This article studies the distributed observer-based event-triggered (ET) optimal control problem for nonlinear multiagent systems (NMASs) over jointly connected digraphs. Since agents cannot get the leader under jointly connected digraphs, a distributed observer is constructed to estimate the unknown leader. At the same time, to enhance the efficiency of communication resources utilization between agents, an ET communication mechanism is developed to schedule the agent communication. Subsequently, neural networks (NNs) are adopted to handle the unknown nonlinearities, and an NN state observer is established to reconstruct the unmeasurable states. By utilizing the backstepping technique and adaptive dynamic programming theory, a distributed observer-based ET optimal control algorithm is developed, in which a critic network is designed with a proposed weight updating law to estimate the cost function. It is proven that the presented ET optimal control approach ensures that all signals of NMASs are uniformly ultimately bounded (UUB), and the cost function is minimized. At last, the theoretical results are applied to marine surface vehicles (MSVs) to validate the efficiency of the developed optimal control strategy.

Accurate and physically interpretable wind power forecasting (WPF) is crucial for ensuring the reliable operation of power grid systems. Wind turbines have operational characteristics significantly influenced by complex environmental factors, such as wind speed fluctuations and intermittency, posing challenges for precise wind power modeling. Although deep learning models have become a promising data-driven solution in WPF, their common “closed-box” nature makes it difficult to balance forecast accuracy with the rationality of physical mechanisms. Therefore, based on the neural basis expansion analysis (NBEATSx) network architecture, this article proposes a multistep WPF method, named physics-informed adaptive-weight NBEATSx. This method realizes the deep integration of physical prior knowledge and data-driven models, providing a novel technical path for solving the joint optimization problem of accuracy and interpretability in WPF. The operational constraints of wind turbines, such as cut-in, rated, cut-out wind speeds, and rated power, are explicitly embedded into the network structure. A dynamic trainable weighting mechanism is leveraged for stack outputs, instead of the traditional aggregation strategy of direct summation. The experimental results based on a dataset of a 2-MW wind turbine show that the proposed method is significantly superior to the benchmark models and NBEATSx variants in terms of forecast accuracy and robustness.

Practically inaccessible precise probability distribution for disturbance poses significant challenges to stochastic active fault detection (AFD) in achieving satisfactory detection accuracy. In this paper, without making specific distribution assumption on disturbance, a distributionally robust data-driven approach is proposed to AFD for stochastic linear dynamic systems. On the basis of constructing a data-driven stable kernel representation-based residual generator, the distributional uncertainty of disturbance is characterized by the mean-covariance-based ambiguity set of residual both for the fault-free and faulty cases. To minimize the energy of input while guarantee tolerable false alarm rate (FAR) and missed detection rate (MDR), the design of AFD system is formulated as an optimization problem subject to distributionally robust chance constraints (DRCCs). By bridging the DRCCs with deterministic constraints in the probabilistic context, the targeting optimization problem is then converted into a generalized eigenvalue-eigenvector problem, by solving which analytical solutions of the input and separating hyperplane for online detection are derived. Hence, the developed AFD system can not only ensure the FAR and MDR criteria not exceeding predefined levels, but also improve the robustness of the system against distributional uncertainties of disturbance. Besides, a batch-wise realization algorithm is developed for continuous online fault detection. A simulation study based on a four-tank system is demonstrated to validate the effectiveness of the proposed approach.

In this article, we investigate the problem of distributed fault detection for a class of cyber-physical system whose physical layer consists of numerous subsystems, each modeled as a linear discrete-time system. Considering the influence of process noise and measurement noise, the state estimation of each subsystem is completed using a distributed Kalman filter (DKF), in which the one-step prediction is corrected not only by the local innovation but also by the measurement errors of the neighbors at the previous step. Leveraging the DKF, a local residual generator is designed for each subsystem. The parameters of the DKF are then determined by minimizing the estimation error and the upper bound of its covariance in the fault-free case, which ensures the robustness of the residual. Furthermore, by utilizing the instantaneous $T^{2}$ test statistic and the sliding window-based $T^{2}$ test statistic of the residual signals, the corresponding residual evaluation function and fault detection threshold are established to facilitate fault detection for each subsystem. In the proposed fault detection scheme, each subsystem only transmits information to its neighbors, ensuring that each subsystem can detect its faults in a distributed manner. Additionally, a sufficient condition is provided to guarantee the mean square boundedness of the estimation error in the fault-free case. Finally, a power network system is employed to demonstrate the effectiveness of the proposed scheme.

This article investigates the problem of fault estimation in nonlinear uncertain manipulator systems with time-delay. A novel fault estimation scheme is proposed, which optimizes the iterative learning (IL) estimator performance using a neural network (NN)-based reinforcement learning (RL) approach. Specifically, first, with the purpose of enhancing robustness and adaptability of RL, a new adaptive exponential reward function is designed. Then, to improve the performance of fault estimation, speed and accuracy are designed as optimization objectives. Simultaneously, by leveraging the IL estimator, the NN is continuously optimized in each iteration process to mitigate the issues of gradient vanishing and explosion. Further, by incorporating the H$\mathrm{\infty }$performance index into the observer, an asymptotically convergent estimated error can be attained. Finally, numerical simulations are conducted to demonstrate the effectiveness of our method.

In this article, a distributed semi-consensus-based data-driven fault detection scheme is developed based on the process variables collected by sensor networks to ensure the safety of the large-scale dynamic processes. For our purpose, the distributed data-driven process modeling scheme is developed for dynamic systems first by considering the communication topology of the sensor networks. Then, a distributed Kalman filter-based fault detection approach is developed aiming at achieving optimal detection performance at each sensor node. Specifically, the distributed iterative learning algorithm is implemented to calculate the needed parameter matrices for Kalman filter-based residual generator offline with the aid of average consensus algorithm. It is followed by a distributed fusion of local residual signals to perform online optimal fault detection. To avoid the detection delay caused by the traditional average consensus method, the semi-consensus algorithm is developed for the first time to ensure the timely detection of potential faults. A case study on the multiphase flow facility process is given in the end to demonstrate the proposed method.

In this article, an$\mathit {H_{i}/H_{\infty }}$optimization approach to fault detection (FD) is proposed for high-speed train traction motor under complex environment and working conditions. Considering the inherent system nonlinearity, the dynamics of the traction motor are firstly described by a Takagi–Sugeno (T-S) fuzzy model subject to$\mathit {l}_{2}$norm-bounded disturbances and additive faults. Then, a T–S fuzzy observer-based fault detection filter (FDF) is proposed as a residual generator, and, in order to enhance simultaneously the robustness of residual to disturbances and the sensitivity to fault, the design of the FDF is formulated as the maximization problem of finite horizon$\mathit {H_{-}/{H}_{\infty }}$and$\mathit {H_{\infty }/{H}_{\infty }}$indices. Moreover, an$\mathit {H_{i}/H_{\infty }}$optimization approach is developed to find a solution of the T–S fuzzy FDF, which can achieve an optimal tradeoff between the sensitivity to fault and the robustness to disturbances. It shows that the optimal solution is not unique, and the feasible solutions including static and dynamic postfilter are obtained by recursive computing of Riccati equations. Finally, a case study of traction motor in CRH5 EMUs is presented to exhibit the efficacy of the developed FD approach.

Anomaly monitoring of key performance indicators (KPIs) is the core to guarantee the stable operation of wastewater treatment process (WWTP). One issue that has not been considered in WWTP is that KPIs can only be sporadically sampled, which is not conductive to the real-time monitoring. To solve this problem, a trend feature-based anomaly monitoring method is proposed. First, a fused multistep prediction strategy is designed to establish the nonlinear relationship between infrequent KPIs and the variables, with adaptive algorithm updating the parameters. Second, an autoregressive model is used to represent the variation trends, and a convex optimization problem, with the balance of small residuals and stable trends, is solved to extract trend features of KPIs. Third, the monitoring index, based on the$\ell _{2}$-norm of the trend features, is utilized to identify the abnormal KPIs. The operating data from WWTP are applied to demonstrate the effectiveness of the proposed monitoring method.

In this article, an integrated design diagram for a stable kernel representation (SKR)-based data-driven fault detection (FD) system and performance criteria is proposed for stochastic dynamic systems in the probabilistic sense. A new distributionally robust FD system is developed using input and output data in the absence of a system model and perfect probability distributions for noises and random faults. To be specific, an SKR-based data-driven primary residual generator is first constructed. By introducing the so-called mean-covariance based ambiguity sets, families of probability distributions of the primary residual in fault-free and the concerned multiple faulty cases are characterized. The FD system design is then formulated as a distributionally robust optimization problem in the sense of minimizing the missed detection rate (MDR) with a predefined upper bound of false alarm rate (FAR). With the aid of worst-case conditional value-at-risk, a matrix-valued distribution independent solution to the targeting FD problem is derived without posing specific distribution assumptions. The developed FD system is, thus, robust against the distributional uncertainties of noises and random faults. Simultaneously, a tighter upper bound of MDR for an identical FAR criterion is achieved in comparison with the vector-valued distributionally robust FD method. An experimental study on a laboratory setup of a three-tank system shows the applicability of the proposed method.

This article is concerned with the development of a new event-triggered parity space fault detection (FD) scheme. A linear discrete-time system model with varying sampling periods is presented for handling the problem of event-triggered FD and a new parity relation is established. Based on this, an event-triggered residual generator is constructed and the generated residual is completely decoupled from event-triggered transmission error. The design of the parity matrix is formulated into an optimization problem and an optimal solution of the parity matrix is obtained by using singular value decomposition. The issue of residual evaluation is also considered in the event-triggering implementation. The novelties of this article are twofold. First, a new event-triggered parity relation is obtained and the parity space-based residual signal achieves complete decoupling with the event-triggered transmission error. Second, the calculation of the parity matrix is independent of event parameters. So the design of the parity space-based residual generator and event generator can be carried out independently. Finally, a simulation example is considered to demonstrate the effectiveness of the proposed method.

In this paper, a novel robust fault detection (FD) approach called parity space vector machine (PSVM) is proposed for linear discrete-time systems. Aiming to achieve a tradeoff between false alarm rate (FAR) and FD rate (FDR) simultaneously, we focus our study on an integrated design of parity space-based FD in the context of residual generation and residual evaluation. Without a prior knowledge of the distribution of the unknown inputs, we propose to construct a PSVM model and formulate the underlying FD problem as a distribution-free Bayes optimal classifier, where the FAR and FDR indicate the worst-case classification accuracies of future residuals for the fault free case and faulty case. Then a bank of parity space vectors and corresponding thresholds can be designed integratedly by applying the techniques of the minimum error minimax probability machine and, at the same time, an optimal tradeoff between FAR and FDR is achieved. Finally, the effectiveness of the proposed approach is demonstrated on a longitudinal control system of unmanned aerial vehicle and further comparison with a traditional parity space-based FD is also addressed.

Near-infrared (NIR) spectroscopy plays a critical role in online analysis of difficult-to-measure properties of petrochemicals. In industrial applications, a calibration model among NIR spectra and properties must be established. However, it is a challenge to obtain a precision NIR model in the majority of petrochemical processes since industrial data present strong non-Gaussian and uncertainty characteristics. To deal with these problems, in the present work a probabilistic regression modeling method based on a biased minimax probability machine (BMPM) is proposed, without assuming any specific distributions for the data, in this article. In addition, a multiple locally weighted updating approach with a new supervised similarity distance is introduced to cope with process changes. The greatest advantage of the proposed approach is that it has superior capability in dealing with uncertainties and variations. The effectiveness of the method is illustrated through its application in an actual gasoline blending process and a simulated fermentation process.

In this article, an optimal data-driven approach is proposed to deal with the problem of distribution independent fault detection (FD) for stochastic linear discrete-time systems. For this purpose, an observer-based residual generator is first constructed using process input and output data. Without exact probability distributions for noises and faults, the so-called confidence sets are constituted in terms of mean and covariance matrix to characterize residual in fault-free and faulty cases. On this basis, a stochastic optimization FD problem is formulated, which allows an integrated design of residual evaluation function and threshold toward maximizing fault detection rate (FDR) for an acceptable false alarm rate (FAR) in the worst-case setting. Furthermore, a data-driven formulation of the underlying FD problem is studied, wherein the estimation uncertainties caused by the deviation of empirical mean and covariance matrix from their real values are concerned. The robustness of the FD system is investigated in the probabilistic context. Confidence levels of the obtained FAR and FDR are achieved quantitatively. The main advantages of the proposed FD approach lie in its independence of probability distributions for noises and faults, the robustness to the estimation uncertainties and the quantitative probabilistic evaluation to the confidence levels of FAR and FDR. A case study on a three-tank system illustrates the effectiveness of the demonstrated approach.

In this paper, we focus our study on analysis of fault diagnosis performance for satellite attitude control systems subject to l2-norm-bounded process disturbances and measurement noises, which concerns with fault detectability and fault isolability. For an observer-based fault detection (FD), a major concern is to answer if the choice of a threshold satisfies an acceptable trade-off between fault detection rate (FDR) and false alarm rate (FAR). The smaller a threshold is, the better is the FDR, but the poorer is the FAR. In addition to this, knowledge of fault isolability is useful for answering how difficult it is to isolate a fault from another one. The main contributions of this paper are the probabilistic performance evaluation of the FD system in the context of FAR and a contribution analysis-based method of fault isolation. First, an extended Hi/H∞optimization-based FD scheme is applied to the satellite attitude control systems and a recursive algorithm is presented to the implementation of online FD. Second, regarding the uncertain statistical characteristics of the unknown inputs, randomized algorithms are developed to verify the achievable FAR for a prescribed given threshold. Especially, without knowing the l2-norm boundedness of the unknown inputs, a probabilistic estimation of worst case threshold is also obtained to guarantee an acceptable level of FAR. Third, a contribution analysis-based method of fault isolation is proposed for satellite attitude control systems. Finally, the effectiveness of the proposed algorithms is verified through a satellite attitude control system.

This paper deals with the fault detection filter design problem for linear time invariant time-delay systems with unknown input. The core of our study is to a) take the behavior of delayed state and measurement into consideration when the observer-based fault detection filter is constructed; b) solve the formulated fault detection filter design problem by combining of using the left eigenstructure assignment approach and H/sub /spl infin// optimization technique. Through a suitable choice of the filter gain matrices and residual weighting matrix, the residual can be completely decoupled from the delay-free unknown input, while the influence of the delayed unknown input on residual is minimized in the sense of H/sub /spl infin// norm. Numerical simulation is used to illustrate the efficiency of the proposed method.