This letter investigates the distributed fusion estimation problem for uncertain systems, where noise statistics are unavailable. A scenario optimization framework is employed to handle model uncertainties, in which sampled uncertainty realizations are transformed into linear matrix inequality (LMI) constraints. By solving the resulting convex problems, local estimator gains are obtained, ensuring bounded mean-square error. Furthermore, an explicit upper bound for the fusion error is derived, and optimal fusion weights are determined through an LMI-based criterion. Finally, target tracking systems are provided to demonstrate the advantages and effectiveness of the proposed methods. The influence of the violation and confidence parameters on estimation accuracy and computational complexity is further analyzed.

This paper presents an innovative Central Pattern Generator (CPG)-driven framework for rehabilitation trajectory planning, which leverages biomotor control principles to achieve precise control over exoskeleton robot gait, with the capacity for real-time adjustment in response to patient feedback. We have also developed a wearer ability assessment method that facilitates the adaptive modulation of robotic assistance modes, enhancing the personalization and effectiveness of rehabilitation training by quantifying patients’ capabilities in performing rehabilitation tasks. Moreover, we introduce an advanced approach combining super-twisting algorithms with generalized momentum methods to accurately estimate external torques without additional force sensors, thereby reducing system burden and improving response speed and accuracy. These integrated technological advancements pave the way for future developments in rehabilitation robotics and offer a more efficient and personalized rehabilitation treatment plan for hemiplegic patients.

This letter is concerned with the pose estimation problem on Lie groups. In general, robots naturally move on the special Euclidean Lie groups, which provides the motivation to model the measurement uncertainty on Lie algebras and project it onto Lie groups. Then, a Lie-group-based pose estimation method under inverse covariance intersection fusion is proposed, in which the obtained estimates are more accurate than in vector spaces. Since the unknown common information shared among the measurements is taken into account, the proposed Lie-group-based pose estimation method has the advantages of higher precision and better consistency. Finally, the effectiveness of the proposed method is verified through simulations.

The coexistence of high-frequency phasor measurement units (PMUs) and conventional SCADA systems raises the challenge of heterogenous-source and multi-rate measurements which significantly degrades the performance of power system dynamic state estimation. In this work, a deep reinforcement learning (DRL) assisted robust cubature Kalman filtering (CKF) scheme is proposed to handle measurements from hybrid sources and with different time scales. In specific, a multi-rate measurement function reconstruction approach is designed with an independent discretization mechanism to lift the present limitation of requiring an integer multiple relationship of the sampling rates from multiple sources in most of existing works. Embedded with this discretization mechanism, a deep reinforcement learning assisted two-parameter linear exponential smoothing method is proposed to reconstruct the slow measurement model with online adjustable estimation parameters. A generalized correntropy loss criterion is also included in the robust CKF to counter the non-Gaussian noise and the noise distribution variation caused by the reconstruction. Comparisons results demonstrate that the proposed DRL-based robust CKF method can achieve better accuracy and robustness under various operating scenarios.

This paper addresses the problem of designing probability-guaranteed set-membership secure estimation algorithms for energy-constrained multi-sensor systems with multi-rate asynchronous samplings. An event-triggered strategy (ETS) is employed to minimize data transmission overhead while maintaining estimation accuracy by transmitting only essential data. A novel measurement model is proposed to accurately characterize the operation of the multi-sensor system under ETS, taking into account both high- and low-energy transmission (HLET) modes and random denial-of-service (DoS) attacks, which impact communication energy consumption and data security. To cope with the challenges posed by uncertain sampling periods, a new fusion estimation model is established, including a redefined fusion estimation weight matrix and the formulation of a probability-guaranteed set-membership secure fusion estimation algorithm. Furthermore, a recursive optimization algorithm based on linear matrix inequalities is utilized to determine the minimum ellipsoid of the design parameters. The effectiveness of the proposed algorithm is validated through simulation studies.

In this paper, a non-force-sensing variable admittance control approach is proposed for lower limb rehabilitation exoskeleton robots. This approach aims to provide satisfactory assistance and rehabilitation-training performance for users of such exoskeletons. Our method initiates with a novel fixed-time sliding mode observer that estimates human-machine interaction torques according to generalized momentum. This observer-based torque estimation strategy can estimate the interaction torque precisely, thereby enabling a non-force-sensing effect. Next, a variable admittance control framework is formulated for lower limb exoskeleton robots to ensure superior compliance. This framework comprises two essential components. First, a newly designed adaptive fixed-time sliding mode controller based on a class$\kappa _{\infty } $function for the inner loop, which operates without requiring prior knowledge of the upper bound of lumped perturbations and guarantees precise gait trajectory-tracking performance. Second, a variable-parameter admittance model for the outer loop, which utilizes an exponential function to dynamically adjust the admittance parameters, thereby achieving a balance between the exoskeleton’s compliance and gait-correction efficacy. Finally, both simulation and experimental results are presented and analyzed to validate the effectiveness and superiority of the proposed non-force-sensing variable admittance control approach. Specifically, simulation results demonstrate that the root-mean-square (RMS) values of the inner-loop tracking errors for the proposed method are reduced by 26.1% and 20.4% at the hip and knee joints, respectively, compared with the top-performing benchmark algorithm. Meanwhile, the precision of the outer-loop observation is improved by 21% and 18% at these joints. Experimental validation further shows reductions of 14.2% and 20.1% in the RMS inner-loop tracking errors at the hip and knee joints, respectively, versus this benchmark algorithm.Note to Practitioners—Motivated by the problem of how to realize effective control of lower limb exoskeleton robots to provide the wearers with appropriate comfort and gait-correction effect, this paper formulates an adaptive variable admittance control framework. In the inner loop of this framework, a novel gait trajectory-tracking controller using adaptive sliding mode is designed to ensure high tracking accuracy. In the outer loop, a new adaptive observer is designed to estimate the human-robot interaction torque, and an adaptive admittance model is formulated to provide appropriate compliance for the robot. The proposed strategies are experimentally validated and can be utilized in real-word applications. The work of this paper has reference significance for the development of lower limb exoskeleton technologies.

Networked systems are increasingly the target of cyberattacks that exploit vulnerabilities within digital communications, embedded hardware, and software. Arguably, the simplest class of attacks – and often the first type before launching destructive integrity attacks – are eavesdropping attacks, which aim to infer information by collecting system data and exploiting it for malicious purposes. A key technology of networked systems is state estimation, which leverages sensing and actuation data and first-principles models to enable trajectory planning, real-time monitoring, and control. However, state estimation can also be exploited by eavesdroppers to identify models and reconstruct states with the aim of, e.g., launching integrity (stealthy) attacks and inferring sensitive information. It is therefore crucial to protect disclosed system data to avoid an accurate state estimation by eavesdroppers. This survey presents a comprehensive review of the existing literature on privacy-preserving state estimation methods, while also identifying potential limitations and research gaps. Our primary focus revolves around three types of methods: cryptography, data perturbation, and transmission scheduling, with particular emphasis on Kalman-like filters. Within these categories, we delve into the concepts of homomorphic encryption and differential privacy, which have been extensively investigated in recent years in the context of privacy-preserving state estimation. Finally, we shed light on several technical and fundamental challenges surrounding current methods and propose potential directions for future research. Note to Practitioners—With the increasing openness and anonymization of the networked estimation systems, privacy concerns require to be paid more attention. The essence of the privacy-preserving approaches is to seek certain tradeoffs among privacy budget and various performance metrics, such as utility and energy. Cryptographic methods are suitable for high-performance processors because they need sufficient computation resources to generate and operate complicated secret keys. By contrast, perturbation methods can be realized faster, but the adverse impact on the legitimate systems should be limited not to violently disrupt the desired operations. In conclusion, the choice of these encryption approaches depends on practical demands. Moreover, general state-space models, which can represent most real-world dynamics, are the basis of the reviewed methods. Thus these approaches can be easily deployed to practical engineering systems to effectively guarantee their privacy, providing significant application values.

To defend the cyber–physical system (CPSs) from cyber-attacks, this work proposes an unified intrusion detection mechanism which is capable to fast hunt various types of attacks. Focusing on securing the data transmission, a novel dynamic data encryption scheme is developed and historical system data is used to dynamically update a secret key involved in the encryption. The core idea of the dynamic data encryption scheme is to establish a dynamic relationship between original data, secret key, ciphertext and its decrypted value, and in particular, this dynamic relationship will be destroyed once an attack occurs, which can be used to detect attacks. Then, based on dynamic data encryption, a unified fast attack detection method is proposed to detect different attacks, including replay, false data injection (FDI), zero-dynamics, and setpoint attacks. Extensive comparison studies are conducted by using the power system and flight control system. It is verified that the proposed method can immediately trigger the alarm as soon as attacks are launched while the conventional$\chi^{2}$detection could only capture the attacks after the estimation residual goes over the predetermined threshold. Furthermore, the proposed method does not degrade the system performance. Last but not the least, the proposed dynamic encryption scheme turns to normal operation mode as the attacks stop.

The Dijkstra algorithm is a classic path planning method, which in a discrete graph space, can start from a specified source node and find the shortest path between the source node and all other nodes in the graph. However, to the best of our knowledge, there is no effective method that achieves a function similar to that of the Dijkstra's algorithm in a continuous space. In this study, an optimal path planning algorithm called convex dissection topology (CDT)-Dijkstra is developed, which can quickly compute the global optimal path from one point to all other points in a 2D continuous space. CDT-Dijkstra is mainly divided into two stages: SetInit and GetGoal. In SetInit, the algorithm can quickly obtain the optimal CDT encoding set of all the cut lines based on the initial point Xinit. In GetGoal, the algorithm can return the global optimal path of any goal point at an extremely high speed. In this study, we propose and prove the planning principle of considering only the points on the cutlines, thus reducing the state space of the distance optimal path planning task from 2D to 1D. In addition, we propose a fast method to find the optimal path in a homogeneous class and theoretically prove the correctness of the method. Finally, by testing in a series of environments, the experimental results demonstrate that CDT-Dijkstra not only plans the optimal path from all points at once, but also has a significant advantage over advanced algorithms considering certain complex tasks.

Automatic modulation classification (AMC) is an important technology for the monitoring, management, and control of communication systems. In recent years, machine learning approaches are becoming popular to improve the effectiveness of AMC for radio signals. However, the automatic modulation open-set recognition (AMOSR) scheme that aims to identify the known modulation types and recognize the unknown modulation signals is not well studied. Therefore, in this paper, we propose a novel multi-modal marginal prototype framework for radio frequency (RF) signals (MMPRF) to improve AMOSR performance. First, MMPRF addresses the problem of simultaneous recognition of closed and open sets by partitioning the feature space in the way of one versus other and marginal restrictions. Second, we exploit the wireless signal domain knowledge to extract a series of signal-related features to enhance the AMOSR capability. In addition, we propose a GAN-based unknown sample generation strategy to allow the model to understand the unknown world. Finally, we conduct extensive experiments on several publicly available radio modulation data, and experimental results show that our proposed MMPRF outperforms the state-of-the-art AMOSR methods.

Covariance intersection (CI) fusion is one of the most popular methods for combining estimates when the correlations among local estimation errors are unknown. Considering practical communication constraints, CI fusion tends to be performed in hierarchical and sequential forms, i.e., hierarchical CI (HCI) fusion and sequential CI (SCI) fusion. However, existing HCI and SCI fusion are sensitive to some uncertainties, i.e., the hierarchy structure and the fusion order, which make their fusion performances unreliable. To solve this problem, this article proposes hierarchy-structure-independent HCI fusion and fusion-order-independent SCI fusion by analogy with batch CI fusion, which can avoid possible negative effects caused by the aforementioned uncertainties. Finally, two simulations verify the effectiveness and advantages of the proposed methods.

This article studies the distributed dimensionality reduction fusion estimation problem with communication delays for a class of cyber-physical systems (CPSs). The raw measurements are preprocessed in each sink node to obtain the local optimal estimate (LOE) of a CPS, and the compressed LOE under dimensionality reduction encounters with communication delays during the transmission. Under this case, a mathematical model with compensation strategy is proposed to characterize the dimensionality reduction and communication delays. This model also has the property of reducing the information loss caused by the dimensionality reduction and delays. Based on this model, a recursive distributed Kalman fusion estimator (DKFE) is derived by optimal weighted fusion criterion in the linear minimum variance sense. A stability condition for the DKFE, which can be easily verified by the exiting software, is derived. In addition, this condition can guarantee that the estimation error covariance matrix of the DKFE converges to the unique steady-state matrix for any initial values and, thus, the steady-state DKFE (SDKFE) is given. Note that the computational complexity of the SDKFE is much lower than that of the DKFE. Moreover, a probability selection criterion for determining the dimensionality reduction strategy is also presented to guarantee the stability of the DKFE. Two illustrative examples are given to show the advantage and effectiveness of the proposed methods.

This article is concerned with the distributed Kalman filtering problem for interconnected dynamic systems, where the local estimator of each subsystem is designed only by its own information and neighboring information. A decoupling strategy is developed to minimize the impact of interconnected terms on the estimation performance, and then the recursive and distributed Kalman filter is derived in the minimum mean-squared error sense. Moreover, by using Lyapunov criterion for linear time-varying systems, stability conditions are presented such that the designed estimator is bounded. Finally, a heavy duty vehicle platoon system is employed to show the effectiveness and advantages of the proposed methods.

This article is concerned with the distributed networked fusion estimation problems for unstable systems with limited communication capacity, where the system and measurement noises are unknown but bounded. To overcome the unboundedness of measurement information for unstable systems, it is proposed to quantize the innovations that are sent to the fusion center over bandwidth constrained channels. By using the bounded recursive optimization idea, the design problems of local stable estimators and distributed fusion criterion under the quantized innovations are converted into two different convex optimization problems that can be easily solved by the standard software. The target tracking system is employed to demonstrate the effectiveness of the proposed methods.

This paper investigates the modeling and stabilization problem for cyber-physical systems (CPSs) under time-delay attacks. First of all, the attack-induced delays are divided into multiple equilong subintervals and each subinterval is separated into a nominal part and an uncertain part. Then, the system is considered to dwell in different subsystems when the attack-induced delays fall into different subintervals. In this way, the CPS is modeled as a discrete-time switched system with norm-bounded uncertainties. Moreover, the mode-dependent controller is designed to defend the time-delay attacks and guarantee the exponential stability of the closed-loop CPS, which is switched according to the attack-induced delays and implemented combined with the packet-based control strategy. Finally, the experiments of a networked inverted pendulum control system are given to demonstrate the effectiveness of the proposed method.

This paper studies the alarm response problem of false data injection (FDI) attacks for nonlinear physical dynamical process in cyber-physical systems. Considering the real-time attack detecting, multi-sensor fusion strategy is used to enhance the reliabilty which can also potentially improve the detection speed. Multiple finite-level logarithmic quantizers are used for estimators to reduce the size of data packages containing residual message due to the limited bandwidth. Then the optimal weight for each local estimator is derived by solving a predefined convex optimal problem. By using the proposed fusion method, a more accurate evaluation threshold is obtained, which further improves the performance of alarm response. At last, a simulation example of civil aircraft is used to illustrate the effectiveness of the proposed method.

This paper is concerned with the fault detection problem of planetary gearbox in wind energy conversion systems (WECSs). An effective method based on empirical mode decomposition (EMD) and multi-scale convolutional neural network (MSCNN) is proposed. Specifically, the non-stationary vibration signals of the gearbox are decomposed by using the EMD, so that its signal-to-noise ratio (SNR) and characteristic information are improved. Then, a hierarchical convolutional neural network is applied to adaptively extract multi-scale features from the decomposed signal components. Finally, a binary classifier based on cross entropy is employed to automatically realize the classification of the obtained multi-scale features. The effectiveness and superiority of the proposed method are verified on the experiments with vibration data sets from a true WECS.

This paper investigates the leader-following consensus issue with event/self-triggered schemes under an unreliable network environment. First, we characterize network communication and control protocol update in the presence of denial-of-service (DoS) attacks. In this situation, an event-triggered communication scheme is first proposed to effectively schedule information transmission over the network possibly subject to malicious attacks. In this communication framework, synchronous and asynchronous updated strategies of control protocols are constructed to achieve leader-following consensus in the presence of DoS attacks. Moreover, to further reduce the cost induced by event detection, a self-triggered communication scheme is proposed in which the next triggering instant can be determined by computing with the most updated information. Finally, a numerical example is provided to verify the effectiveness of the proposed communication schemes and updated strategies in the unreliable network environment.

This paper studies the distributed dimensionality reduction fusion estimation problem for a class of cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. The problem is modeled under the resource constraints (i.e., bandwidth or energy) for the defender and attacker. Based on a new attack and compensation model, a recursive distributed Kalman fusion estimator (DKFE) is designed for the addressed CPSs. Though the optimization objects of the defender and attacker are opposite, the corresponding optimization problems are established based on different available information. In this case, an explicit form of suboptimal dimensionality reduction is given against DoS attacks, while an effective attack strategy is proposed for the attacker. A stability condition is derived such that the mean square error of the designed DKFE is bounded. Two illustrative examples are given to show the effectiveness of the proposed methods.

State estimation plays an essential role in the monitoring and supervision of cyber-physical systems (CPSs), and its importance has made the security and estimation performance a major concern. In this case, multisensor information fusion estimation (MIFE) provides an attractive alternative to study secure estimation problems because MIFE can potentially improve estimation accuracy and enhance reliability and robustness against attacks. From the perspective of the defender, the secure distributed Kalman fusion estimation problem is investigated in this paper for a class of CPSs under replay attacks, where each local estimate obtained by the sink node is transmitted to a remote fusion center through bandwidth constrained communication channels. A new mathematical model with compensation strategy is proposed to characterize the replay attacks and bandwidth constrains, and then a recursive distributed Kalman fusion estimator (DKFE) is designed in the linear minimum variance sense. According to different communication frameworks, two classes of data compression and compensation algorithms are developed such that the DKFEs can achieve the desired performance. Several attack-dependent and bandwidth-dependent conditions are derived such that the DKFEs are secure under replay attacks. An illustrative example is given to demonstrate the effectiveness of the proposed methods.

In this paper, we consider a periodic estimation problem in sensor networks with a shared communication channel. The transmission constraint is inevitable in a single-channel-based sensor network if the sensors are heterogeneous or deployed far away from each other. A novel stochastic competitive transmission strategy is presented to deal with the transmission constraint, such that the sensors communicate with the fusion center (FC) in a strict asynchronous manner. A periodic mixed storage strategy combing the zero-input and the hold-input mechanisms is presented to describe periodic updating of the stored information in the sensors' buffers. A recursive Kalman filtering algorithm is derived for the FC to periodically generate estimates of state variables describing an object by using a linear continuous-time stochastic model. Two simulation examples are presented to show the effectiveness of the proposed results.

This paper studies the distributed robust fusion estimation problem with stochastic and deterministic parameter uncertainties, where the covariance of the Gaussian white noise is unknown, and the covariances of the random variables in the stochastic uncertainties are in a bounded set. By using the discrete-time stochastic bounded real lemma and the matrix analysis approach, each local robust estimator is derived to guarantee an optimal estimation performance for admissible uncertainties, and then necessary and sufficient condition for the distributed robust fusion estimator is presented to obtain an optimal weighting fusion criterion. Note that the local robust estimation problem and the distributed robust fusion estimation problem are both converted into convex optimization problems, which can be easily solved by standard software packages. The advantage and effectiveness of the proposed methods are demonstrated through state monitoring for target tracking system and stirred rank reactor system.

This paper is concerned with the design of networked multi-sensor fusion estimation system (NMFES). The Kalman filtering problem is considered for the NMFES with random observation delays, packet dropouts and missing measurements caused by sensor failures. For each observation subsystem, the sensor failure phenomenon is described by a Bernoulli distributed white sequence with a known conditional probability, and the packet dropout phenomenon and randomly delayed measurements are described by multiple binary random variables. Without resorting to the augmentation technique, an optimal recursive fusion filter for NMFES is obtained in the linear minimum variance sense by using the innovation analysis method. The dimension of the designed filter is the same to the original system, which can help reduce computation costs as compared with the augmentation method. Moreover, the performance of the designed Kalman filter is dependent on the missing rates of the measurements, the upper bounds of random delays and the occurrence probabilities of delays. Finally, the effectiveness of the proposed results is demonstrated by an illustrative example.

An error-driven adaptive model-based control system, for optimizing machine or assembly plant performance and operation under normal and fault conditions, is proposed. In such complex system it is imperative to differentiate between a system failure and a sensor failure or between process noise and measurement noise. In this paper, we present a comprehensive approach based on a hierarchical, multilevel control techniques. The approach is designed to provide sensor measurement validation, associates a degree of integrity with each measurement, identifies faulty sensors, and estimates the actual system states and sensor values in spite of faulty measurements. Using Virtual Machine Model concept, the method is achieved in three steps: state prediction, fault detection & sensor measurement and system online update or correction. A combination of flexible least square algorithm and adaptive Kalman filtering method are implemented to learn and predict system behavior. The experimental results show that the proposed model and algorithms can efficiently identify faulty components, reduce noise errors injected by sensors/system and thus providing self healing. The Virtual Machine Model (VMM) architecture described in this paper has proved to have several advantages over traditional models, the proposed model allows easy application provisioning, upgrades and maintenance, it provides fault tolerance, speedy disaster recovery and high availability platform.