Time series anomaly detection is crucial for ensuring the stability and security of Cyber-Physical Systems (CPSs). In this study, we propose an unsupervised anomaly detection method utilizing Conditional Variational Auto-Encoder (CVAE) to effectively detect anomalies. A Transformer encoder is employed to extract complex temporal features from the time series, which are then passed to the CVAE. To refine the reconstructed sequences generated by the CVAE, we apply two Long Short-Term Memory (LSTM) layers. Furthermore, pseudo-labels generated from the training dataset using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm serve as conditional inputs to the CVAE. During training, we adopt a jointly optimized loss function that combines the CVAE loss and classification loss to enhance model performance. Anomalies are subsequently detected based on the classification outputs using a percentile-based threshold. We evaluate our method on four benchmark datasets, and the experimental results demonstrate that it surpasses the best baseline by 2.95% in terms of the average F1 score.

Time series data are widely present in the operation of Cyber-Physical Systems (CPSs), such as network traffic, sensor measurements, and other real-time data streams. Anomaly detection is a critical task in CPS time series analysis, requiring models to effectively extract features that distinguish anomalies, thereby improving system reliability and maintainability. In this study, we propose an unsupervised anomaly detection method based on sparse attention mechanism, which learns to highlight anomalous deviations from normal temporal associations. The method employs Transformer architecture with sparse attention implemented via BigBird, which effectively captures long-term dependencies while reducing computational complexity. In the preprocessing stage, a One-Dimensional Convolutional Neural Network (1D-CNN) is employed to embed the raw time series into a more expressive feature space. During the anomaly detection stage, association discrepancies are utilized to assess the degree of abnormality, combined with the Peak Over Threshold (POT)-based dynamic thresholding method for anomaly identification. Experimental results on four benchmark datasets for unsupervised time series anomaly detection demonstrate that the proposed method improves the F1 score by 2.41% compared to the best existing baseline. These results validate the method’s effectiveness and robustness in CPS anomaly detection tasks.

This paper addresses filtering problems for uncertain Cyber-physical systems that are susceptible to replay attacks and quantization errors. Specifically, a novel random replay attack is proposed, and an attack compensation term is introduced to mitigate its impact on the system. The paper also establishes a time-discrete model of Cyber-physical systems with uncertain parameters due to logarithmic quantization errors using the Delta operator. By using the Lyapunov function and linear matrix inequalities (LMIs) approach, the sufficient conditions for the system to exhibit mean-square exponential stability and$L_{2}-L_{\infty}$performance are given. At last, a truck-trailer system as the example is shown to demonstrate the robustness and effectiveness of the proposed filter.

This paper investigates the attack detection problem for linear parameter-varying (LPV) based-model Cyber-physical system (CPS). Considering the time-varying delay, limited communication, fault signal, and the actuator cyber-attack, an H ∞ observer is constructed, so that the system can detect the attack signal. On the basis of the parameter-dependent Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, adequate criteria are provided that ensure the system satisfies the asymptotic stability and H ∞ performance. Moreover, the infinite-dimensional feasibility criteria are converted to a finite-dimensional set of LMIs by using the basic functions and grid technology. Finally, a simulated example verifies the validity of the offered attack detection method.

In this paper, the H−/H∞detection for faults and attacks in a Cyber-physical system (CPS) is studied. The complex network environment with random delay, limited communication, actuator cyber attack and sensor cyber attack is considered. And the above system with fault and attack coexisting is discretized by delta operator in high-speed sampling. A set of H−/H∞observers is constructed, which enables the system to detect the possible fault signal and attack signal respectively and quickly. By using Lyapunov-Krasovskii functional and linear matrix inequalities approach, the sufficient conditions for the system to have asymptotic stability and H−/H∞performance are given. The feasibility and effectiveness of the proposed method are analyzed through several simulation examples.

In this paper, the problem of multi-sensor H∞filter for networked control systems with unknown communication delays is investigated. A filter for the unknown communication delays system is developed to guarantee the exponentially mean-square stability of the closed-loop system provided its equivalent robust filter is designed. The measured output is prone to sensor saturation which has sector-nonlinearities capability to measure the physical plant. The unknown communication delays are considered in the sensor to the controller link. Given the limitations in communication delays, a filtering scheme is designed via linear matrix inequalities (LMIs) and Lyapunov stability theory. A simulation result is given to prove the effectiveness of the proposed method.

A fault detection filter for uncertain delta operator systems based on T-S fuzzy model is designed. The phenomena of limited communication, packet dropouts, time delay and the uncertainty in the system are considered simultaneously in filter design. Then, by constructing the Lyapunov functional in delta domain, sufficient conditions for the augmented system with asymptotical stability and H∞performance are proposed. Furthermore, the desired filter parameters can be obtained via linear matrix inequalities (LMIs). Finally, simulation results certify the effectiveness of the presented method.

In this paper, the fault detection problem for a multi-packet transmission network control system with limited communication and random delay is studied. The communication sequence method is introduced to deal with the limited communication problems in the system, and a multi-packet transmission is equivalent to a Markov jump process. A fault detection filter based on delta domain is established for the system model to generate the residual signal. The residual and fault signals are further used to generate the residual error so that the fault signal can be detected intuitively. Through linear matrix inequality (LMI) method and Lyapunov-Krasinskii stability theory, the designed H∞fault detection filter's stability conditions are gained. Finally, a numerical simulation example is shown to demonstrate the availability of the proposed method.

This paper investigates the design of H2/H∞filter for networked system with multi-channel packet loss, delay and disorder in the way of delta operator. In every different channel, the filter is described by a two-state Markov chain. The filtering error system is modeled by a Markov jump system with multiple modes. Sufficient conditions for the stochastic stable filtering error system are proposed by Lyapunov functional approach. We get the parameters of the H2/H∞filter by linear matrix inequalities (LMIs). The designed filter guarantees a prescribed performance index. Number examples illustrate the feasibility of the proposed method.

This paper is concerned with the problem of H∞ filtering for uncertain delta operator systems with random delays and packet dropout. The discussed networked control systems are modeled as parameter uncertain systems with stochastic packet dropout, and the random delays are described by a Markov stochastic process. Sufficient conditions for the asymptotical stability of filtering error systems with H∞ performance are proposed by Lyapunov functional approach in delta domain. The parameterization expression of the designed filter is obtained in terms of linear matrix inequalities. A numerical example shows the effectiveness of the presented method.

This paper is concerned with the problem of H∞ filtering for networked control systems. A Bernoulli distributed is used to represent random time-delays and a switched sequence to illustrate limited communication in the considered system. Sufficient conditions that make the filtering error system to be exponentially stable with H∞performance, are proposed in terms of linear matrix inequalities (LMI) and Lya-punov-Krasovskii functional in delta domain. The parameters of the designed H∞filter are also developed. A numerical example is provided to show the effectiveness of the presented method.

In this paper, the problem of H∞ filtering for networked control systems using delta operator is investigated, which includes two-channel packet dropouts and mixed random delays. Random communication packet dropouts exist in both channels from sensors to controllers and from controllers to actuators. They are represented by two independent Bernoulli distributed white sequences. The mixed random time-delays consist of network induced time delay and discrete infinite distributed delays. A networked-based model is considered with a Markov stochastic process and the H∞filtering error system is constructed by using Lyapunov-Krasovskii functional in delta domain. A sufficient condition for stochastic stability of the filtering error system with an H∞performance is obtained in terms of linear matrix inequalities (LMI). The explicit expression of the desired H∞filter is given. A numerical example shows the effectiveness of the proposed method.

This paper utilizes a switched systems approach to deal with the problem of fault detection for uncertain delta operator networked control systems (NCSs) with packet dropouts and time-varying delays. A fault detection filter is designed under an arbitrary switching law. The sufficient conditions that are obtained in terms of linear matrix inequalities (LMI), multiple Lyapunov functions (MLF) and average dwell-time (ADT) approach, ensure the NCSs under consideration are exponentially stable and satisfy H -infinity performance. The explicit expression of the desired filter parameters is given. The effectiveness of the proposed method is verified by a numerical example.

In this paper, the delta operator is applied to describe the networked control system with time-varying delay and random packet loss. A robust fault detection filter based on the observer is proposed to generate the residual signal, thus making the residual systems to be asymptotically stable and satisfy the H-infinity performance in delta domain. The parameters of the designed fault detection filter are obtained by linear matrix inequalities(LMIs). The numerical example is provided to verify that the proposed filter can effectively detect faults.

Considering time-delay networked control systems with packet dropout and limited communication, the fault detection is studied via delta operator. Depicting the model of data losses as Bernoulli distribution and exploiting limited output channels for data transmission, an H∞fault detection filter and a residual generator are developed on the basis of the state observer. Then, sufficient conditions for the residual systems to be asymptotically stable and ensure the H∞performance index are given in terms of Lyapunov functional technique and linear matrix inequalities (LMIs) approach in delta domain. The designed filter can ensure that the residual signal is sensitive to failures. Finally, the applicability of the presented method is demonstrated by a simulation example.