Filtering Error System Research Articles

Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model

This paper investigates the event-triggered dissipative filtering problem for a class of networked semi-Markov jump systems. As a first attempt, the event-triggered communication scheme is introduced to save the limited network bandwidth and preserve the fixed system performance. By using the stochastic analysis, the information on the sojourn time between the mode jumps of the underlying systems is fully considered. By employing time-delay approach, the filtering performance analysis for the considered systems is presented, and then a co-design approach for the event-triggered mechanism and the dissipative filter is adopted such that the filtering error system is strictly dissipative. Finally, a numerical comparative example is used and a mass-spring system model as a realistic example is also provided to show the reduced conservatism and applicability of the proposed filtering scheme.

Non-fragile [formula omitted] filtering for delayed Takagi–Sugeno fuzzy systems with randomly occurring gain variations

In this study, we consider a non-fragile H∞ filter design for a class of continuous time delayed Takagi–Sugeno (T–S) fuzzy systems. The filter design is assumed to include randomly occurring gain variations according to the filter's implementation. Two independent Bernoulli distributions are employed to describe these random phenomena. We focus mainly on the design of a non-fragile filter so the filtering error system is asymptotically mean-square stable with the prescribed H∞ performance in the presence of both randomly occurring gain variations and a time delay. A sufficient condition is developed by employing the Lyapunov functional approach. Based on this condition, an improved H∞ filter for delayed T–S fuzzy system is described, which is free of randomly occurring gain variations. The filter parameters are obtained by solving a set of linear matrix inequalities. The effectiveness and the advantages of the proposed techniques are demonstrated by two numerical examples.

Positive L 1-gain filter design for positive continuous-time Markovian jump systems with partly known transition rates

The paper is concerned with the problem of positive L 1-gain filter design for positive continuous-time Markovian jump systems with partly known transition rates. Our aim is to design a positive full-order filter such that the corresponding filtering error system is positive and stochastically stable with L 1-gain performance. By applying a linear co-positive Lyapunov function and free-connection weighting vectors, the desired positive L 1-gain filter is provided. The obtained theoretical results are demonstrated by numerical examples.

H∞ filter design for nonlinear systems with quantised measurements in finite frequency domain

ABSTRACTThis paper deals with the problem of finite frequency (FF) H∞ full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi–Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency ℓ2 gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H∞ performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H∞ attenuation level can be obtained by our developed approach in comparison with another result in the literature.

On dissipative filtering over unreliable communication links for stochastic jumping neural networks based on a unified design method

This paper is concerned with the dissipative filtering problem for a class of stochastic jumping neural networks. The model under consideration is subject to unreliable communication links, which result in some network-induced phenomena such as packet dropouts, sensor nonlinearity and unknown/partly known mode information. A set of Bernoulli distributed white sequences are introduced to govern these phenomena occurring in a random way. The aim is to design a mixed filter, which ensures that the filtering error system is extended stochastically dissipative. Such a mixed filter has the advantages of both the model independent filter and the asynchronous filter. With the help of Lyapunov–Krasovskii methodology and an improved matrix decoupling approach, sufficient conditions for the existence of such a filter are presented by solving some convex optimization problems. A numerical example is given to verify the effectiveness of the proposed method.

Positive L1-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates

This paper deals with the problem of positive L1-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates. By implying an appropriate co-positive type Lyapunov function and free-connection weighting vectors, sufficient conditions for stochastic stability of the filtering error system are established. Then, the L1-gain performance is analyzed. Based on the obtained results, a positive full-order filter is designed to ensure that the corresponding filtering error system is positive and stochastically stable with L1-gain performance. All the conditions are derived in linear programming. Finally, the obtained theoretical results are demonstrated by a numerical example.

A Delay‐Dependent Approach to Robust Fast Adaptive Fault Estimation Design for Uncertain Neutral Systems with Time‐Varying Interval Delay

AbstractThis paper studies the problem of robust fault estimation for neutral systems, which are subjected to uncertainties, actuator fault, time‐varying interval delay, and norm‐bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, we focus on the design of a fault estimation filter that guarantees stability in the filtering error system with a prescribed H∞ performance. A novel Lyapunov‐Krasovskii functional is employed, which includes time delay information. A delay‐dependent criterion of robust fault estimation design is obtained by employing the free‐weighting matrices technique, and the proposed result has advantages over some existing results, in that it is less conservative and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is proposed in terms of the linear matrix inequality (LMI) by the Schur complements and the cone complementary linearization algorithm. Finally, illustrative examples are provided to show the effectiveness of the proposed method.

H∞filter design for linear time-invariant systems with polytopic uncertainties in finite frequency domain

SUMMARY This paper deals with the problem of finite frequency H∞ full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

Security-guaranteed filtering for discrete-time stochastic delayed systems with randomly occurring sensor saturations and deception attacks

In this paper, the security-guaranteed filtering problem is studied for a class of nonlinear stochastic discrete time-delay systems with randomly occurring sensor saturations (ROSSs) and randomly occurring deception attacks (RODAs). The nonlinearities in systems satisfy the sector-bounded conditions, and the time-varying delays are unknown with given lower and upper bounds. A novel measurement output model is proposed to reflect both the ROSSs and the RODAs. A new definition is put forward on the security level with respect to the noise intensity, the energy bound of the false signals, the energy of the initial system state, and the desired security degree. We aim at designing a filter such that, in the presence of ROSSs and RODAs, the filtering error dynamics achieves the prescribed level of security. By using the stochastic analysis techniques, a sufficient condition is first derived under which the filtering error system is guaranteed to have the desired security level, and then, the filter gain is designed by solving a linear matrix inequality with nonlinear constraints. Finally, a numerical example is provided to demonstrate the feasibility of the proposed filtering scheme. Copyright © 2016 John Wiley & Sons, Ltd.

Unified filters design for singular Markovian jump systems with time-varying delays

This paper considers the problem of unified mode-dependent and mode-independent filters design for continuous-time singular systems with Markovian jumping parameters and time-varying delays. The main objective of this paper is to design the L2−L∞, H∞, passivity, strict (Q, S, R)-dissipativity, very-strict passivity filters in a unified framework so as to ensure that the filter error system is stochastically admissible and extended dissipative. By tuning the weighting matrices, the extended dissipativity performance can reduce to the L2−L∞ performance, H∞ performance, passivity, strict (Q, S, R)-dissipativity and very-strict passivity, respectively. A mode-dependent and delay-dependent stochastic Lyapunov–Krasovskii functional is proposed to reflect the information of Markovian jump modes and the time-varying delays, and a set of linear matrix inequalities (LMIs) are utilized to derive sufficient conditions which guarantee that the desired unified filters can be constructed. Three numerical examples including an oil catalytic cracking process (OCCP) are employed to verify the usefulness and effectiveness of the main results obtained.

Fault Detection for Underactuated Manipulators Modeled by Markovian Jump Systems

This paper is concerned with the fault detection problem for underactuated manipulators based on the Markovian jump model. The purpose is to design a fault detection filter such that the filter error system is stochastically stable and the prescribed probability constraint performance can be guaranteed. The existence conditions for a fault detection filter are proposed through the stochastic analysis technique, and a new fault detection filter algorithm is employed to design the desired filter gains. In addition, the cone complementarity linearization procedure is employed to cast the filter design into a sequential minimization problem, which can be solved efficiently using existing optimization techniques. A numerical example is exploited to illustrate the effectiveness of the proposed method.

Co-design of H∞ Filter and Scheduling Strategy for NCS with Stochastic Nonlinearities and Multiplicative Noises via Delay-Partitioning Method

The co-design problem of H filter and scheduling strategy for NCS with stochastic nonlinearities and multiplicative noises is addressed in this paper. With consideration of communication constraints, the NCS are first modeled as a set of discrete-switched subsystems by applying scheduling strategy. Then a novel Lyapunov-Krasovskii functional and delay-partitioning technique are used to design an available filter such that the filtering error system is asymptotically mean-square stable and achieves a prescribed H performance level. A numerical example is given to illustrate the effectiveness of the proposed method.

Distributed non-fragile filtering in sensor networks with energy constraints

This paper investigates the distributed filtering problem for sensor networks with energy constraint and filter gain variation. Firstly, two strategies are proposed to reduce energy consumption, i.e., the measurement size and the transmission rate reduction strategies. To reduce the measurement size, a useful measurement selection policy is introduced to choose which element of local measurements is transmitted. The selected measurement, which has a smaller size than the original one is then stochastically transmitted. In order to reflect the imprecision in filter implementation, the additive filter gain variation problem is considered. Based on the switched system approach and some stochastic system analysis methods, a sufficient condition is obtained such that the filtering error system is exponentially stable in the mean-square sense, and a prescribed H∞ performance level is guaranteed. Filter gains are shown to be determined by solving a set of linear matrix inequalities (LMIs). Finally, a simulation example is given to demonstrate the effectiveness of the proposed design.

Non-fragile [formula omitted] filtering for nonlinear discrete-time delay systems with randomly occurring gain variations

In this paper,the problem of H∞ filtering for a class of nonlinear discrete-time delay systems is investigated. The time delay is assumed to be belonging to a given interval, and the designed filter includes additive gain variations which are supposed to be random and satisfy the Bernoulli distribution. By the augmented Lyapunov functional approach, a sufficient condition is developed to ensure that the filtering error system is asymptotically mean-square stable with a prescribed H∞ performance. In addition, an improved result of H∞ filtering for linear system is also derived. The filter parameters are obtained by solving a set of linear matrix inequalities. For nonlinear systems, the applicability of the developed filtering result is confirmed by a longitudinal flight system, and an additional example for linear system is presented to demonstrate the less conservativeness of the proposed design method.

Distributed piecewise filtering design for large-scale networked nonlinear systems

This paper investigates the problem of distributed piecewise filtering for discrete-time large-scale nonlinear systems. The considered large-scale system is composed of a number of nonlinear subsystems and exchanges its information through communication network. Each nonlinear subsystem is described by a Takagi-Sugeno (T-S) model, and data-packet dropouts happen intermittently in communication network, and its stochastic variables are assumed to satisfy the Bernoulli random-binary distribution. Our objective is to design a distributed piecewise filter such that the filtering error system is stochastically stable with an performance. Based on a piecewise Lyapunov function and some convexifying techniques, less conservative results are developed for the distributed piecewise filtering design of the considered system in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is validated by two examples.

Finite-time passive filtering for a class of neutral time-delayed systems

In this paper, the finite-time passive filtering problem of a class of neutral time-delayed systems is considered. The exogenous disturbances are unknown but norm bounded. A sufficient condition for passivity and finite-time stability of the combined system is derived and proved by means of Lyapunov functional methods and linear matrix inequalities (LMIs) techniques. The dynamic of the filtering error system is ensured to be finite-time bounded with a prescribed dissipation performance level [Formula: see text]. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Resilient [formula omitted]∞ filtering for discrete-time systems

This paper studies the problem of resilient H∞ filtering for discrete-time systems with norm-bounded uncertainties. The filter to be designed is assumed to have additive gain variations. Attention is focused on the design of a resilient H∞ filter such that the filtering error system is asymptotically stable and has a prescribed H∞ performance with respect to the uncertainty effects. Three different approaches are developed to design the H∞ filter, and the design conditions are presented in terms of solutions to linear matrix inequalities (LMIs). Finally, an illustrative example is provided to show the effectiveness of the proposed approaches.

Distributed ${\mathcal{H}}_{\infty}$ Filtering for a Class of Discrete-Time Markov Jump Lur’e Systems With Redundant Channels

This paper investigates the problem of distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for a class of discrete-time Markov jump Lur'e systems over sensor networks with stochastic switching topologies. As a first effort, the redundant channels are considered to use in the data transmission to strive against the fragility of networks commonly configured by a single channel in the communication networks subject to quantization and randomly occurring packet dropouts. By constructing a Lur'e-type Lyapunov function interconnected with a cone-bounded nonlinearity, the filtering performance analysis for the underlying systems is carried out first. Then, a new class of distributed filters, which can be used to reflect the mismatching characteristic of modes jumping between the target plants and the proposed filters, is designed such that the filtering error system is stochastically stable and achieves a prescribed average H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index. A numerical example is provided to show the effectiveness of the proposed filtering scheme.

Distributed non-fragile filtering for T-S fuzzy systems with event-based communications

This paper is concerned with the distributed non-fragile filtering for a class of discrete-time Takagi–Sugeno (T-S) fuzzy systems with event-based communication. Firstly, for the purpose of reducing communication, a general event generator is employed for sensors to determine the event time instant and then broadcast the measurement output to the filters. Each sensor node is capable to make its own decision to broadcast the current measurement only when its local measurement output error exceeds a specified threshold. Secondly, filter gain variation phenomenon reflecting the filter implementation uncertainties is also taken into account as the sensor networks are prone to uncertain disturbance in their application. A unified modeling is proposed to capture the event-based communication, packet dropouts and filter gain variations, which approximates the practical sensor network more closely. Based on the fuzzy Lyapunov functional, sufficient conditions have been presented such that the filtering error system is asymptotically stable with a prescribed weighted disturbance attenuation level. The filter gain parameters are determined by solving an optimization problem. Finally, a simulation study is given to show the effectiveness of the proposed new design.

Robust Filtering for a Class of Networked Nonlinear Systems With Switching Communication Channels.

This paper is concerned with the problem of robust filter design for a class of discrete-time networked nonlinear systems. The Takagi-Sugeno fuzzy model is employed to represent the underlying nonlinear dynamics. A multi-channel communication scheme that involves a channel switching phenomenon described by a Markov chain is proposed for data transmission. Two typical communication imperfections, network-induced time-varying delays and packet dropouts are considered in each channel. The objective of this paper is to design an admissible filter such that the filter error system is stochastically stable and ensures a prescribed disturbance attenuation level bound. Based on the Lyapunov-Krasovskii functional method and matrix inequality techniques, sufficient conditions on the existence of the desired filter are obtained. A numerical example is provided to illustrate the effectiveness of the proposed design approach.