This paper investigates the problem ofl2-l∞proportional-integral state estimation for stochastic nonlinear systems over decode-and-forward relay networks subject to packet losses. The system model is formulated to capture the effects of stochastic nonlinearities and state saturations, thereby reflecting practical engineering conditions. To alleviate transmission distance limitations, a decode-and-forward relay is introduced into the wireless channel to support communication from the sensor to the remote estimator, which enhances the reliability of long-distance data transmission. The objective is to design a proportional-integral state estimator that guarantees a prescribed finite-horizonl2-l∞performance level for the estimation error dynamics, despite the presence of stochastic nonlinearities, state saturations, packet losses, and decoding errors. A sufficient condition for the existence of such an estimator is established, and the corresponding estimator gains are obtained by solving a set of matrix equalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed state estimation scheme.

This article is concerned with the recursive state estimation issue for a class of nonlinear cyber-physical systems (CPSs) with token bucket protocols (TBPs) subject to sensor failures and false data injection (FDI) attacks. In the system under consideration, measurement signals are transmitted to the remote estimator only when there are sufficient tokens in the bucket to meet the token consumption. During network transmissions, the signals are exposed to FDI attacks, which occur randomly and follow a Bernoulli distribution. The primary objective is to develop a state estimation algorithm that can handle the TBP, sensor failures, and FDI attacks simultaneously. Initially, the upper bound of the estimation error covariance is derived using an intensive stochastic technique and the induction approach. Subsequently, the desired estimator gains are recursively computed to minimize this upper bound. Finally, an example is presented to demonstrate the effectiveness of the proposed estimation scheme.

This paper addresses the problem of distributed state estimation for smooth nonlinear systems over sensor networks by means of a generalized fuzzy proportional-integral observer (PIO). A sensor network is employed to collect system measurements, with a pull-type gossip protocol governing the intermittent data exchange among neighboring nodes. Under the gossip protocol, each sensor node randomly selects one neighbor to request data, facilitating distributed information updating. Furthermore, considering challenges such as long-distance communication and complex environmental conditions, signal transmission is subject to amplitude fading. To accommodate the characteristics of the gossip protocol, a generalized fuzzy PIO with a flexible structure is developed. Sufficient conditions are derived to guarantee the$H\_{\infty }$estimation performance of the proposed observer. Based on established conditions, the parameters of both the gossip protocol and the fuzzy PIO are co-designed via a particle-swarm-optimization-based iterative algorithm, with emphasis on enhancing observer robustness. Finally, an engineering-oriented simulation example is presented to illustrate the effectiveness of the proposed methodology.

This article investigates the proportional-integral-derivative (PID) containment control problem for a class of linear MAS with multirate measurements under the constraint of sensor resolution. The sensors of agents are classified into two distinct groups, characterized by their relatively fast and slow sampling periods. The concept of sensor resolution is introduced to quantify the ability of sensors to detect the smallest changes in information. A PID controller with an improved structure is proposed to achieve containment control, ensuring that follower agents remain within the convex hull formed by the leader agents. The closed-loop system is reformulated into a simplified representation, incorporating both sampling characteristics and communication topology. Sufficient conditions are then derived to guarantee the exponentially ultimate boundedness of the tracking error. Based on these conditions, an iterative algorithm is developed for computing the required controller gains. Finally, a simulation study, along with comparative analyses, is conducted to validate the effectiveness of the proposed approach.

This article investigates the recursive state estimation problem for a class of nonlinear cyber-physical systems (CPSs) operating under a token bucket strategy regulated by a random access protocol (RAP). Communication between sensor nodes and the remote estimator takes place over a shared network, where only one sensor node is permitted to access the network at each time instant to prevent data collisions. The transmission sequence of sensor nodes is governed by RAP scheduling, which is modeled as a sequence of independent and identically distributed variables representing the selected node granted network access. To efficiently manage limited communication resources, a token bucket strategy is employed. The measurement signal from the selected node is transmitted to the estimator only if a sufficient number of tokens are available in the bucket to meet the required token consumption. The objective is to design a state estimation algorithm that minimizes the estimation error covariance (EEC) by appropriately determining the estimator gain at each time step. The desired estimator gain is computed recursively by solving two Riccati-like difference equations. Finally, an illustrative example is presented to validate the effectiveness of the proposed estimation method.

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.

This article is concerned with the finite-horizon$H_{\infty}$state estimation problem for a specific class of nonlinear complex dynamical networks (CDNs) which are subject to random couplings and packet dropouts. The random coupling strengths among network nodes are characterized by a set of random variables with known statistical information. Three sequences of Bernoulli distributed random variables are utilized to model the packet dropouts over different communication channels. A decode-and-forward relay-based strategy is implemented to enhance the quality of communication by controlling the signal transmission in each sensor-to-estimator channel. The primary goal of this investigation is to create an appropriate state estimator for each node of the CDN, enabling the fulfillment of a specific$H_{\infty}$performance requirement for the estimation error dynamics over a finite horizon. Through the use of stochastic analysis techniques and matrix operations, a preliminary sufficient condition is given to meet the finite-horizon$H_{\infty}$performance requirement. The expected estimator gains are subsequently determined, which are defined in terms of the solutions to a series of recursive matrix inequalities. The effectiveness of the proposed relay-based estimation scheme is ultimately demonstrated through a numerical example.

The robust filtering problem is tackled for a class of shift-varying two-dimensional systems with uncertain-variance noises under the scheduling of the weighted try-once-discard (WTOD) protocol. The measurements collected from the sensors are transmitted to a remote filter via a shared network. To alleviate the communication burden and obviate the network congestion, the WTOD protocol is adopted to orchestrate the data transmission, where a sensor node is solely permitted to broadcast its information to the remote filter at every transmission step. Moreover, the resilient filter is exploited to regulate the possible gain perturbation. The objective of the addressed problem is to design a robust filter in a recursive structure such that, in the simultaneous presence of the uncertain-variance noises and the WTOD protocol, the minimal upper bounds (UBs) on the filtering error variances (EVs) are developed for the considered system. First, by means of induction and stochastic analysis technique, certain UBs in terms of coupled recursive difference equations are derived for the actual EVs. Then, a proper filter is carefully designed which achieves the minimization of the obtained UBs at each step. Finally, an illustrative example is presented to verify the usefulness of the proposed protocol-based filtering method.

This article tackles the recursive filtering problem for an array of 2-D systems over sensor networks with a given topology. Both the measurement degradations of the network outputs and the stochastic perturbations of network couplings are modeled to reflect engineering practice by introducing some random variables with given statistics. The goal of the addressed problem is to devise the distributed recursive filters capable of cooperatively estimating the true state in order to ensure locally minimal upper bound (UB) on the second-order moment of the filtering error (also viewed as the general error variance). For this purpose, the general error variance regarding the underlying target plant is first provided to facilitate the subsequent filter design, and then a certain UB on the error variance is constructed by exploiting the stochastic analysis and the induction approach. Furthermore, in view of the inherent sparsity of the sensor network, the gain parameters of the desired distributed filters are determined, and the proposed recursive filtering algorithm is shown to be scalable. Finally, an illustrative example is given to demonstrate the validity of the established filtering strategy.

This paper addresses the recursive filtering problem for shift-varying linear repetitive processes (LRPs) with limited network resources. To reduce the resource occupancy, a novel event-triggered strategy is proposed where the concern is to broadcast those necessary measurements to update the innovation information only when certain events appear. The primary goal of this paper is to design a recursive filter rendering that, under the event-triggered communication mechanism, an upper bound (UB) on the filtering error variance is ensured and then optimized by properly determining the filter gains. As a distinct kind of 2-D systems, the LRPs are cast into a general Fornasini-Marchesini model by using the lifting technique. A new definition of the triggering-shift sequence is introduced and an event-triggered rule is then constructed for the transformed system. With the aid of mathematical induction, the filtering error variance is guaranteed to have a UB which is subsequently optimized with appropriate filter parameters via solving two series of Riccati-like difference equations. Theoretical analysis further reveals the monotonicity of the filtering performance with regard to the event-triggering threshold. Finally, an illustrative simulation is given to show the feasibility of the designed filtering scheme.

This paper is concerned with the robust finite-horizon filter design problem for a class of two-dimensional (2-D) time-varying systems with norm-bounded parameter uncertainties and incomplete measurements. The incomplete measurements cover randomly occurring sensor delays and missing measurements that are presented in a unified form by resorting to a stochastic Kronecker delta function. The occurrences of the sensor delays and missing measurements are governed by stochastic variables with known probability distributions. The main aim of the addressed problem is to design a recursive filter with appropriate gain parameters that ensure the local minimum of certain upper bound on the estimation error variance at each time instant. With the aid of the inductive approach and the 2-D Riccati-like difference equations, one of the first few attempts is made to tackle the robust filter design problem for 2-D uncertain systems with random sensor delays over a finite horizon. Sufficient conditions are provided for the existence of an upper bound on the estimation error variance, an algorithm is then developed to derive such an upper bound, and finally the desired filter is designed to minimize the obtained upper bound. The filter design procedure is of a recursive form that facilitates the online calculation. A numerical simulation is carried out to show the effectiveness of the developed filtering scheme.

This paper investigates the state estimation problem for a class of 2-D time-varying systems with error variance constraints, where the implemented estimator gain is subject to stochastic perturbations. Redundant channels are utilized as a protocol to strengthen the transmission reliability and the channels' packet dropout rates are described by mutually uncorrelated Bernoulli distributions. The objective of the addressed problem is to design a resilient estimator such that an upper bound on the estimation error variance is first guaranteed and then minimized at each time step, where the considered gain perturbations are characterized by their statistical properties. By employing the induction method and the variance-constrained approach, an upper bound on the estimation error variance is first constructed by means of the solutions to two Riccati-like difference equations and, subsequently, a locally minimal upper bound is achieved by appropriately designing the gain parameter. Then, an effective algorithm is proposed for designing the desired estimator, which is in a recursive form suitable for online applications. Finally, a numerical simulation is provided to demonstrate the usefulness of the proposed estimation scheme.

This paper is concerned with the recursive filtering problem for a class of nonlinear 2-D time-varying systems with degraded measurements over a finite horizon. The phenomenon of measurement degradation occurs in a random way depicted by stochastic variables satisfying certain probabilities distributions. The nonlinearities under consideration are dealt with through the Taylor expansion, where the high-order terms of the linearization errors are characterized by norm-bounded parameter uncertainties. The objective of the addressed problem is to design a filter which guarantees an upper bound of the estimation error variance and subsequently minimizes such a bound with the desired gain parameters. By means of mathematical induction, an upper bound is first derived for the estimation error variance by constructing two sets of Riccati-like difference equations, and then the obtained bound is minimized by properly selecting the filter parameter at each time step. Both the minimal upper bound and the desired filter parameter are suitable for recursive online computation. Furthermore, the effect of the stochastic measurement degradation on the filtering performance is discussed. Finally, a simulation example is presented to demonstrate the effectiveness of the designed filter.