The iterative sampling procedure employed by diffusion models (DMs) often leads to significant latency. To address this, we propose Stochastic Consistency Distillation (SCott) to enable accelerated text-to-image generation, where high-quality generations can be achieved with just 2-4 sampling steps or even1 step, and further improvements can be obtained by additional cost, e.g., 4 steps. In contrast to vanilla consistency distillation (CD) which distills the ordinary differential equation solvers-based sampling process of a pre-trained teacher model into a student, SCott explores the possibility and validates the efficacy of integrating stochastic differential equation (SDE) solvers into CD to fully unleash the potential of the teacher. SCott is augmented with elaborate strategies to control the noise strength and sampling process of the SDE solver. An adversarial loss is further incorporated to strengthen the sample quality with rare sampling steps. Empirically, on the MSCOCO-2017 5K dataset with a Stable Diffusion-V1.5 teacher, SCott achieves an FID of 21.9, surpassing that of the 1-step InstaFlow (23.4) and the 4-step UFOGen (22.1). Moreover, SCott can yield more diverse samples than other consistency models for high-resolution image generation, with up to 16% improvement in a qualified metric.

In this article, the set-membership state estimation problem is investigated for a class of nonlinear complex networks under the FlexRay protocols (FRPs). In order to address practical engineering requirements, the multirate sampling is taken into account which allows for different sampling periods of the system state and the measurement. On the other hand, the FRP is deployed in the communication network from sensors to estimators in order to alleviate the communication burden. The underlying nonlinearity studied in this article is of a general nature, and an approach based on neural networks is employed to handle the nonlinearity. By utilizing the convex optimization technique, sufficient conditions are established in order to restrain the estimation errors within certain ellipsoidal constraints. Then, the estimator gains and the tuning scalars of the neural network are derived by solving several optimization problems. Finally, a practical simulation is conducted to verify the validity of the developed set-membership estimation scheme.

This article is concerned with the joint state and unknown input (SUI) estimation for a class of artificial neural networks (ANNs) with sensor resolution (SR) under the encoding-decoding mechanisms. The consideration of SR, which is an important specification of sensors in the real world, caters to engineering practice. Furthermore, the implementation of the encoding-decoding mechanism in the communication network aims to accommodate the limited bandwidth. The objective of this study is to propose a set-membership estimation algorithm that accurately estimates the state of the ANN without being influenced by the unknown input while accounting for the SR and the encoding-decoding mechanism. First, a sufficient condition is derived to ensure an ellipsoidal constraint on the estimation error. Then, by addressing an optimization problem, the design of the estimator gains is accomplished, and the minimal ellipsoidal constraint on the state estimation error is obtained. Finally, an example is provided to confirm the validity of the proposed joint SUI estimation scheme.

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.

This article investigates the control problem for a sort of repetitive discrete-time nonlinear systems subject to random packet dropouts and limited communication bandwidth. In order to compensate the impacts from the constraints on bandwidth, this work designs a communication protocol by designing a two-description coding scheme in combination with the scalar uniform quantization technique. The proposed protocol makes use of two independent channels to transmit data separately, thereby improving the channel utilization efficiency and reducing the probability of packet dropout. Then, with the proposed protocol and the iterative dynamic linearization approach, an adaptive iterative learning controller associated with a parameter estimation strategy is provided for the nonlinear system under investigation. The control law is data-driven, which therefore does not require knowledge of the model. Subsequently, the sufficient condition is derived under which the tracking error is forced to convergent. Finally, with the purpose to show the correctness of our theoretical results, we carry out two numerical simulations to test the effectiveness of the proposed control strategy.

This paper investigates the problem of outlier-resistant distributed fusion filtering (DFF) for a class of multi-sensor nonlinear singular systems (MSNSSs) under a dynamic event-triggered scheme (DETS). To relieve the effect of measurement outliers in data transmission, a self-adaptive saturation function is used. Moreover, to further reduce the energy consumption of each sensor node and improve the efficiency of resource utilization, a DETS is adopted to regulate the frequency of data transmission. For the addressed MSNSSs, our purpose is to construct the local outlier-resistant filter under the effects of the measurement outliers and the DETS; the local upper bound (UB) on the filtering error covariance (FEC) is derived by solving the difference equations and minimized by designing proper filter gains. Furthermore, according to the local filters and their UBs, a DFF algorithm is presented in terms of the inverse covariance intersection fusion rule. As such, the proposed DFF algorithm has the advantages of reducing the frequency of data transmission and the impact of measurement outliers, thereby improving the estimation performance. Moreover, the uniform boundedness of the filtering error is discussed and a corresponding sufficient condition is presented. Finally, the validity of the developed algorithm is checked using a simulation example.

Secure state estimation is becoming more popular due to the inherent vulnerabilities of communication networks in essence, which could give rise to potential data leakage and manipulation of microgrids. The paper addresses the issue of secure distributed state estimation for a class of microgrids with potential outliers occurring in sensor measurements. First, a secure distributed estimator is constructed by introducing both an artificial saturation rule to achieve outlier resilience and a variable decomposition strategy to safeguard data security, where the generated dynamic key is a time-varying sequence satisfying the predetermined constraint. Deep variance analysis is carried out to profoundly disclose the relationship between private and public estimation error covariance, in accordance with the employed decomposition rule. An upper bound of error covariance is determined by two sets of recursive matrix equations in contrast to that of traditional distributed estimation. Furthermore, the desired estimator gains are obtained recursively with the aid of optimizing the upper bound obtained above. In the end, a simulation example is proposed to confirm the effectiveness and security of the proposed algorithm.

A practical yet challenging scenario in transfer learning is unsupervised domain adaptation (UDA), where knowledge is transferred from a labeled source domain to unlabeled target domains. The crucially important role of domain-variant characteristics is often neglected by most existing UDA methods, which can deteriorate adaptation performance and result in negative transfer. In this article, an optimal unsupervised domain adaptation (OUDA) algorithm is proposed in order to address this issue, which balances the invariance of domain-sharing features and the variance of domain-specific features. In the proposed approach, a gradient adversarial adaptation (GAA) method is introduced to align the gradient directions of source and target features within the same category, thereby facilitating knowledge transfer. In addition, a local manifold embedding (LME) technique is proposed to preserve the intrinsic geometric structure of the original feature space while implementing distribution alignment, providing distinguishable features for UDA. To stabilize the process of knowledge transfer, an evolutionary control strategy is developed to adaptively control the tradeoff between the GAA and LME by employing the particle swarm optimization algorithm. Extensive experiments are conducted on cross-domain natural gas pipeline fault diagnosis, and the results on nine cross-domain classification tasks indicate that our OUDA algorithm outperforms the existing state-of-the-art UDA methods. Moreover, the performance analysis in terms of accuracy, loss, and domain divergence demonstrates the superior stability of the proposed OUDA algorithm in dealing with unsupervised knowledge transfer.

In this article, the optimized distributed filtering problem is studied for a class of saturated systems with amplify-and-forward (AF) relays via a dynamic event-triggered mechanism (DETM). The AF relays are located in the channels between sensors and filters to prolong the transmission distance of signals, where the transmission powers of sensors and relays can be described by a sequence of random variables with a known probability distribution. With the purpose of alleviating the communication burden and preventing data collision, the DETM is used to schedule the transmission cases of nodes by dynamically adjusting the triggered threshold according to the practical requirements. An upper bound matrix (UBM) of the filtering error (FE) covariance is first provided under the sense of variance constraint and the proper filter gain is further constructed via minimizing the proposed UBM. In addition, the boundedness evaluation regarding the trace of the UBM is provided. Finally, simulation experiments are used to illustrate the usefulness of the developed distributed recursive filtering scheme.

This article is concerned with the distributed set-membership estimation problem for a class of discrete time-varying systems over binary sensor networks. For the binary sensors, the cases of fixed and time-varying thresholds are considered. In both the cases, the information useful for state estimation purposes is extracted by utilizing the crossings of binary measurements at two adjacent time instants, and then distributed estimators are constructed for each sensor node with the aid of the available measurements, where a set of vector saturation functions is introduced to resist the adverse effect of outliers during signal transmission. A novel distributed set-membership performance index is provided by averaging over the ellipsoidal constraints of all the sensor nodes, and the local performance analysis method is employed to establish sufficient criteria that guarantee the existence of desired estimators whose parameters are then derived for every node by recursively optimizing certain ellipsoids in the sense of matrix trace. The applicability and feasibility of the distributed set-membership schemes developed in this article are verified by two illustrative examples.

Video-based person reidentification (Re-ID) is a prominent computer vision topic due to its wide range of video surveillance applications. Most existing methods utilize spatial and temporal correlations in frame sequences to obtain discriminative person features. However, inevitable degradation, e.g., motion blur contained in frames, leading to the loss of identity-discriminating cues. Recently, a new bio-inspired sensor called event camera, which can asynchronously record intensity changes, brings new vitality to the Re-ID task. With the microsecond resolution and low latency, it can accurately capture the movements of pedestrians even in the degraded environments. In this work, we propose a Sparse-Dense Complementary Learning (SDCL) Framework, which effectively extracts identity features by fully exploiting the complementary information of dense frames and sparse events. Specifically, for frames, we build a CNN-based module to aggregate the dense features of pedestrian appearance step by step, while for event streams, we design a bio-inspired spiking neural network (SNN) backbone, which encodes event signals into sparse feature maps in a spiking form, to extract the dynamic motion cues of pedestrians. Finally, a cross feature alignment module is constructed to fuse motion information from events and appearance cues from frames to enhance identity representation learning. Experiments on several benchmarks show that by employing events and SNN into Re-ID, our method significantly outperforms competitive methods. The code is available at https://github.com/Chengzhi-Cao/SDCL.

Non-local interactions play a vital role in boosting performance for image restoration. However, local window Transformer has been preferred due to its efficiency for processing high-resolution images. The superiority in efficiency comes at the cost of sacrificing the ability to model non-local interactions. In this paper, we present that local window Transformer can also function as modeling non-local interactions. The counterintuitive function is based on the permutation-equivariance of self-attention. The basic principle is quite simple: by *randomly shuffling* the input, local self-attention also has the potential to model non-local interactions without introducing extra parameters. Our random shuffle strategy enjoys elegant theoretical guarantees in extending the local scope. The resulting Transformer dubbed *ShuffleFormer* is capable of processing high-resolution images efficiently while modeling non-local interactions. Extensive experiments demonstrate the effectiveness of ShuffleFormer across a variety of image restoration tasks, including image denoising, deraining, and deblurring. Code is available at https://github.com/jiexiaou/ShuffleFormer.

Deep reinforcement learning (DRL) algorithms have proven effective in robot navigation, especially in unknown environments, by directly mapping perception inputs into robot control commands. However, most existing methods ignore the local minimum problem in navigation and thereby cannot handle complex unknown environments. In this paper, we propose the first DRL-based navigation method modeled by a semi-Markov decision process (SMDP) with continuous action space, named Adaptive Forward Simulation Time (AFST), to overcome this problem. Specifically, we reduce the dimensions of the action space and improve the distributed proximal policy optimization (DPPO) algorithm for the specified SMDP problem by modifying its GAE to better estimate the policy gradient in SMDPs. Experiments in various unknown environments demonstrate the effectiveness of AFST.

In this article, the sliding mode control problem is addressed for a class of sampled-data systems subject to deception attacks. The sampling periods undergo component-wise random perturbations that are governed by a Markovian chain. The component of the sampled output is transmitted via an individual communication channel that is vulnerable to deception attacks, and Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the deception attacks initiated by the adversaries. A sliding mode controller is designed to drive the state into the sliding domain around the specified sliding surface, and sufficient conditions are derived to guarantee the exponentially ultimate boundedness of the resultant closed-loop system in the mean-square sense. Furthermore, an optimization problem is established to pursue locally optimal control performance. Finally, a simulation example is given to verify the effectiveness and advantages of the developed controller design approach.

In this article, the distributed formation-containment (FC) control issue is investigated for a class of discrete-time multiagent systems (DT-MASs) under the event-triggered communication mechanism. In order to save the communication cost and improve the utilization of communication resources, a novel dynamic event-triggered (DET) mechanism is developed by adding an auxiliary variable for each agent system, which is able to dynamically adjust the triggering threshold. A distributed FC control scheme under the DET mechanism is proposed for all the leaders and followers based on the available relative outputs. The purpose of the addressed problem is to design the FC controller such that all the leaders achieve a formation shape and all the followers converge into such a convex hull. To this end, the considered DT-MASs are first decoupled into a diagonal form by resorting to the property of the Laplacian matrix as well as the inequality technique. Then, two sufficient conditions are established to ensure the desired FC performance. Furthermore, the corresponding FC controller parameters are obtained in terms of the solutions to two matrix inequalities which only depend on the maximum and minimum nonzero eigenvalues of the Laplacian matrix. Finally, an illustrative example is provided to verify the validity of the developed control scheme.

In this article, the problem of consensus control is investigated for a class of multiagent systems (MASs) with both stochastic noises and nonidentical exogenous disturbances. The signal transmission among agents is implemented through a digital communication network subject to both uniform quantization and round-robin protocol as a reflection of network constraints. The consensus strategy is designed by adopting the estimates of the relative states of the agent to its neighbors, which renders the distributed nature of the controller. A new consensus concept, namely, quasiconsensus in probability, is employed to evaluate the state response of the agents to the stochastic noises, the exogenous disturbances, and the quantization error. An augmented system is first formed that relies on the deviations of the individual state from the average state, the observer error of the relative state, as well as the relative measurement output. Based on the augmented model, an analysis approach on dynamical behaviors is developed to facilitate the consensus analysis of MASs by means of the switching Lyapunov function technique and the stochastic analysis methods. Then, the existence condition and the explicit expression of the time-varying gain matrices are proposed for the expected controller by resorting to the feasibility of several matrix inequalities. Numerical simulation results are presented to demonstrate the applicability of the theoretical results.

This work investigates the stabilization problem of uncertain stochastic Markovian jump systems (MJSs) under communication constraints. To reduce the bandwidth usage, a discrete-time Markovian chain is employed to implement the stochastic communication protocol (SCP) scheduling of the sensor nodes, by which only one sensor node is chosen to access the network at each transmission instant. Moreover, due to the effect of amplitude attenuation, time delay, and random interference/noise, the transmission may be inevitably subject to the Rice fading phenomenon. All of these constraints make the controller only receive the fading signal from one activated sensor node at each instant. A merge approach is first used to deal with two Markovian chains; meanwhile, a compensator is designed to provide available information for the controller. By a compensator and mode-based sliding-mode controller, the resulting closed-loop system is ensured to be input-to-state stable in probability (ISSiP), and the quasisliding mode is attained. Moreover, an iteration optimizing algorithm is provided to reduce the convergence domain around the sliding surface via searching a desirable sliding gain, which constitutes an effective GA-based sliding-mode control strategy. Finally, the proposed control scheme is verified via the simulation results.

In this article, a resilient$H_{\infty }$approach is put forward to deal with the state estimation problem for a type of discrete-time delayed memristive neural networks (MNNs) subject to stochastic disturbances (SDs) and dynamic event-triggered mechanism (ETM). The dynamic ETM is utilized to mitigate unnecessary resource consumption occurring in the sensor-to-estimator communication channel. To guarantee resilience against possible realization errors, the estimator gain is permitted to undergo some norm-bounded parameter drifts. For the delayed MNNs, our aim is to devise an event-based resilient$H_{\infty }$estimator that not only resists gain variations and SDs but also ensures the exponential mean-square stability of the resulting estimation error system with a guaranteed disturbance attenuation level. By resorting to the stochastic analysis technique, sufficient conditions are acquired for the expected estimator and, subsequently, estimator gains are obtained via figuring out a convex optimization problem. The validity of the$H_{\infty }$estimator is finally shown via a numerical example.

In this article, a resilient set-membership approach is put forward to deal with the state estimation problem for a sort of discrete-time memristive neural networks (DMNNs) with hybrid time delays under the weighted try-once-discard protocol (WTODP). The WTODP is utilized to mitigate unnecessary network congestion occurring in the channel between DMNNs and the state estimator. In order to ensure resilience against possible realization errors, the estimator gain is permitted to undergo some norm-bounded parameter drifts. Our objective is to design a resilient set-membership estimator (RSME) that is capable of resisting gain variations and unknown-but-bounded noises by confining the estimation error to certain ellipsoidal regions. By resorting to the recursive matrix inequality technique, sufficient conditions are acquired for the existence of the expected RSME and, subsequently, an optimization problem is formalized by minimizing the constraint ellipsoid (with respect to the estimation error) under WTODP. Finally, numerical simulation is carried out to validate the usefulness of RSME.

In this article, the robust finite-horizon state estimation problem is investigated for a class of time-varying complex networks (CNs) under the random access protocol (RAP) through available measurements from only a part of network nodes. The underlying CNs are subject to randomly occurring uncertainties, randomly occurring multiple delays, as well as sensor saturations. Several sequences of random variables are employed to characterize the random occurrences of parameter uncertainties and multiple delays. The RAP is adopted to orchestrate the data transmission at each time step based on a Markov chain. The aim of the addressed problem is to design a series of robust state estimators that make use of the available measurements from partial network nodes to estimate the network states, under the RAP and over a finite horizon, such that the estimation error dynamics achieves the prescribed$H_{\infty }$performance requirement. Sufficient conditions are provided for the existence of such time-varying partial-node-based$H_{\infty }$state estimators via stochastic analysis and matrix operations. The desired estimators are parameterized by solving certain recursive linear matrix inequalities. The effectiveness of the proposed state estimation algorithm is demonstrated via a simulation example.

This paper deals with the scalable distributed H∞-consensus filtering problem for a class of discrete time-varying systems subject to multiplicative noises and censored measurements over sensor networks (SNs). For the underlying SN, it is assumed that only the measurement outputs from partial sensor nodes are available. Also, the phenomenon of censored measurements is taken into account to reflect the limited capability in measuring. A new H∞-consensus performance index is put forward to evaluate the disturbance rejection level of the filters against the simultaneous presence of external disturbances, initial conditions, as well as censoring effects. By utilizing the vector dissipativity theory and the recursive matrix inequality technique, sufficient conditions are established under which the prescribed H∞-consensus performance index is achieved. The parameters of the desired distributed filters are calculated via solving certain matrix inequalities, where such a calculation is conducted in a local sense so as to preserve the scalability of the filter design. Finally, a numerical simulation example is provided to demonstrate the validity and applicability of the proposed filtering strategy.

This paper is coped with the robust sliding-mode-based control problem for a class of discrete nonlinear systems in the presence of mixed-delays and packet losses with uncertain missing probability. Both the time-varying state delays and the infinite distributed state delays are considered. Also, the data packet losses are modeled by a Bernoulli distributed stochastic variable with uncertain missing probability and an update rule is employed to characterize the signal transmitted to controller side. A sliding function is first constructed and the desired stochastic mean-square stability of sliding motion is ensured by providing a sufficient condition based on the matrix inequality technique. Besides, a new discrete SMC strategy is designed to guarantee that the state trajectories are driven onto the bounded band of predesigned sliding surface and maintain them therein during subsequent time. Finally, the effectiveness of the developed sliding-mode control technique is verified by some simulations with comparative results.

This paper addresses the H∞state estimation issue for a sort of memristive neural networks in the discrete-time setting under randomly occurring mixed time-delays and fading measurements. The main purpose of the addressed issue is to propose a state estimator design algorithm that ensures the error dynamics of the state estimation to be stochastically stable with a prespecified H∞disturbance attenuation index. We put forward certain switching functions to account for the discrete-time yet state-dependent characteristics of the memristive connection weights. By resorting to the robust analysis theory and the Lyapunov-functional analysis theory, we derive some sufficient conditions to guarantee the desired estimation performance. The derived sufficient conditions rely not only on the size of discrete time-delays and the probability distribution law of the distributed time-delays but also on the statistics information of the coefficients of the adopted Rice fading model. Based on the established existence conditions, the gain matrices of the desired estimator are obtained by means of the feasibility of a set of matrix inequalities that can be checked efficiently via available software packages. Finally, the numerical simulation results are provided to show the validity of the main results.

This article is concerned with the distributed recursive filtering issue for stochastic discrete time-varying systems subjected to both state saturations and round-robin (RR) protocols over sensor networks. The phenomenon of state saturation is considered to better describe practical engineering. The RR protocol is introduced to mitigate a network burden by determining which component of the sensor node has access to the network at each transmission instant. The purpose of the issue under consideration is to construct a distributed recursive filter such that a certain filtering error covariance's upper bound can be found and the corresponding filter parameters' explicit expression is given with both state saturations and RR protocols. By taking advantage of matrix difference equations, a filtering error covariance's upper bound can be presented and then be minimized by appropriately designing filter parameters. In particular, by using a matrix simplification technique, the sensor network topology's sparseness issue can be tackled. Finally, the feasibility for the addressed filtering scheme is demonstrated by an example.

In this paper, the observer-based stabilization problem is investigated for a class of discrete-time nonlinear stochastic networked control systems (NCSs) with exogenous disturbances. The signal transmission from the sensors to the observer is implemented via a shared digital network, in which both uniform quantization effect and stochastic communication protocol (SCP) are taken into account to reflect several network-induced constraints. The notion of input-to-state stability in probability is introduced to describe the dynamical behaviors of the closed-loop stochastic NCS that is effectively characterized by a general nonlinear stochastic difference equation with Markovian jumping parameters. A theoretical framework is first established to felicitate the dynamics analysis of the closed-loop system in virtue of the switched Lyapunov function method and the stochastic analysis techniques. By making full use of the quantized measurement output under the scheduling of the SCP, the existence conditions for an observer-based controller are established under which the closed-loop system is input-to-state stable in probability. Then, the explicit expression of the gain matrices of the desired controller is given by resorting to a set of feasible solutions of certain matrix inequalities. The effectiveness of the theoretical results is demonstrated by a numerical simulation example.

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

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.

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time stochastic memristive neural networks (DSMNNs) with time-varying delays and missing measurements. The DSMNN is subject to both the additive deterministic disturbances and the multiplicative stochastic noises. The missing measurements are governed by a sequence of random variables obeying the Bernoulli distribution. For the purpose of energy saving, an event-triggered communication scheme is used for DSMNNs to determine whether the measurement output is transmitted to the estimator or not. The problem addressed is to design an event-triggered estimator such that the dynamics of the estimation error is exponentially mean-square stable and the prespecified disturbance rejection attenuation level is also guaranteed. By utilizing a Lyapunov-Krasovskii functional and stochastic analysis techniques, sufficient conditions are derived to guarantee the existence of the desired estimator, and then, the estimator gains are characterized in terms of the solution to certain matrix inequalities. Finally, a numerical example is used to demonstrate the usefulness of the proposed event-triggered state estimation scheme.