. Based on the average dwell time approach, sufficient conditions for desired H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters are established in the form of linear matrix inequalities. Under the obtained conditions, the filtering error system is exponentially stable and can achieve a weighted H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the obtained results.

Memory fault detection filtering design for uncertain systems with finite frequency specifications

AbstractThis article is concerned with the memory fault detection filtering design in finite frequency domain for discrete‐time systems with polytopic uncertainties. Under the assumption that both disturbances and faults are restricted to finite frequency ranges, that is, the low, middle, or high frequency range, an admissible memory fault detection filter is developed by using historical information of the system. It is shown that the asymptotic stability with prescribed performance of the closed‐loop filtering error system is guaranteed. It is also shown that by using historical system outputs along with parameter‐dependent Lyapunov functions, the better performance of the resulting fault detection filter is obtained. With the aid of Projection lemma, sufficient conditions for the fault detection filtering design are established by solving an optimization problem in the form of a set of linear matrix inequalities (LMIs). Finally, three examples are presented to demonstrate the effectiveness and advantages of the proposed approach.

Event-Triggered $H_\infty$ Filtering for Networked Switched Systems With Packet Disorders

This paper deals with event-triggered H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for switched continuous-time systems with quantization. A multiple periodic sampling-based event-triggering strategy is adopted to select those “necessary” sampled signals to be transmitted. As a result, the amount of communication and the frequency of signal updates can be reduced significantly. Regarding the nonideal communication network, we consider network-induced delays and packet disorders, which are common during packet transmission through networks. In order to cope with packet disorders, an active packet loss approach is introduced. As such, a new time-delay system model is established, by which the filtering error system is modeled as a switched system with an interval time-varying delay. Then, by employing piecewise Lyapunov functional method and average dwell time technique, some criteria are derived to ensure that the filtering error system can achieve a prescribed level of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Moreover, the relationship between switching instants and the data updating instants in filter is discussed in detail, and the filter gains and event-triggering parameters can be jointly designed in terms of solutions to some linear matrix inequalities. Finally, numerical simulation is provided to verify the effectiveness of the proposed method.

H∞ deconvolution filter for two‐dimensional numerical systems using orthogonal moments

AbstractIn this article, we propose the issue of H∞ deconvolution filtering for two‐dimensional (2D) systems described by the Fornasini–Marchesini local state‐space model. The main challenge is the design of a deconvolution filter to rebuild the 2D signal so that the filter error system is asymptotically stable and preserves a guaranteed H∞ performance. To overcome this issue, we use some free matrix variables to eliminate coupling between Lyapunov matrix and system matrices to obtain sufficient conditions in linear matrix inequality form to ensure the desired stability and performance of the error systems in the first time. Moreover, we use the orthogonal moments to extract the feature vectors to generate the input system, with the minimum information with and without noise. Simulation examples are provided to show that the new design technology proposed in this article achieves better H∞ performance than the existing design methods. Finally, this work can be very helpful tools for the practitioners in telecommunication, and data scientists to aid them in deconvolution, diagnostic, and transmission.