Class Of Discrete Time-varying Systems Research Articles

Covariance intersection based event-triggered distributed state estimation under channel independent DoS attacks

This paper investigates the event-triggered distributed state estimation problem for a class of discrete time-varying systems in the presence of denial-of-service (DoS) attacks, where each sensor node selectively shares its local information with neighbors. In contrast to the previous studies where the DoS attacks are considered on sensor-to-filter channels, we deal with the situation that DoS attacks jam each filter-to-filter communication channel independently. To reduce the communication rate and save network resources, a novel event-triggered communication strategy is presented that takes into account the impact of DoS attacks and is specialized for each communication channel. Based on the covariance intersection fusion rule and weight rearrangement method, a distributed state estimation algorithm is proposed. Further, the consistency of estimates and mean-square boundedness of estimation errors are proved under system collective observability and some other mild assumptions. Lastly, a numerical simulation is conducted to demonstrate the developed results and the effectiveness of the proposed algorithm.

A component-based coding–decoding approach to set-membership filtering for time-varying systems under constrained bit rate

This paper is concerned with the set-membership filtering (SMF) problem for a class of discrete time-varying systems with unknown-but-bounded noises under bit rate constraints. The communication between sensor nodes and filters is implemented through a wireless digital communication network with limited bandwidth. A bit rate constraint is first established to quantify the extent to which the network is constrained. A component-based coding–decoding procedure is proposed that enables individual decoder to decode messages from different components scattering in different physical locations. Based on this procedure, a decoded-measurement-based recursive SMF scheme with a prediction–correction structure is put forward. The desired parameters of the set-membership filter can be calculated recursively by the proposed recursive SMF scheme. Furthermore, the co-design issue of the bit rate allocation protocol and the filter gain is converted into the mixed-integer nonlinear programming problem that is solved by means of the particle swarm optimization and the recursive filtering algorithms. Finally, numerical simulations on two scenarios are conducted to validate the effectiveness of the proposed SMF approach.

Distributed recursive fault estimation with binary encoding schemes over sensor networks

In this paper, we investigate the distributed recursive fault estimation problem for a class of discrete time-varying systems with binary encoding schemes over a sensor network. The fault signal with zero second-order difference is taken into account to reflect the sensor failures. Since the communication bandwidth in practice is constrained, the binary encoding schemes are exploited to regulate the signal transmission from the neighbouring sensors to the local fault estimator. In addition, due to the influence of channel noises, each bit might change with a small crossover probability. In the presence of sensor faults and bit errors, an upper bound for the estimation error covariance matrix is ensured and minimized at each time step via designing the gain matrices of the estimator. Finally, the effectiveness of the method is verified by a simulation.

A Local Approach to Distributed $H_{\infty }$-Consensus State Estimation Over Sensor Networks Under Hybrid Attacks: Dynamic Event-Triggered Scheme

This paper deals with the distributed <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula>-consensus state estimation problem for a class of discrete time-varying systems with integral measurements over sensor networks. The addressed target plant has its output modeled as integral measurement so as to account for the interval time taken for sample collection. The signal transmissions between an individual sensor node and its neighboring nodes are first scheduled by a dynamic event-triggered scheme (ETS) for the purpose of energy saving, and such transmissions are further prone to hybrid cyber-attacks (comprising denial-of-service and deception attacks). A distributed estimator is constructed for each node by using the available information from itself and its neighboring nodes such that the estimation error dynamics achieves the prescribed <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula>-consensus performance in mean square sense. A local performance analysis method is developed to establish sufficient conditions that ensure the existence of the desired distributed estimators, and the corresponding estimator gains are then obtained by solving certain recursive matrix inequalities. The effectiveness of the proposed distributed estimation algorithm is illustrated through extensive simulation studies, where comparative experiments are conducted on time-triggered scheme, static ETS and dynamic ETS.

Event-based joint state and fault estimation: The envelope-constrained [formula omitted] criterion

In this paper, the joint state and fault estimation problem is investigated for a class of discrete time-varying systems under the dynamic event-triggering mechanism. The actuator fault and the sensor fault are, respectively, considered in the state and measurement equations where only the changing rate of the actuator fault is needed. The dynamic event-triggering scheme is used to decrease unnecessary transmissions from the sensor to the estimator. To facilitate the joint estimator design, a novel descriptor system model is constructed by aggregating the system state and the sensor fault. The main aim of the addressed problem is to design a joint estimator to ensure that the estimation error dynamics simultaneously achieves the finite-horizon H∞ performance and the envelope constraint. Sufficient conditions are provided to obtain the desired joint estimator parameters by solving a series of recursive matrix inequalities. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed estimation method. The major novelty of this study is that we make one of the very first few attempts to deal with the multi-objective joint state and fault estimation issue under the dynamic event-trigging transmission mechanism.

Distributed set-membership estimation for state-saturated systems with mixed time-delays via a dynamic event-triggered scheme

This paper is focused on the distributed estimation issue in the form of set-membership (SM) for a class of discrete time-varying systems suffering mix-time-delays and state-saturations. The phenomena of time-delays and state-saturations are introduced to better describe insightful engineering. During local measurements transmission between sensors over a resource-limited sensor network, to prevent data collisions and resource-consumption, a newly dynamic event-triggering strategy (DETS) is designed to dispatch the local measurements transmission for each sensor to its neighbors. Compared with the most existing static ETSs, this DETs can mitigate the total number of triggering times and enlarge interval time between consecutive triggering instants. Then, some novel adequate criteria for designing the desired event-based SM estimators are derived such that the plant’s true state always resides in each sensor’s ellipsoidal region regardless of the simultaneous presence of bounded noises, mixed time delays and state-saturations. Subsequently, a recursive optimization algorithm is formulated such that the minimal ellipsoids, the estimators gains and event-triggering weighted matrices are acquired simultaneously. A verification simulation is presented to illustrate the advantages of the design approach of the developed state estimator.

Distributed set-membership filtering for time-varying systems: A coding–decoding-based approach

In this paper, the distributed set-membership filtering problem is studied for a class of discrete time-varying systems over digital wireless sensor networks. In order to make full utilization of limited bandwidth of the communication channels connecting sensor nodes, a new coding–decoding communication strategy is implemented to regulate the data transmission between individual nodes. Under the scheduling of the proposed communication strategy, the transmitted signal will be converted to certain codewords belonging to a finite set before transmission according to the corresponding coding rules. Sufficient criteria are firstly established for the solvability of the addressed filtering problem in terms of a series of matrix inequalities. Subsequently, a sub-optimal problem is presented with the purpose of seeking the locally optimal distributed filter. Finally, two simulation examples are given to demonstrate the proposed filtering algorithm.

Input-Output Finite-Time Generalized Dissipative Filter of Discrete Time-Varying Systems With Quantization and Adaptive Event-Triggered Mechanism.

This article discusses the issue of input-output finite-time generalized dissipative filter design for a class of discrete time-varying systems. First, an adaptive event-triggered mechanism (AETM) with an adaptive law is proposed to adjust the threshold in the AETM according to the error between the system states and the filter states. Such an AETM determines whether the measurement output should be transmitted or not, which is more effective to economize the communication resources comparing with the traditional event-triggered mechanism. Second, in view of network-induced delays, the quantization and the AETM, a time-varying filter error system (TV-FES) is modeled. Then, a new augmented time-varying Lyapunov functional containing triple sum terms is provided. Based on the new finite-sum inequality and improved reciprocally convex combination lemma, delay-dependent conditions are obtained, which can ensure the TV-FES to be input-output finite-time stable and satisfy the given generalized dissipative performance. Moreover, the recursive linear matrix inequalities are presented to obtain the desired filter gains. Finally, numerical examples demonstrate the superiority and feasibility of the proposed method in this article.

Set-Membership filtering with incomplete observations

This study addresses the set-membership estimation problem for a class of discrete time-varying systems with incomplete observations. A set-membership filter is developed and a recursive algorithm is proposed to calculate the state estimate ellipsoid which contains the true value. To solve the problem that the conventional set-membership filter cannot guarantee the stability when applied to discrete time-varying systems with incomplete observations, a quantitative analysis method about incomplete observations is developed and a tight bound of the estimation error is found based on interval analysis and some bounded noise assumptions. In terms of bounded assumptions, the relationship between the bound of estimated error and the data dropout rate is obtained. If the data dropout rate is less than a maximal value, the set-membership filter is asymptotically stable. The proposed filter is applied to a two-state example to demonstrate the effectiveness of theoretical results.

A novel set‐membership control strategy for discrete‐time linear time‐varying systems

A novel set-membership control strategy is investigated for a class of discrete time-varying systems with unknown-but-bounded noises. Different from some existing set-membership estimation based control methods, the proposed control strategy is designed by using state estimation sets instead of some specific estimation points. The controlled performance requirement is modelled as a new set-membership performance constraint which ensures that the controlled output meets the requirement at any time instant. First, the set-membership filtering method is used for obtaining the ellipsoidal state estimation set. Second, a set-membership controller is constructed by utilising the state estimation which is arbitrarily chosen from the corresponding estimation set. Accordingly, sufficient conditions are derived such that the controlled system is asymptotically stable and satisfies the proposed performance constraint in the presence of unknown-but-bounded noises at each time instant. Then, a constructive computational algorithm is provided to describe the proposed control strategy. Finally, illustrative simulation examples are presented to demonstrate the effectiveness of the proposed method.

A dynamically event-triggered approach to recursive filtering with censored measurements and parameter uncertainties

In this paper, a dynamically event-triggered filtering problem is investigated for a class of discrete time-varying systems with censored measurements and parameter uncertainties. The censored measurements under consideration are described by the Tobit measurement model. In order to save the communication energy, a dynamically event-triggered mechanism is utilized to decide whether the measurements should be transmitted to the filter or not. The aim of this paper is to design a robust recursive filter such that the filtering error covariance is minimized in certain sense for all the possible censored measurements, parameter uncertainties as well as the effect induced by the dynamically event-triggered mechanism. By means of the mathematical induction, an upper bound is firstly derived for the filtering error covariance in terms of recursive matrix equations. Then, such an upper bound is minimized by designing the filter gain properly. Furthermore, the boundedness is analyzed for the minimized upper bound of the filtering error covariance. Finally, two numerical simulations are exploited to demonstrate the effectiveness of the proposed filtering algorithm.

Near-Optimal Resilient Control Strategy Design for State-Saturated Networked Systems Under Stochastic Communication Protocol.

In this paper, the near-optimal resilient control strategy design problem is investigated for a class of discrete time-varying system in simultaneous presence of stochastic communication protocols (SCPs), gain perturbations, state saturations, and additive nonlinearities. In the sensor-to-controller network, only one sensor is permitted to get access to the communication media so as to avoid possible data collisions. Described by a Markov chain, the SCP is employed to determine which sensor should obtain the access to the network at a certain time. Furthermore, two kinds of well-recognized complexities (i.e., state saturations and additive nonlinearities) are considered in the system model and the phenomenon of controller gain perturbation is also taken into special consideration. Accordingly, the resilient control strategy is designed by: 1) deriving a certain upper bound on the associate cost function of underlying systems and 2) minimizing such an upper bound through the utilization of the completing-the-square technique and the Moore-Penrose pseudo inverse. The resilient control strategy is obtained in an iterative manner by solving a set of coupled backward Riccati-like recursions. Furthermore, based on the proposed control strategies, the infinite horizon case is considered and the corresponding upper bound of the cost function is explicitly provided. Finally, numerical simulations are carried out on power systems in order to verify the validity of the proposed resilient control algorithms.

Consistent distributed state estimation with global observability over sensor network

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that the gain parameter optimization in a networked Kalman filter requires a centralized framework. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, an upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor’s measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios.

UIO-based Fault Estimation for a Class of Time-varying Systems with Event-triggered Transmissions

This paper addresses the fault estimation problem for a class of discrete time-varying systems by resorting to the unknown input observer (UIO) technique. The system is assumed to be subject to unknown inputs and stochastic additive disturbances. The sensor can decide whether to send the current measurement to the filter according to the difference between the current measurement and the last transmitted one. A set of filters is obtained such that the effects of unknown inputs on the estimation results can be integrated into uncertainties with known bounds and each filter corresponds one possible fault. Upper bounds of the state and fault estimation error covariances are calculated in the simultaneous presence of the unknown inputs and event-triggered measurements, and then the filter gains are determined recursively to minimize the bounds. The residual matching method is employed to isolate the faults and the outputs of the filters can be used to realize fault estimation. The effectiveness of the proposed method is demonstrated by a simulation example.

Distributed networked set-membership filtering with ellipsoidal state estimations

This paper addresses the problem of distributed networked set-membership filtering with ellipsoidal state estimations for a class of discrete time-varying systems in the presence of unknown-but-bounded process and measurement noises. Both global and local ellipsoidal state estimations are provided to locate the true state (target) via a distributed filtering network. A new geometric method based on Minkowski sum is proposed to produce the global ellipsoidal estimation. A novel convex optimization approach is developed to derive some sufficient conditions on the existence of local networked set-membership filters and to obtain the local ellipsoidal estimations by exchanging information among neighboring filters via communication networks. An experiment is conducted based on a 2-kW single-phase grid-connected power generation system platform to demonstrate the feasibility and the effectiveness of the proposed method in the real application.

Local Condition Based Consensus Filtering With Stochastic Nonlinearities and Multiple Missing Measurements

This paper is concerned with the distributed $H_{\infty }$ -consensus filtering problem for a class of discrete time-varying systems with stochastic nonlinearities and multiple missing measurements. The stochastic nonlinearities are formulated by statistical means and the missing measurements are characterized by a set of random variables obeying Bernoulli distribution. A novel $H_{\infty }$ -consensus performance index is proposed to measure both the filtering accuracy of every node and the consensus among neighbor nodes. Then, a new concept called stochastic vector dissipativity is proposed wherein the dissipation matrix is formulated by a nonsingular substochastic matrix, which is skillfully constructed by a new defined interval function on the out-degree. A set of local sufficient conditions in terms of the recursive linear matrix inequalities is presented for each node such that the proposed $H_{\infty }$ -consensus performance can be guaranteed for the local augmented dynamics over the finite horizon. Furthermore, a novel algorithm proposed here can be implemented on each node. Finally, an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithm.

Tobit Kalman filter with fading measurements

This paper is concerned with the Tobit Kalman filtering problem for a class of discrete time-varying systems with both censored and fading measurements. The censored measurements are described by the Tobit measurement model and the fading measurements are characterized by the Lth-order Rice fading channel model capable of accounting for not only the packet dropout but also the communication phenomenon. The measurement fading occurs in a random way where the fading probabilities are regulated by a set of mutually independent Gaussian random variables. By resorting to the state augmentation technique and the orthogonality projection principle, the Tobit Kalman filter (TKF) is designed in the presence of fading measurements. In the course of filter design, several state-augmentation-induced terms are introduced, all of which can be calculated recursively or off-line. A numerical example concerning the estimation of ballistic roll rates is provided to illustrate the usefulness of the proposed filter.

A Resilient Approach to Distributed Filter Design for Time-Varying Systems Under Stochastic Nonlinearities and Sensor Degradation

This paper is concerned with the distributed filtering problem for a class of discrete time-varying systems with stochastic nonlinearities and sensor degradation over a finite horizon. A two-step distributed filter algorithm is proposed where the sensor nodes collaboratively estimate the states of the plant by exploiting the information from both the local and the neighboring nodes. The goal of this paper is to design the distributed filters over a wireless sensor network subject to given sporadic communication topology. Moreover, a resilient operation is guaranteed to suppress random perturbations on the actually implemented filter gains. An upper bound is first derived for the filtering error covariance by utilizing an inductive method and such an upper bound is subsequently minimized via iteratively solving a quadratic optimization problem. To account for the topological information of the sensor networks, a novel matrix simplification technique is utilized to preserve the sparsity of the gain matrices in accordance with the given topology, and the analytical parameterization is obtained for the gain matrices of the desired suboptimal filter. Furthermore, a sufficient condition is established to guarantee the mean-square boundedness of the estimation errors. Numerical simulation is carried out to verify the effectiveness of the proposed filtering algorithm.

Distributed event‐triggered networked set‐membership filtering with partial information transmission

This study addresses the problem of distributed event-triggered set-membership filtering for a class of discrete time-varying systems in the presence of unknown-but-bounded noises. First, an event-triggered mechanism is introduced to choose those necessary data packets to be transmitted. Second, a partial information transmission scheme is proposed, by which, once an event is triggered, not all the information of the data packet, but parts of them are released to the communication network. As a result, communication network resources can be saved significantly. Third, some sufficient conditions on distributed networked set-membership filtering are derived using a time-varying convex optimisation approach. Moreover, based on an intersection method, a novel global estimation is proposed to integrate the local estimations by locating the intersection of all the local estimations within a volume-minimal external ellipsoid. Finally, simulation results demonstrate the feasibility and effectiveness of the proposed methods.

Local condition-based finite-horizon distributed H∞-consensus filtering for random parameter system with event-triggering protocols

This paper investigates the distributed H∞-consensus filtering problem for a class of discrete time-varying systems with random parameters and event-triggering protocols. An event-triggering protocol for each node is employed to reduce the burden of the network communication. A novel matrix named by information matrix is proposed to describe the complicated correlations among the elements of random matrix. By virtue of the presented information matrix, a weighted covariance matrix can be easily obtained to analyze the system with random parameters. With the aid of the newly constructed dissipation matrix and vector supplied rate functions, a set of local coupled conditions for each node is obtained such that the stochastic vector dissipativity-like over the finite-horizon of the filtering error dynamics can be guaranteed. As well, these sufficient conditions together could effectively solve the distributed H∞-consensus filtering problem. Notably, the designed filtering algorithm can be implemented on each node to obtain the desirable distributed filter gains. Finally, the effectiveness and applicability of the proposed algorithm is illustrated by a numerically simulative example.