This article aims at investigating distributed interval estimation methods for continuous-time linear time-invariant (LTI) systems. By allying a robust observer design method and interval analysis techniques, we develop a novel two-step interval estimation method for LTI systems whose outputs are measured by a series of nodes connected via a given directed graph. First, a distributed observer formed by a group of local observers is designed via an $H_{\infty } $ approach to obtain an accurate point-valued estimation. This estimation is completed by a reliable interval-valued estimation achieved by a rigorous set-valued analysis of the estimation error dynamics. In order to further enhance the accuracy of the estimated intervals, an elimination by inconsistency technique is applied to characterize the smallest common interval containing the actual state vector of the system. Compared with the existing distributed interval observer approaches, the proposed method can effectively enhance the tightness of the estimated state intervals. Simulation results are shown to support the theoretical findings.

This paper addresses the fault detection and isolation (FDI) problem for discrete-time Lipschitz nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. A zonotopic set-membership estimation framework is proposed to robustly handle system uncertainties and bounded disturbances. First, an$H_\infty$observer is designed based on linear matrix inequality (LMI) conditions to ensure robust performance. The estimation error is bounded within a recursively propagated zonotope, where generator growth is controlled via zonotope order reduction. Second, a fault detection scheme is developed by constructing residual zonotopes and checking whether the residual lies within the associated bounding boxes. Third, to achieve fault isolation, two augmented observers are designed, respectively addressing actuator fault isolation and sensor fault isolation. For actuator fault isolation, a state-augmented observer is proposed to eliminate the influence of sensor faults in the residual. For sensor fault isolation, a disturbance-augmented observer is constructed to decouple the actuator fault effect. In both cases, zonotopic residual bounds are derived to detect and isolate the fault source. Finally, simulation results on a fuzzy nonlinear system illustrate the effectiveness and robustness of the proposed fault detection and isolation approach.

Focusing on state estimation in nonlinear time-delay systems, this article proposes a novel particle-based zonotopic hybrid filtering algorithm. First, linearization errors are bounded using zonotopes, and the overall search space is constructed via the Minkowski sum of state, noise, delay, and linearization uncertainties. This zonotopic space is then optimized using the$F$-norm to yield a compact prediction domain, completing the prefiltering stage. A particle swarm is subsequently introduced to search for the optimal estimate. To address particle degeneracy and computational cost, a boundary reflection strategy is employed to resample outliers. The optimal particle set is then transformed into a recursively updated ellipsoidal representation, providing tight bounds on the estimated states. The proposed algorithm is validated on a nonlinear bounded-noise state estimation task using experimental data from a representative battery case, demonstrating its general effectiveness and applicability.

This paper studies the asymptotic consensus tracking control problem for a class of stochastic nonlinear multiagent systems (MASs) with output constraints and unknown control gains. Firstly, the Nussbaum technique is introduced to solve the difficulty of the unknown control gains in the stochastic nonlinear MASs. Meanwhile, a$ tan$-type nonlinear mapping (NM) function is used to ensure that the output of each agent satisfies the predefined output constraints. Furthermore, the “explosion of complexity” problem caused by the traditional backstepping design methods is handled by using the command filter technique. The developed distributed adaptive asymptotic consensus tracking control strategy ensures that all the signals in the closed-loop system are bounded in probability and the consensus tracking errors of all agents converge to zero in probability. Finally, a simulation example proves the effectiveness of the proposed control strategy.Note to Practitioners—In this paper, the asymptotic consensus tracking control problem is studied for a class of the stochastic nonlinear MASs. In nature, there are many meaningful movements of multi-agents with stochastic disturbances. It is particularly challenging to achieve the asymptotic consensus tracking control problem for stochastic nonlinear MASs, which involves the unknown control gains and output constraints. Therefore, the Nussbaum technique is used to solve the difficulty of the unknown control gains, meanwhile the command filter technique is introduce to solve the “explosion of complexity” problem in the backstepping design process. Moreover, the designed control strategy and stability analysis for the studied system is based on the nonlinear mapping technique and Lyapunov method, which makes the developed methodology more engineering-oriented.

A novel sensor fault detection framework based on zonotopic set-membership estimation is proposed for autonomous underwater vehicles in the context of unknown but bounded perturbations. First, the zonotopic propagation and intersection properties are utilized to derive the prediction state set and the measurement state set. Then, two methods, namely, projection and polytopic conversion, are provided to examine whether there is an intersection between these two sets. The intersection checking could be used to ascertain the occurrence of sensor faults. To analyze the detection performance of the proposed methods, a minimum detectable fault set is introduced. Finally, pool experiments are conducted to validate the effectiveness of the proposed methods.

The idea of stacking layers is adopted to construct a deep multivariate statistical model, hierarchical canonical correlation analysis (HCCA). Its hierarchical structure is motivated form the deep network. The proposed HCCA model has the features of low computational complexity, strong correlative feature extraction, and causal interpretability. Its correlation advantages are theoretically demonstrated, then the evaluation metrics about accuracy and complexity are presented. The HCCA-based fault monitoring method is proposed for industrial processes, and the variable contributions are analyzed based on the residual statistic. The experiment results on Tennessee Eastman and real industry wastewater treatment processes show an average fault detection rate of 87.91$\%$and 99.49$\%$. It also decreases an average false alarm rate to 0.92$\%$and 0.32$\%$, respectively.

This article presents a novel physics-constrained zonotopic Kalman filter method for online capacity prediction of lithium-ion batteries. To describe capacity degradation, a state-space formulation is devised using the autoregressive model and an indirect representation of capacity. The approach consists of three steps: First, a zonotopic Kalman filter is proposed to estimate model parameters and parameter intervals. Subsequently, considering the capacity regeneration phenomenon, a physics-based constraint term is presented to optimize parameters, which updates the estimated model parameters obtained by the zonotopic Kalman filter. Finally, parameters and interval estimation are utilized to predict the future short-term capacity. The case study demonstrates the validity of our approach. Moreover, comparisons with the ellipsoid-based extended Kalman filter and predictive maintenance toolbox suggest that our approach can obtain more precise capacity prediction and tighter capacity interval results.

A novel state estimation and fault detection (FD) method with a three-stage zonotopic Kalman filter (TS-ZKF)-basedH∞augmented state observer is proposed for a time-delay system with an actuator fault. First, the time-delay system is augmented to decouple the state delay and actuator fault. Second, an observer is designed for the augmentation system by using theH∞performance index, and the interval of state estimation is obtained. Then, the size of the zonotope is minimized to further reduce the state estimation residual and to narrow the interval. The actuator fault estimation and its bounds of the original system are extracted from the augmented state estimate vector. Finally, a numerical simulation and a case on the buck–boost circuit both verify the conservatism and accuracy of the proposed algorithm.

In this work, we consider the detection of velocity sensor faults for autonomous underwater vehicles in a bounded error context. The nonlinearity of autonomous underwater vehicles is handled via a Takagi–Sugeno fuzzy technique. The fault detection is achieved by solving a zonotopic enclosure problem based on zonotopic reachability analysis. To improve fault detection performance, a novel observer structure and H$_{-}$performance index are introduced. The performance of the presented approach is analyzed utilizing a hidden fault set. Experimental examples are given to validate the effectiveness of the presented approach.

In this article, we propose a polynomial chaos expansion (PCE) approach to interval estimation for uncertain Takagi–Sugeno fuzzy systems by considering time-invariant parameter uncertainties. First, we design the observer to get the point-valued estimates, where the accuracy of interval estimation is ensured by optimizing the gain matrices of the designed observer. Second, to obtain the interval estimation results of real states, the error dynamics is split into a random process with stochastic uncertainties and a bounded process with set-based uncertainties. Different from the interval estimation methods presented in the literature, which use only zonotopic analysis for interval estimation, we use the PCE approach in conjunction with zonotopic analysis for interval estimation, where the random process is analyzed using PCE in conjunction with the zonotopic method, and the bounded process is studied using the zonotopic analysis method. Moreover, a numerical simulation is proposed, and its results illustrate that the presented approach can decrease the conservatism of interval estimation and facilitate more interval estimation accuracy compared to an advanced interval observer design approach. Finally, interval estimation is performed for a vehicle lateral dynamic model to illustrate the applicability and superiority of the presented approach.

This paper proposes a two-step interval estimation method for discrete-time Takagi-Sugeno fuzzy nonlinear systems with parameter uncertainties. First, a novel observer structure without redundant parameters is proposed to obtain point-valued estimation for the considered system. Compared with the T-NL observer structure recently presented in the literature, the proposed observer structure is more concise and can simplify the design process. To improve the estimation accuracy, an H∞ design method that can simultaneously optimize all design parameters by solving linear matrix inequalities is proposed to design the proposed observer. Second, interval estimation is achieved by zonotopic analysis on the error dynamics of the designed observer. Comparison studies show that the proposed method not only has broader application scopes but also can obtain more accurate estimation results than a state-of-the-art interval observer design method. Moreover, the proposed method is applied to a missile control system to estimate the intervals of the attack angle and pitch rate.

To ensure system reliability and maintain power supply in fault conditions, this article proposes a fault-tolerant sun-pointing controller based on physics-guided neural networks for handling sensor faults. The proposed controller gains the fault tolerance ability by learning from the behavior of the nominal controller, which integrates a physics-based model with a deep learning model to exploit implicit physical insights during the learning process. The proposed controller enhances the intrinsic interpolative nature of the pure deep learning model, thereby improving fault tolerance for unknown faults. Furthermore, a novel loss function that incorporates the physics-based model is proposed. The loss function assigns different loss terms to the fault-free and the fault datasets, facilitating accurate utilization of loss terms. Unlike traditional active fault-tolerant control schemes, the proposed method requires no explicit fault detection and diagnosis module. The effectiveness of the proposed controller is validated through hardware-in-the-loop simulations. The results indicate that the proposed controller outperforms the pure deep learning controller, as evidenced by a shorter sun-pointing convergence time and more precise angular velocity.

This article investigates the state interval estimation problem for discrete-time linear time-varying descriptor systems subject to unknown but bounded system uncertainties. We propose a zonotope-based interval estimation method in an optimization framework. First, we present a novel zonotope-based interval estimator structure, in which the estimated interval bounds of each state component have design parameters independent of those of the other state components. Then, the widths of the jointly estimated intervals enclosing every state component are simultaneously minimized by solving parallel$L_{1}$optimization problems via linear programming. Finally, a simulation study shows the effectiveness and higher accuracy of the proposed method compared with existing methods.

This article investigates the adaptive event-triggered output-feedback control problem for a class of switched stochastic nonlinear systems with actuator faults. In the existing works, the developed results on adaptive control for switched stochastic nonlinear systems are almost based on the average dwell-time method, and how to construct a desired adaptive controller in the frame of the mode-dependent average dwell time (MDADT) remains a control dilemma. By presenting a general adaptive control rule based on the MDADT, this article implements the adaptive output-feedback control for the switched stochastic system under interest. In the process of controller design, fuzzy-logic systems, a flexible approximator, are utilized to approximate the unknown nonlinear functions. The dynamic surface design approach is employed to avoid taking derivatives of the constructed virtual controls to decrease the difficulty of complex calculation greatly. Meanwhile, a switched observer is designed to estimate the unknown states. In the frame of backstepping design, an event-triggered-based adaptive output-feedback controller is constructed such that all signals existing in the closed-loop system are ultimately bounded under a class of switching signals with MDADT property. Finally, the simulation results show the validity of the proposed control strategy.

In this work, an actuator fault detection problem for discrete-time Takagi–Sugeno fuzzy systems is tackled in a bounded error context where both state disturbances and measurement noise are assumed to be unknown but bounded with known bounds. First, a peak-to-peak performance synthesis method is applied to design a robust residual generator against the considered process disturbances and measurement noise. Meanwhile, an improved zonotopic approach is proposed to compute tight adaptive thresholds for residual evaluation. Then, a reliable set-membership fault detection strategy with the aid of generated residual signals and adaptive thresholds is introduced. Finally, the viability of the proposed method is demonstrated via a numerical simulation. Then, an experimentation on a 3-D Crane system is performed to show its practicability.

This article proposes two adaptive asymptotic tracking control schemes for a class of interconnected systems with unmodeled dynamics and prescribed performance. By applying an inherent property of radial basis function (RBF) neural networks (NNs), the design difficulties aroused from the unknown interactions among subsystems and unmodeled dynamics are overcome. Then, in order to ensure that the tracking errors can be suppressed in the specified range, the constrained control problem is transformed into the stabilization problem by using an auxiliary function. Based on the adaptive backstepping method, a time-triggered controller is constructed. It is proven that under the framework of Barbalat's lemma, all the variables in the closed-loop system are bounded and the tracking errors are further ensured to converge to zero asymptotically. Furthermore, the event-triggered strategy with a variable threshold is adopted to make more precise control such that the better system performance can be obtained, which reduces the system communication burden under the condition of limited communication resources. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

This article studies the security synthesis of cyber–physical systems subject to stealthy attacks via zonotopic set theory. The set is used to quantify the effect of potential stealthy attacks on systems. Control performance and security level are characterized using$L_{\infty }$performance index and the radius of the attack-induced state set, respectively. Sufficient design conditions are given to optimize the security while guaranteeing a prescribed level of control performance. Simulation examples are conducted to demonstrate the effectiveness of the proposed method.

In this study, consensus issue for general linear continuous-time multiagent systems (MASs) in a directed network is addressed. Suppose that the neighbors’ transmitted information is impacted by a communication delay, explicit consensus criteria are, respectively, obtained for both known delay and unknown delay cases. Especially, a new protocol applying the delay information is proposed if the delay is available. Furthermore, it is proved that the influence of delay can be eliminated thoroughly if the agent dynamic is at most critically unstable or the network topology satisfies the presented criteria. Finally, two simulation paradigms are performed to clarify the practicality of the newly developed methods.

This article deals with the fault detection and isolation problems for a class of uncertain discrete-time Takagi-Sugeno (T-S) fuzzy system based on the combination of the H-infinity observer and the zonotope method (ZM). For fault detection (FD) purpose, first, a Luenberger-like H-infinity observer, which is robust to disturbance in a sense of H-infinity performance index is designed under the assumption of the feasibility of an linear matrix inequality. Second, the ZM is applied to the H-infinity observer error dynamic system such that the interval state estimation can be calculated iteratively if the system suffers from neither actuator nor sensor faults. Third, a residual is constructed and its interval estimation is also given, and furthermore, based on the residual interval estimation, an FD scheme is developed. After this, we discuss the fault isolation issue in the similar way to alarm the appearance of the exact type fault: actuator or sensor fault. It is the ZM is applied onto the Luenberger-like observer, the fault detection and isolation performances are improved greatly. Finally, a numerical simulation example is given and some comparisons are also made to the existing results to verify the effectiveness and to show the advantages of proposed method.

In this work, the problem of event-based fault detection is addressed for unmanned surface vehicles (USVs) under denial-of-service (DoS) jamming attacks. A fault detection filter (FDF) is deployed to generate residual for USV systems with external disturbance and system faults. A resilient event-triggered mechanism is implemented to reduce the bandwidth occupation of communication network and energy consumption of USV system as well as mitigating the influence of DoS attacks. Based on the established framework, a switched residual system is constructed and a criterion is deduced to ensure the exponential stability and weighted$H_{\infty }$performance of residual system via piecewise Lyapunov functional approach. The FDF and resilient event-triggered mechanism are co-designed. Simulation results are provided to testify the efficient performance of the devised resilient event-triggered fault detection method.

A novel block-level perceptual image watermarking framework is proposed in this study, including tri-directional correlation and a block-level just noticeable difference (JND) model. Specifically, the difference in the discrete cosine transform (DCT) coefficients of two blocks is calculated based on three directions in the neighborhood, called the tri-directional correlation (TriDC). Additionally, the representative alternating current (AC) coefficients along horizontal, vertical, and diagonal directions, which can describe structural patterns, are projected and merged for TriDC differences. Then, the difference of the DCT coefficient is modulated to a predefined zone depending on the JND-based offset. Finally, the extent of the watermarked AC coefficients is determined with perceptual JND adjustment. The experimental results demonstrate that the proposed scheme can protect most common image processing attacks; and has better robustness compared with recent zone modulation watermarking schemes and traditional watermarking methods.

This article deals with the problem of fault detection for discrete-time Lipschitz nonlinear systems subject to a class of restricted frequency-domain specifications. We present a novel observer structure with more design parameters, which can be applied to enhance the observer performance. The performances of fault sensitivity and disturbance robustness are characterized using finite-frequency$H_{-}$and$H_{\infty }$indices, respectively. Less restrictive design conditions are obtained based on a reformulated Lipschitz property. Moreover, to detect faults timely, a novel dynamic threshold is synthesized based on zonotopic set-membership techniques. Simulation examples are conducted to demonstrate the viability and validity of the presented method.

In this paper, the consensus achievement for first-order multi-agent systems is researched over undirected graph. Suppose that the system is unstable and exactly knows the communication delay that affects the actually transmitted information, consensus gain in the protocol is designed with the delay information. Then, conditions are obtained to guarantee consensus for any large yet bounded communication delay. At the end of the article, an example is given to demonstrate the validity of the conclusion.

This paper presents a novel interval fault estimation approach by using zonotope technique for discrete-time linear parameter-varying systems in the presence of bounded parametric uncertainties, measured perturbation, and system disturbance. First, an augmented descriptor system is generated by using augmentation technique. Thus, the problem of interval fault estimation is transformed into the interval augmented state estimation. Then, an outer approximation of the new augmented state estimation domain is computed by using zonotope method. A zonotope should be consistent with the given outputs, perturbation, disturbance, and parametric uncertainties. Besides, it is minimized at each sampled time via an analytic formulation. Finally, a vehicle lateral dynamic nonlinear model is utilized to show the feasibility and effectiveness of the proposed zonotopic fault estimation technique.

This paper proposes a novel interval observer design method for discrete-time Takagi-Sugeno fuzzy systems with parametric uncertainty, disturbances, and measurement noise. We present a new structure of interval observer with more design parameters, which can be used to broaden the application scope of interval observer design. For improving the accuracy of interval estimation, an L∞norm-based approach is used in the design of interval observer to attenuate the effect of the unknown disturbances, noise, and parametric uncertainty. Furthermore, the design conditions are formulated into a set of linear matrix inequalities, which can be efficiently solved. Numerical simulations are given to illustrate the effectiveness of the proposed method.