Filtering Error System Research Articles

Hidden Markov model‐based filtering for 2‐D Markov jump Roesser systems subject to analog fading channels

AbstractThis article considers the filtering problem for 2‐D Markov jump Roesser systems, in which the measurement signal is transmitted via analog fading channels. The time‐varying amplitude attenuation of the analog fading channels is described by the fading gain modeled as a random variable. The hidden Markov model is used to deal with the mode mismatch phenomenon between the plant and the filter, then a full‐order asynchronous filter is designed for 2‐D Markov jump Roesser systems under analog fading channels. The purpose is to introduce a filter to guarantee that the filtering error system is not only asymptotically mean square stable, but also satisfies the disturbance attenuation performance. An improved decoupling method is proposed to acquire the 2‐D filter parameters such that the conservatism of the 2‐D filter designed law can be effectively reduced. Finally, a verification example and Darboux equation are given to illustrate the validity of the introduced asynchronous filter design law.

Energy-to-peak filtering for uncertain discrete-time singular bilinear systems with multipath data packet dropouts

In this paper, the energy-to-peak filtering problem for the uncertain discrete-time singular bilinear systems is studied. This paper considers the uncertainties that consist of real systems and the possible data packet dropouts when performance output signals and measurement output signals are transmitted over digital channels. In the course of the study, the phenomenon is elucidated utilising the Bernoulli random binomial distribution. The goal is to design the desired filter, so that the filtering error system is admissible, and meets the specified energy-to-peak performance index. The design conditions of energy-to-peak filters for uncertain discrete-time singular bilinear systems are given by introducing the Lyapunov function and using linear matrix inequalities (LMIs). The impact of uncertainty on singular bilinear systems is addressed using a two-step approach. At last, a numerical illustration is provided to demonstrate the validity of the design.

Dissipativity-based robust filter design for singular fuzzy systems with dynamic quantization and event-triggered mechanism

This paper focus on the design issue of event-based dissipative filter for quantized nonlinear singular systems. To save the communication resource, we employ a dynamic quantizer to quantized the measurement output signal prior to transmitting it to the filter via digital communication. Furthermore, the paper also presents an event-triggered mechanism for determining the transmission of the quantized signal. The intention of this paper is to try to propose an event-triggered filter to ensure that the filtering error system (FES) is admissible and satisfies strictly dissipativity performance, in the presence of dynamic quantization and occurring uncertainties. The Lyapunov function is utilized to establish a sufficient condition for the FES to meet the strictly dissipative performance. Depending on the obtained conditions, the required filter parameters are proposed using the standard linear matrix inequality (LMI) technique. Ultimately, the effectiveness of the developed method is verified by an actual circuit simulation.

Dynamic event-triggered non-fragile filtering for singular Markovian jump systems with packet dropouts

The problem of dynamic event-based non-fragile filtering for discrete-time singular Markovian jump systems is investigated in this paper, considering network-induced delays and packet dropouts. The random packet dropout is described by a Bernoulli-distributed stochastic variable with a known distribution law. To save limited network resources, an improved dynamic event-triggered scheme is proposed. By utilizing the Lyapunov-Krasovskii stability theory, a sufficient criterion is derived to ensure the stochastic admissibility of the resulting filter error system with a desired H∞ performance index. Based on the derived criterion, a co-design algorithm for the non-fragile filter and the dynamic event-triggered scheme is proposed by solving a set of linear matrix inequalities. The effectiveness and advantages of the proposed method are illustrated by two simulation examples.

Dissipative filtering for uncertain positive Roesser system under the try-once-discard protocol

This article addresses the problem of dissipative filtering for the delayed positive Roesser system with uncertainties under the try-once-discard communication protocol. To estimate the output of the addressed two-dimensional system, both positive lower- and upper-bounding filters are constructed, where the signals from the sensor nodes to the remote filters are transmitted through a shared communication network. To avoid the undesired data congestion phenomenon, the try-once-discard protocol is implemented to dynamically schedule the transmission sequence of the sensor nodes. Then, sufficient conditions are derived to design appropriate filters ensuring that the filtering error systems are positive, two-dimensional [Formula: see text]- γ-dissipative, and asymptotically stable. Finally, one numerical example is presented to demonstrate effectiveness of the designed filters.

Event-Triggered Resilient Filtering With the Interval Type Uncertainty for Markov Jump Systems.

The problem of event-triggered resilient filtering for Markov jump systems is investigated in this article. The hidden Markov model is used to characterize asynchronous constraints between the filters and the systems. Gain uncertainties of the resilient filter are the interval type in this article, which is more accurate than the norm-bounded type to model the uncertain phenomenon. The number of linear matrix inequalities constraints can be decreased significantly by separating the vertices of the uncertain interval, so that the difficulty of calculation and calculation time can be reduced. Moreover, the event-triggered scheme is applied to depress the consumption of network resources. In order to find a balance between reducing bandwidth consumed and improving system performance, the threshold parameter is designed as a diagonal matrix in the event-triggered scheme. Utilizing the convex optimization method, the sufficient conditions are derived to guarantee that the filtering error systems are stochastically stable and satisfy the extended dissipation performance. Finally, a single-link robot arm system is delivered to certify the effectiveness and advantages of the proposed method.

Finite-time ℋ∞ filtering for Markov jump systems with uniform quantization

This paper is concerned with finite-time ℋ ∞ filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time ℋ ∞ performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.

Networked fault detection for fuzzy systems using a quantizer with event-triggered strategy

This paper concerns with the problem of fault detection for networked fuzzy systems. Considering the digital communication channel, quantization is adopted to make the data transmission feasible and the induced data distortion is converted into a bounded uncertain term. For the purpose of saving network resources, a new quantizer with an event-triggered strategy is designed to reduce the length and the number of the transmitted data packets, simultaneously. In the process of stability analysis, the T-S fuzzy model approach is employed to approximate the nonlinear networked system, and a more flexible fuzzy design method is presented to get the fault detection filter which can detect the sensor fault in the presence of external disturbance. And sufficient conditions are constructed to guarantee the stability of the filter error system in terms of linear matrix inequalities. Finally, the simulation example is given to verify the feasibility of the method.

Distributed event-triggered finite-time H∞ filtering for switched systems on sensor networks with two-channel network attacks and asynchronous modes

This paper addresses the problem of distributed event-triggered finite-time H∞ filtering for switched systems on sensor networks, subject to two-channel network attacks and asynchronous modes. To tackle the issue posed by the switched event-triggered communication mechanism and network attacks, a distributed filter with switching signal is introduced. Additionally, considering the mismatched behavior between switched systems and distributed filters caused by the event-triggered communication mechanism and network attacks, a piecewise vector modal function which considers all switching conditions is proposed for handling the problem of the sensor network’s filtering error system containing multiple switching signals. By utilizing the multiple Lyapunov functional method and the average dwell time switching mechanism, sufficient conditions are derived to guarantee that the filtering error system with synchronous and asynchronous modes is both finite-time bounded and satisfies the H∞ performance index. Finally, an example is presented to demonstrate the validity of the results.

Event-triggered H∞ robust filtering for nonlinear semi-Markov switching systems

This paper studies the filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper.

Asynchronous-Switching-Based Distributed Interval Filtering for Positive Markov Jump Linear Systems Under Denial-of-Service Attack

This article presents an asynchronous distributed interval filtering method for discrete-time positive Markov jump linear systems (MJLSs) with bounded disturbance under the denial-of-service attack. By designing an asynchronous switching-distributed mechanism that depends on a randomly occurred attack, the proposed positive filter can monitor the real-time range of estimated states against the attack. The filtering error systems are modeled as a class of MJLSs with two attack-dependent Markov chains. Some analysis and design results are derived such that the error systems are positive and stochastically internally stable with satisfied <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain performance. The remote power monitoring in telecommunication systems is used for numerical verification.

Distributed H ∞ Consensus Filtering for Parabolic Distributed Parameter Systems with Multiple Missing Measurements: A Mobile Sensing Approach

This paper investigates the distributed H ∞ consensus filtering issue for a class of distributed parameter systems with bounded disturbance. In a framework of optimizing performance, a new approach to improving filter performance is proposed by employing mobile sensor networks. Moreover, the information missing in mobile sensor networks is modeled as a conditional probability distribution. The aim of the filtering challenge is to construct a distributed consensus filter such that the filtering error system is globally asymptotically stable in the mean square, and what disturbances do to the estimation accuracy is attenuated at the H ∞ consensus performance level. Utilizing the Lyapunov direct approach and the spatial operator technique, several sufficient criteria are given for the proposed filter to satisfy the H ∞ consensus performance constraint. Finally, a numerical simulation is given to demonstrate the effectiveness of the design scheme of the proposed filter.

Event-triggered filter of positive semi-Markovian jump systems with Weibull distribution

This paper focuses on the event-triggered filter design of positive semi-Markovian jump systems with Weibull distribution. The considered systems are subject to random uncertainty and sensor fault. A linear programming-based filter design approach is proposed. First, an event-triggering condition is established by virtue of sensor output signals. Under the event-triggering condition, the filtering error system is transformed into an interval system. The positivity of the filtering error system is reached by considering the positivity of the lower bound of the interval system. By using a stochastic co-positive Lyapunov function, the filtering error system is stochastically stable with an ℓ1-gain performance by exploring the corresponding performance of the upper bound of the interval system. Then, additive and multiplicative models following the Bernoulli distribution are introduced to describe the random uncertainties of the systems. Consequently, the event-triggered filter is designed in terms of linear programming and a matrix decomposition approach. Moreover, the proposed filter design is developed for the systems subject to sensor faults. Finally, two examples are provided to illustrate the effectiveness of the proposed design.

Event-Triggered Finite-Time &amp;lt;i&amp;gt;H&amp;lt;/i&amp;gt;&amp;lt;sub&amp;gt;∞&amp;lt;/sub&amp;gt; Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Asynchronous finite-time [formula omitted] filtering for linear neutral semi-Markovian jumping systems under hybrid cyber attacks

This paper concerns asynchronous finite-time event-triggered H∞ filtering design for neutral semi-Markovian jumping systems (S-MJSs) under malicious hybrid attacks. Firstly, based on event-triggered mechanism (ETM), time-delay and random cyber attacks, asynchronous filtering is addressed. Secondly, sufficient conditions are deduced that the filtering error system is stochastic H∞ finite-time bounded (SH∞FTB). Meanwhile, we provide novel results on stochastic H∞ finite-time contractively bounded (SH∞FTCB) for the S-MJSs under ETM and cyber attacks. Finally, an example with engineering background is presented to exemplify the effectiveness of our results.

Nonstationary Filtering for Fuzzy Markov Switching Affine Systems With Quantization Effects and Deception Attacks

This article focuses on the issue of nonstationary filtering for uncertain fuzzy Markov switching affine systems (FMSASs) with quantization effects and deception attacks (DAs). The resulting FMSASs are comprised of Markov switching piecewise-affine systems over a set of operating regions. To characterize the multinetwork-induced constraints, the measurement output is quantized before being transmitted, and a compensation scheme is applied to tackle the quantized measurement output loss intermittently. Meanwhile, the randomly occurring DAs are involved, in which the attack behaviors are identified by the bounded stochastic signals. Differently, to deal with the multinetwork-induced constraints, a novel nonstationary region-dependent affine filter strategy is developed. By resorting to a mode-dependent and region-dependent Lyapunov functional and S-procedure theory, sufficient conditions are elicited such that the filtering error system is mean-square exponentially stable. Finally, the practicability of the derived results is verified by a practical tunnel diode circuit model.

H ∞ filtering of discrete-time Markovian jump singular systems via bounded real lemma and supermartingale-liked approach

This paper addresses the filtering for discrete-time Markovian jump singular systems (MJSSs). While the existing researches have only given the sufficient conditions, in this paper a sufficient and necessary condition is established to guarantee that the filtering error system is regular, causal, stochastically stable and performance in light of supermartingale-liked approach and property of conditional expectation as well as – bounded real lemma. For obtaining the filter, an equivalent matrix inequality to the obtained one in nonlinear form is provided in terms of congruence transformation. Thus the desired filter can be developed by choosing matrix variables with certain structures. Finally, two simulations are provided to show the effectiveness of the proposed techniques in this paper.

Composite hierarchical anti-disturbance control for dynamic positioning system of ships based on robust wave filter

The composite hierarchical anti-disturbance control (CHADC) strategy is investigated for dynamical position system of ships(DP) with multiple disturbances, which include slowly varying environmental disturbances, first-order wave-induced disturbances and additional disturbances. The ship’s velocities and the slowly varying environmental disturbances are estimated by designing state observer and disturbance observer, respectively. Subsequently, a robust wave filter (RWF) is constructed to deal with the first-order wave-induced disturbances, which assures a prescribed performance level for the filter error system. The CHADC strategy is proposed by integrating stochastic disturbance observer-based control (DOBC) theory, RWF method with H∞ control, such that high control accuracy of the DP system can be realized. Efficacy of the proposed control strategy is illustrated through the example of a supply ship.

Event‐triggered positive L1 filter design for positive Markovian jump systems with quantization

AbstractThis paper is concerned with the design of positive filter for positive Markovian jump systems (PMJSs) with adaptive event‐triggered mechanism and quantization. Considering the mode jump of the system, a new adaptive event‐triggered condition is established, which not only can regulate the communication threshold according to the error of dynamic systems, but also can avoid the asynchronous phenomenon between the system mode and the filter mode. In order to further reduce the burden of communication, a new positive filter with the quantized measure system output is developed, and the design condition which ensures the filter error system to be stochastically stable with performance is presented which can be solved in terms of linear programming (LP) technique. It is illustrated that there is no Zeno phenomenon. The proposed results are applied to the power allocation in a mobile telecommunication system, and it is shown that compared with the existing results, the event‐triggered filter of this paper has some advantages.

Adaptive event‐triggered dissipative filter design for semi‐Markov jump systems under hybrid network attacks

AbstractThis article investigates the adaptive event‐triggered dissipative filter design for semi‐Markov jump systems under hybrid network attacks, in which hybrid network attacks consist of deception attack on the transmission of system state information and denial of service attack on the transmission of mode information. In order to save network communication resources, a novel adaptive event‐triggered mechanism is proposed, which can automatically adjust the event triggered threshold according to the filter error system changes. Next, a switched filtering error model is constructed by considering hybrid network attacks, adaptive event‐triggered scheme and time delays. Sufficient conditions are given to ensure that the filtering error system satisfies mean square exponential stability and strictly dissipative. Furthermore, filtering parameters and event triggered parameters are solved by linear matrix inequality technique. Finally, two examples are given to verify the validity of the proposed method.