Networked multi-sensor systems operating under the FlexRay protocol (FRP) are widely used in automotive industry, where reliable state estimation under bounded uncertainties is of fundamental importance. In such systems, the measurement information from multiple sensors is transmitted to the estimator through a network governed by the FRP, which induces scheduling constraints and switching behaviors in the estimation process. These characteristics make it challenging to guarantee accuracy and boundedness of the state estimates using conventional methods. This paper investigates the zonotopic set-membership fusion estimation (SMFE) problem for multi-sensor systems under the FRP. The research objective is to design a parallel fusion estimation algorithm for the transformed switched system, to establish a sufficient condition guaranteeing the ultimate boundedness of the radii of the resulting zonotopes, and to improve the transient estimation performance. An SMFE algorithm is proposed to recursively calculate the zonotopes that constrain the system state by exploiting the properties of zonotopes. A sufficient condition is derived to ensure the ultimate boundedness of the output zonotopes’ radii, which explicitly takes into account both the scheduling of the FRP and the adverse effect of zonotope order reduction on estimation performance. Furthermore, a matrix-inequality-based method is developed to construct an additional enclosing zonotope, based on which a tighter zonotope is obtained at each time instant to enhance the transient performance. The efficacy of the proposed SMFE method is demonstrated through two simulation experiments.

This article is concerned with the zonotopic set-membership fusion estimation (SMFE) problem for a class of complex networks (CNs). The measurements of the CNs are transmitted to a remote fusion center through a shared communication network. Due to the limited network bandwidth, the transmissions of the measurement information occur intermittently, and the nodes' transmission intervals may exceed their sampling periods. To enhance the utilization of the measurement information, each node of the CN is equipped with a buffer for real-time data storage, so that the fusion center can utilize more measurement information at time instants when the node's transmission interval is larger than its sampling period. The aim of this article is to design SMFE algorithms based on both the parallel fusion scheme and the data-compression fusion scheme, respectively, using the data received at the fusion center. First, by iterating the state equation of the CN, a batch processing method is proposed to process the input data of the fusion center concurrently. Subsequently, by employing the zonotopic set-membership estimation (SME) technique, the desired SMFE algorithms are designed. Moreover, sufficient criteria are established to ensure that the sizes of the output zonotopes of the SMFE algorithms remain uniformly bounded. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed algorithms.

This paper investigates the state estimation problem for power distribution networks subject to dynamic quantization effects and hybrid cyber-attacks, where measurement signals are transmitted from sensors to a remote filter via open digital communication networks. To enhance bandwidth utilization and ensure reliable data transmission, a dynamic quantization mechanism is introduced, which effectively accommodates the dynamic characteristics of power signals. Furthermore, the system is vulnerable to hybrid cyber-attacks that may occur simultaneously in a random manner, including denial-of-service attacks and false data injection attacks, characterized by Bernoulli distributed random variables. The primary objective of this work is to develop a recursive unscented Kalman filter capable of addressing the combined challenges of measurement nonlinearities, dynamic quantization effects, and hybrid cyber-attack scenarios. By solving Riccati-like difference equations, an upper bound on the filtering error covariance is derived, and subsequently minimized through the design of time-varying filter gains. Extensive simulations on the IEEE 69 distribution test system demonstrate the effectiveness of the proposed filtering algorithm.

This paper is concerned with the set-membership filtering problem for active power distribution systems that are influenced by unknown but bounded noises. Both the phenomena of fading channels and limited communication capacity are taken into account. In consideration of the integration of photovoltaic generation systems, an active power distribution system model is formulated which encompasses the conventional power distribution networks and distributed power sources. Network data are transmitted to a remote filter through fading channels, where a component-based dynamic event-triggered mechanism is introduced, by which the transmission frequency is reduced while sustaining the filtering performance, thereby mitigating the transmission load of the communication network. The purpose of this paper is to design a dynamic event-triggered filter such that, when faced with unknown but bounded noises, a set of zonotopes is devised to confine the system states. By minimizing the$F$-radius of these zonotopes, the time-varying filter gain is determined recursively at each time step. Additionally, simulation experiments on the IEEE 34 distribution test system are carried out, through which the efficiency of the proposed filtering methodology is validated.Note to Practitioners— The rapid increase in energy demand, coupled with the fast progression of energy technologies, has resulted in the widespread merging of traditional distribution networks with various other distributed power systems Consequently, these have transformed into active power distribution systems (APDSs), undergoing notable alterations in their distribution network configurations. Challenges like power back-flow and overvoltage, which might seriously compromise the stability, operation, and control of the APDS, can be introduced by this transformation. For addressing these challenges, having precise information about the system state is deemed crucial for the facilitation of real-time monitoring, improved control, and reliable protection of the APDS, and therefore the state estimation problem has been attracting an increasing research interest for ensuring the system’s safe operation and economical dispatch. In this paper, the problem of zonotopic set-membership filtering is examined for the APDS with unknown-but-bounded noises in fading channels. Initially, a component-based dynamic event-triggered mechanism is used in the APDS, which eases the load on communication networks with limited resources, and the fading coefficients are represented as uncertain variables within a specified range. Subsequently, by harnessing mathematical induction and set theory, the state estimation algorithm is introduced, ensuring the real system states are strictly encompassed within zonotopic sets and system states are estimated accurately. In conclusion, simulation experiments on the IEEE 34 distribution test system demonstrate the effectiveness of the introduced filtering algorithm.

This artcle investigates the fusion estimation problem for renewable energy microgrids subject to relay transmissions and cyber-attacks. A filter-and-forward (FaF) relay strategy is adopted to ensure the reliable transmission of power signals from distributed sensors to the remote estimator. This strategy jointly accounts for both sensor-relay and relay-estimator channels when determining signal transmission, and relays with embedded filtering capabilities are considered essential for extracting relay signals from corrupted measurements. In addition, four stochastic sequences governed by Bernoulli distributions are employed to characterize denial-of-service and false data injection attacks, which occur randomly throughout the communication process. The principal objective is to improve estimation accuracy by constructing an estimation scheme capable of operating under the presence of FaF relays and hybrid attacks. Specifically, the proposed scheme consists of two main components: first, the design of a recursive filtering algorithm at each FaF relay for generating the relay signal, and second, the development of a sequential fusion estimation algorithm to enable accurate state estimation. Sufficient conditions are derived to guarantee the mean-square boundedness of both the filtering error and the estimation error. The effectiveness of the proposed estimation methodology is demonstrated through simulation experiments conducted on renewable energy microgrids in a wireless multisensor system.

This article is concerned with the distributed set-membership fusion estimation problem for a class of artificial neural networks (ANNs), where the dynamic event-triggered mechanism (ETM) is utilized to schedule the signal transmission from sensors to local estimators to save resource consumption and avoid data congestion. The main purpose of this article is to design a distributed set-membership fusion estimation algorithm that ensures the global estimation error resides in a zonotope at each time instant and, meanwhile, the radius of the zonotope is ultimately bounded. By means of the zonotope properties and the linear matrix inequality (LMI) technique, the zonotope restraining the prediction error is first calculated to improve the prediction accuracy and subsequently, the zonotope enclosing the local estimation error is derived to enhance the estimation performance. By taking into account the side-effect of the order reduction technique (utilized in designing the local estimation algorithm) of the zonotope, a sufficient condition is derived to guarantee the ultimate boundedness of the radius of the zonotope that encompasses the local estimation error. Furthermore, parameters of the local estimators are obtained via solutions to certain bilinear matrix inequalities. Moreover, the zonotope-based distributed fusion estimator is obtained through minimizing certain upper bound of the radius of the zonotope (that contains the global estimation error) according to the matrix-weighted fusion rule. Finally, the effectiveness of the proposed distributed fusion estimation method is illustrated via a numerical example.

In this article, the state estimation problem is investigated for permanent magnet synchronous motors with sensor degradations under the encoding–decoding scheme. To reduce the network communication burden and enhance data transmission security, a uniform quantization-based encoding–decoding strategy is introduced in the sensor-to-estimator channel, which allows the transmitted power signals to be converted into digital format. Furthermore, the sensor degradation is represented by using a set of independent stochastic variables obeying uniform distributions. The primary objective of this article is to design a recursive state estimation algorithm such that, in the presence of sensor degradations and encoding–decoding strategy, a minimal upper bound on the estimation error covariance is derived by designing an appropriate estimator gain matrix. Simulation experiments for permanent magnet synchronous motors are conducted to validate the efficacy of the proposed recursive state estimation algorithm.

In this article, the sequential fusion estimation problem is investigated for multirate complex networks (MRCNs) with uniformly quantized measurements. The process and measurement noises, which are unknown-yet-bounded (UYB), are restrained into a family of zonotopes, and the multiple sensors are allowed to have different sampling periods. To facilitate digital transmissions, the sensor measurements are uniformly quantized before being sent to the remote estimator. The purpose of this article is to design a sequential set-membership estimator such that, in the simultaneous presence of UYB noises, multirate samplings, and uniform quantization effects, the estimation error (after each measurement update) is confined to a zonotope with minimum F -radius at each time instant. By introducing certain virtual measurements, the MRCNs are first transformed into single-rate ones exhibiting a switching phenomenon. Then, by utilizing the properties of zonotopes, the desired zonotopes are derived, which contain the estimation error dynamics after each measurement update. Subsequently, the gain matrices of the sequential estimator are derived by minimizing the F -radii of these zonotopes, and the uniform boundedness is analyzed for the F -radius of the zonotope containing the estimation error after all measurement updates. Furthermore, sufficient conditions are derived to ensure the existence of the desired uniform upper/lower bounds. Finally, an illustrated example is proposed to show the effectiveness of the proposed sequential fusion estimation method.

This paper is concerned with the set-membership state estimation problem for power harmonics under quantization effects by using the dynamic event-triggered mechanism. The underlying system is subject to unknown but bounded noises that are confined to a sequence of zonotopes. The data transmissions are realized over a digital communication channel, where the measurement signals are quantized by a logarithmic-uniform quantizer before being transmitted from the sensors to the remote estimator. Moreover, a dynamic event-triggered mechanism is introduced to reduce the number of unnecessary data transmissions, thereby relieving the communication burden. The objective of this paper is to design a zonotopic set-membership estimator for power harmonics with guaranteed estimation performance in the simultaneous presence of 1) unknown but bounded noises, 2) quantization effects and 3) dynamic event-triggered executions. By resorting to the mathematical induction method, a unified set-membership estimation framework is established, within which a family of zonotopic sets is first derived that contains the estimation errors and, subsequently, the estimator gain matrices are designed by minimizing the$F$-radii of these zonotopic sets. The effectiveness of the proposed estimation scheme is verified by a series of simulation experiments.

The finite-time state estimation issue is addressed in this paper for discrete time-delayed neural networks (NNs). More than one communication channel is utilized to improve the communication performance. The transmission delays of each channel are modeled by a family of stochastic variables which are independent and identically distributed. The main purpose of this paper is to construct an appropriate state estimation scheme under which the corresponding state estimation error dynamics is finite-time bounded in the mean square. By employing the stochastic analysis approach and introducing a special Lyapunov-like functional, we have developed certain sufficient conditions to achieve the prescribed estimation performance. Furthermore, the exact expressions of the achieved estimator parameters are given by solving a special minimization problem subject to certain inequality constraints. Finally, we propose an illustrative simulation to examine the correctness, as well as the effectiveness, of our proposed state estimation method.