In this paper, a novel barrier function-based adaptive controller is proposed for an n-link flexible-joint (FJ) robotic system to accomplish the task of accurate trajectory tracking control in the presence of system model uncertainties, unknown external disturbances, and nonsmooth nonlinear inputs. Firstly, the traditional n-link robot system expressed by the Lagrangian dynamic function is remodeled as a fourth-order fully-actuated system by introducing the fully-actuated system theory. It results that the problems of complex controller design and computational explosion triggered by backstepping control method are solved successfully. Furthermore, under relaxed assumptions on system uncertainties, i.e., the upper boundary of the lumped system uncertainties is unknown, a barrier function-based adaptive sliding mode controller is designed, then the trajectory tracking errors of system are ensured to converge into a neighborhood of zero in the presence of nonsmooth nonlinear control inputs. Particularly, the convergence errors independent of the upper boundary of system uncertainties can be determined in advance based on practical engineering application. Meanwhile, the closed-loop stability of the FJ robot system under the proposed adaptive controller is rigorously proved based on the Lyapunov stability theorem. Finally, the superior performance of the proposed control approach is demonstrated by the simulation results of a two-link FJ robot system and a comparison study.

In this paper, we focus on the effective approximation ($N\to\infty$ then $\epsilon\to 0$) of stochastic interacting particle systems with fast regime-switching networks on digraph measures (DGMs). DGMs provide a robust approach to capturing sparse, intermediate, and dense network or graph interactions in the mean field, extending beyond traditional methods like graphons. The model can be used to simulate a vehicle's trajectory under different traffic signal states. The main goals are to derive the simplified system (9) as $\epsilon\to 0$ and to capture a class of mean-field limits under the assumption that the switching process tends to a stationary state as time evolutions. Using the martingale method and validating the continuity of the underlying graph heterogeneity, we establish the convergence in law of (1) to a probability measure $\bar{\mu}_t$, which satisfies semi-linear Vlasov-Fokker-Planck equation.

This paper focuses on studying an adaptive neural network predefined-time fault-tolerant control problem for high-order nonlinear systems. The considered plants include external disturbances, unknown nonlinear functions, quantized input signals, actuator, and sensor faults. Radial basis function neural networks (RBF NNs) are employed to address uncertainty in nonlinear systems, simplifying the difficulty of designing the state variable functions by using their structural properties. By employing the backstepping approach combined with the predefined-time Lyapunov stability theory, an adaptive predefined-time fault-tolerant controller is presented. In particular, a novel predefined-time filter is applied to avoid repeated differentiation of virtual control functions. It is proven that the proposed control strategy ensures that all signals in the closed-loop systems remain bounded and the tracking error converges within a predefined settling time in the presence of sensor and actuator faults. Ultimately, numerical and practical examples are provided to validate the effectiveness of the presented control strategy.

In this paper, a model-free inverse reinforcement learning (RL) algorithm based on static output feedback control (OPFB) is proposed to solve the problem of expert trajectory imitation in discrete-time (DT) systems with antagonistic disturbance. In detail, based on the expert-learner framework, the learner uses only the expert and its own input-output data to reconstruct an unknown cost function with antagonistic disturbance, producing the same control gain as the expert to thereby imitate the expert’s trajectory. It is worth noting that the model-free off-policy inverse RL algorithm for static OPFB control proposed in this paper adopts single-loop form and does not require knowledge of system dynamics. At the same time, the convergence of the algorithm is analyzed in detail. The results show that the probing noise added to maintain the excitation condition does not affect the algorithm, and the cost function is not unique when the algorithm converges to the optimal value. Finally, the effectiveness of the algorithm is verified by taking the F-16 aircraft autopilot as an example.

This paper is dedicated to studying the event-based consensus tracking control problem of leader-following multi-agent systems under hybrid attacks. First, different from conventional eventtriggered mechanisms, a dynamic memory event-triggered mechanism is designed to decrease the frequency of communication between agents, which relies on historical error data and instantaneous error data and considers the cumulative impact of historical data on the system. Then, an improved asymmetric Lyapunov-Krasovskii function is presented. Based on the integral inequality and Lyapunov theorem, some stability conditions of multi-agent systems under hybrid attacks are obtained by solving linear matrix inequality. Finally, two simulation examples are given to verify the feasibility and superiority of the proposed method.

The AB/BA trial design is the simplest crossover design for comparing the effects of two treatments. It is widely applied in practice because it enables the direct comparison of two treatments for each individual while effectively controlling for inter-subject variability. However, unmeasured carryover effects can compromise the validity of the results, and this paper proposes the equivalence evaluation method for two treatment effects that account for carryover effects. A novel nonparametric statistical method is developed to quantify the treatment effect and the carryover effect, namely the win probability that a subject receiving one treatment or sequence achieves a better outcome (or "wins" against) compared to a subject receiving the other treatment or sequence. Five simultaneous confidence intervals for these two win probabilities are considered to evaluate the effectiveness of the two treatments, including those based on the normal distribution, t distribution, adjusted t distribution, logit transformation, and inverse-hyperbolic-sine transformation. Simulation results demonstrate that confidence interval procedures based on logit and inverse hyperbolic sine transformations perform well in terms of coverage and average interval width, even for small sample sizes, and hence are recommended for practical applications. Two AB/BA crossover trials involving continuous and ordinal outcomes are utilized to illustrate the proposed methods.

Multi-dimensional arrays are referred to as tensors. Tensor-valued predictors are commonly encountered in modern biomedical applications, such as electroencephalogram (EEG), magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion-weighted MRI, and longitudinal health data. In survival analysis, it is both important and challenging to integrate clinically relevant information, such as gender, age, and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes. Most existing higher-order sufficient dimension reduction regressions for matrix- or array-valued data focus solely on tensor data, often neglecting established clinical covariates that are readily available and known to have predictive value. Based on the idea of Folded-Minimum Average Variance Estimation (Folded-MAVE: Xue and Yin, 2014), we propose a new method, Partial Dimension Folded-MAVE (PF-MAVE), to address regression mean functions with tensor-valued covariates while simultaneously incorporating clinical covariates, which are typically categorical variables. Theorems and simulation studies demonstrate the importance of incorporating these categorical clinical predictors. A survival analysis of a longitudinal study of primary biliary cirrhosis (PBC) data is included for illustration of our method.

Within the sufficient dimension reduction framework, research on nonignorable missing data remains relatively scarce, primarily due to the associated identifiability issues. This paper considers the problem of sufficient dimension reduction when the response is subject to nonignorable missingness. By adopting a flexible semiparametric missingness mechanism to ensure identifiability, we construct three classes of estimating equations based on inverse probability weighting, regression imputation and augmented inverse probability weighting. The novel aspects of our methods also include the incorporation of sufficient dimension reduction techniques in the implementation of these estimating equations to mitigate the high-dimensional effect, and the construction of the estimator for the conditional expectation of the estimating functions given both the covariates and the missingness indicator. We prove that the resulting three estimators are asymptotically normally distributed. Comprehensive simulation studies are conducted to assess the finite-sample performance of our methods, and an application to PM2.5 concentration data is also presented.

This paper proposes a novel Relaxed Total Generalized Variation (RTGV) model for image restoration under Gamma noise, which integrates a convex fidelity term and an RTGV regularization term. The convex fidelity term is designed to balance the regularization intensity between dark and bright regions, while the RTGV regularization term aims to reduce computational complexity in contrast to the traditional Total Generalized Variation (TGV) regularization. The Alternating Direction Multiplier Method (ADMM) is employed to solve the proposed model, and the regularization parameter is adaptively updated at each iteration by incorporating the Generalized Cross Validation (GCV) technique. Numerical experiments demonstrate that the proposed approach outperforms traditional methods in terms of both restoration quality and computational efficiency.

This paper investigates the exponential synchronization problem for a class of nonlinear directed networks with time delays and general unknown transition rates. The considered model incorporates time-delays, directed topological structures, and uncertain transition rates, where the transition rates can be either completely unknown or only partially estimated. A distributed controller is designed within a novel pull-based event-triggered sampling framework, ensuring that the closed-loop system achieves exponential synchronization while significantly reducing the update frequencies of sensors and controllers with performance guarantees. By estimating a positive lower bound for event intervals, the proposed event-triggered schemes effectively exclude Zeno behavior. Event-triggered parameters are systematically designed based on the feasibility conditions of associated matrix inequalities. Numerical simulations are provided to validate the theoretical findings, demonstrating the effectiveness and practical applicability of the proposed approach.

Attack defense and privacy protection are critical for secure consensus control of multiagent systems (MASs). While prior studies have addressed these threats individually or jointly, this paper proposes a novel encoding-decoding-based consensus control strategy for discrete-time MASs under denial-of-service (DoS) attacks, leveraging a buffer-based switching mechanism and dynamic quantization to ensure both information availability and confidentiality. Based on the uniform quantizer, we first perform an encoding-decoding-based algorithm with a dynamic quantization factor. Thus, the information to be transferred to neighbors is encoded by the encoder and the received data from neighbors is decoded by the decoder, which can prevent information from being directly exposed. Furthermore, the problem of information interruption caused by DoS attacks can be solved by introducing a buffer that can save the latest state information when DoS attacks occur. A distributed controller with a switching mechanism is proposed by employing the stored and decoded state information. The linear matrix inequality (LMI) and the Lyapunov function are also used to get the switched control gains and sufficient conditions of the system’s stability. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the developed control strategy.

Drawing on industry convergence theory, this study develops an evaluation index system to quantify cultural-tourism integration. It applies the entropy weight method and a multiple-linear comprehensive index approach to measure both the levels and the spatiotemporal dynamics of culture-tourism integration in 31 Chinese provinces (municipalities and autonomous regions) from 2010 to 2022. A staggered Difference-in-Differences model is then used to estimate the driving effects of integration policies and to uncover the pathways. The results show a steady upward trend in integration, marked regional disparities consistent with a Matthew effect, and a significant overall policy effect on integration levels, with notable heterogeneity across regions. Pathways analysis indicates that policies primarily enhance resource and market integration and that the pathways of policies also influence differ by region. This study advances understanding of how policy drive cultural-tourism integration and provides guidance for promoting high-quality, balanced regional development of culture-tourism.

The operation of a microgrid (MG) system with multiple nodes not only needs to solve the optimization problem of economic dispatch but also has to consider the optimization goals of the safe and environmentally friendly operation. Therefore, the purpose of each node with renewable resources is to collaborate to achieve the optimization of multiple objectives. In this paper we shall design a deep reinforcement learning (DRL) algorithm to perform the multi-objective optimization which can handle continuous action space and determine the specific output power of each device. Unlike the existing algorithms that learn policies with holistic reward signals, the proposed algorithm decomposes the reward into multiple parts and trains multiple critic networks for sub-objectives to get the Pareto optimal solutions. The proposal of single-actor multi-critic architecture not only can avoid task-specific local optimal policies but also does not need to set weight values. The effectiveness of the algorithm is verified by case studies on a modified IEEE-30 bus system and a modified IEEE-118 bus system. After training, the DRL agent can adapt to the high uncertainty of the photovoltaics and exploit the capacity of battery energy storage stations safely, which is more practical in a real system.

The precision matrix is an essential tool for studying the conditional relationships among large groups of variables. This paper develops a Distributed Refitted Cross-Validation (DRCV) procedure to estimate a large precision matrix in distributed settings, whose communication complexity is proportional to the number of non-zero entries in the precision matrix. The proposed method designs two rounds of communication. The first round selects non-zero positions of the precision matrix via node-wise regressions, while the second round constructs a global-debiased estimation for the precision matrix. To address the overfitting issue regarding this inference-after-selection strategy, the proposed method splits observations at each machine into two parts, one for position selection and the other for parameter estimation. DRCV achieves the global estimation consistency with respect to the total sample size under certain conditions and allows the number of machines in distributed settings to increase as the total sample size increases. Numerical studies on simulated datasets and a real high-frequency stock dataset show that DRCV has good estimation performance and a low communication cost.

This paper investigates the Pareto-Nash equilibria for multicriteria normal games and multicriteria networked evolutionary games (MCNEGs) using the semi-tensor product of matrices. Firstly, an easy-to-verify matrix criterion is provided to calculate the Pareto-Nash equilibria of multicriteria normal games. Secondly, an algorithm is established to convert the dynamics of an MCNEG into an algebraic form. Thirdly, based on the algebraic form, a necessary and sufficient condition is presented to verify whether a profile is a Pareto-Nash equilibrium, and the asymptotic stability of an MCNEG to the Pareto-Nash equilibrium set is studied. Finally, an illustrative example is given to demonstrate the correctness of the new results.

In this paper, we analyz the uniform exponential stability of a semi-discrete scheme for a coupled system derived from a one-dimensional wave equation, which is subject to boundary feedback with noncollocated observation. This system was previously studied in [IEEE TAC, 52(2007),371-377], where the Riesz basis methodology was utilized. However, it is critical to acknowledge that the Riesz basis approach is inadequate for addressing the uniform exponential stability of discrete schemes. In contrast, the Lyapunov function offers a more straightforward alternative approach. Therefore, we first establish exponential stability by constructing a global Lyapunov function for the closed-loop system. Subsequently, employing the order reduction method, we derive the semi-discrete finite difference (FD) scheme of the system. Analogous to the demonstration for the continuous case, we construct discrete Lyapunov functions and utilize them to demonstrate that the discretized scheme exhibits uniformly exponential decay as the step size approaches zero.

Advances in high-throughput technologies have vastly expanded our ability to dynamically characterize disease states and associated biomarkers, which play a crucial role in the prevention, detection, and treatment of diseases. In the field of precision medicine, pinpointing patient subgroups that stand to gain the most from specific treatments is of paramount interest. This study explores the challenge of identifying such subpopulations, characterized by disease outcome-biomarker relationship. This complexity is due not only to the dynamic nature of disease outcomes and biomarker profiles but also to the intricate and often nonlinear—interactions between them, necessitating careful consideration. This study employs methods from reproducing kernel Hilbert space (RKHS) to model the complex interactions between outcomes and biomarkers. By utilizing RKHS distance metrics, we identify clusters according to varying patterns in the estimated subject-specific outcome-biomarker relationship functions. Comprehensive numerical simulations were conducted to validate the superior efficacy of our approach in comparison to existing methodologies. Additionally, the utility of our method is further exemplified through its application to real-world datasets.

With the advancement of modern information technology, the collection and analysis of multi-source time series data play an important role in decision-making and process management. However, due to the complexity of capturing the dynamic features for spatio-temporal information, multisource time series forecasting remains a challenging problem. Previous spatio-temporal models usually overlook the integration of physical and spatial dependencies between multivariable data features, as well as the effects of dynamic diffusion. To address these challenges, we propose a Spatio-Temporal Information Dual-layer Diffusion Network (STIDDN) for multi-source time series collaborative forecasting. STIDDN employs residual LSTM networks for temporal dependency modeling of internal features at each station, while the Dual-layer Diffusion Graph Convolutional Network (Dual-DGCN) focuses on capturing both physical and spatial dual-layer dependencies between stations, along with the dynamic diffusion process. By integrating spatio-temporal information through a skip-connection and multi-head attention mechanism, STIDDN achieves effective collaborative forecasting across multiple stations. Extensive experimental results demonstrate that our model consistently outperforms advanced baseline models on two different spatio-temporal prediction task datasets.

Data censoring is a common problem during the process of survival data collection. To maximize the usable information in dataset with censoring, Cox model has been proposed and becomes of a benchmark model in censoring data modelling. However, as data size grows, challenging raises on learning Cox model and its modern extensions. Existing algorithms for training Cox model facing the problems of insufficient sample pair usage and control sample unbalance. In this work, we introduce the batch recombination algorithm : a chain-based method that better uses sample pairs while keeping control sample balance. We show that, under mild conditions, parameter estimates from stochastic gradient descent using our recombinated batch are consistent. Confidence interval can also be established using asymptotic distribution. Extensive numerical experiment both on simulated data and real data, linear and neural network Cox model show efficiency and accuracy of the proposed method.

NMDS codes and MDS codes have critical theoretical and practical value. In this paper, we develop a general construction of 3-dimensional NMDS codes of lengths from $2^m$ to $2^m+2$ by selecting suitable generator matrices and determine their weight enumerators, where $m\geq2$ is an integer. In particular, we construct two types of 3-dimensional MDS codes and analyze the properties of the subfield codes of one of them. Then we derive some optimal locally recoverable codes via the NMDS codes. It is worth noting that all the NMDS and MDS codes are near Griesmer and Griesmer codes, respectively. Furthermore, the duals of the NMDS codes achieve length and dimension optimality, and of the MDS codes achieve distance optimality under the sphere packing bound. Finally, we use some of the codes constructed to build $s$-sum sets (where $s>1$ is odd), strongly regular graphs and $3$-designs.

To estimate physical parameters in a grey-box model with linear regressions, a two-step approach with much reduced computational complexity is developed. First, the parameters of the linear regression model are estimated via the simple linear least square method, before they are fed into a nonlinear optimization problem of a much reduced dimension. It is discovered that the right formulation of the optimization criterion depends on the input-output data, and can be expressed in terms of the singular value decomposition of the data matrix. It is also found that the estimated physical parameters can be fed back to improve the parameters of the linear regression model. This improvement is a consequence of exploiting the structural information of the system contained in the grey-box model, and thus overfitting to the limited training data can be avoided. Numerical examples are presented to demonstrate the effectiveness of the approach.

This paper investigates a finite-time optimal bipartite containment control problem for multiagent systems (MASs) with input saturation. Firstly, a command-filtered technique is applied to filter the virtual control signals to avoid the problem of “explosion of complexity”. Then, the filter and saturation losses are compensated simultaneously by skillfully constructing auxiliary systems, whose signals converge in finite time. Due to the strong nonlinearity of the Hamilton-Jacobi–Bellman equations and system dynamics, the modified identifier-actor-critic reinforcement learning (IAC-RL) algorithm is employed to approximate the unknown functions and train the optimal controller. Specifically, the cost function in the traditional IAC-RL algorithm is modified to ensure its convergence over a long time. With the help of a correction term, the updating laws of the IAC-RL neural networks are also improved to avoid premature termination during training optimal controllers. Finally, the MASs are proved to be semiglobally practically finite-time stable. The effectiveness of the proposed protocol is proved through numerical and practical examples.

According to the Expected Utility with Uncertain Probabilities (EUUP) proposed by Izhakian and Yermack (2017, 2020), this paper measures market uncertainty of the Chinese stock sectors. The cross-sector uncertainty connectedness is explored using a TVP-VAR based connectedness approach. The results suggest that most of the stock sectors have strong connectedness with each other. Their relationships are heterogeneous under different market states, as well as before and during the emergency events, including the COVID-19 pandemic and the Russia-Ukraine conflict. Three external uncertainty indices, including economic policy uncertainty, climate policy uncertainty, and trade policy uncertainty are employed to investigate their quantile effects on the market connectedness. Most of them have significantly negative effects on the connectedness under bear state, while they are insignificant under bull state. Moreover, their relationships have been changed greatly during the emergency events, compared with the results before. This study highlights the effects of market states and emergencies on the transmission mechanisms of cross-sector uncertainty.

Model checking evaluates whether a statistical model faithfully captures the underlying data-generating process. Classical tests-such as local-smoothing and empirical-process methods-break down in high dimensions. More recent approaches use predictiveness comparisons with flexible machine-learning model fitting procedures to yield algorithm-agnostic tests, yet they require large labeled samples. We introduce a prediction-powered, semi-supervised framework that: (1) imputes responses for unlabeled data via a pretrained model; (2) corrects imputation bias with a rectifier calibrated on labeled data; and (3) adaptively balances these components through a data-driven power-tuning parameter. Building on algorithm-agnostic out-of-sample predictiveness comparisons, our method integrates unlabeled information to enhance power. Theoretical analyses and numerical results demonstrate that the proposed test controls Type I error and substantially improves power over fully supervised counterparts, even under imputation-model misspecification.

Elliptic curves over finite fields have been extensively used to build public key cryptography (a.k.a. Elliptic Curve Cryptography(ECC)). The choice of elliptic curves significantly affects the security and performance of the relevant cryptosystem. At present, standardized curves in ECC are all defined over finite fields of characteristic 2 or large prime characteristic, while those of characteristic 3 have drawn little attention mainly due to their lower efficiency in implementation. In this work, we primarily study ordinary elliptic curves defined over the quadratic extension field of characteristic 3 equipped with the Frobenius endomorphism. All relevant operations of finite field and elliptic curves, implemented by the AVX2 instructions and 256-bit wide SIMD operands, are developed and optimized to ensure both efficient and constant-time execution. At the 128-bit security level, our implementation is approximately 1.8x times faster than the previous work for scalar multiplication on ordinary curves of characteristic 3. To the best of our knowledge, this is the first scalar multiplication implementation on elliptic curves of characteristic 3 which outperforms those on standard curves such as NIST P-256 and SM2.

Polynomial systems arising from the practice are often highly sparse, that is, the number of isolated solutions of a polynomial system is generally far less than their Bézout number. Therefore, the full exploration of the sparsity is an important topic in the field of homotopy method for solving polynomial systems. In this paper, we exploit the product structure of each polynomial to characterize the sparsity and further present a numerical method based on polynomial decomposition, in which the homotopy is the combination of the random product homotopy and the coefficient-parameter homotopy and the method is the combination of the symbolic methods and the numerical methods, to solve polynomial systems. Numerical results show that our polynomial decomposition algorithm is more efficient than the existing homotopy methods in some cases, especially when the system has both sparse and dense polynomials.

In this paper, we propose a class of test procedures to check the fitness of parametric forms of the variance function in regression models when the mean function is unknown. By evaluating the unknown mean function with the classical kernel estimator, the proposed test statistics are built upon a modified minimum distance between a nonparametric fit and a parametric estimator under the null hypothesis for the variance function. Asymptotic properties of the estimator of the parameters in the variance function are discussed, and the large sample distribution of the test statistics under the null hypothesis is established, as well as the consistency and the power under some local alternative hypotheses. Extensive numerical studies demonstrate that the proposed test procedures have satisfactory finite sample performance. Finally, two real data examples further showcase the effectiveness of the proposed test in real applications.

This paper investigates the decentralized linear quadratic control problem for systems with observation and multiplicative noise. The system is controlled by two controllers, where the available information for the second controller involves the first controller. Multiplicative noise and observation arise simultaneously in the system model, which differs from the existing literature. The inapplicability of the separation principle and the highly nonlinear characteristics of the observation-based controller optimization problem make the search for the optimal solution quite difficult. The explicit output feedback controllers are designed based on the linear estimator using the matrix maximum principle. An iterative algorithm is presented to compute the gain matrices, and a sufficient condition is given for the mean-square stability of the system. Finally, a vehicle platoon problem is tackled with the acquired theoretical results.

This paper addresses the security control problem of high-order fully actuated (HOFA) systems under actuator attacks. First, four adaptive control algorithms are proposed to mitigate the effects of these attacks. By selecting appropriate Lyapunov functions, the paper demonstrates that the proposed controllers can ensure the closed-loop system’s state converges to zero, even when subjected to time-invariant actuator attacks. Furthermore, the adaptive controllers guarantee the system’s uniform ultimate boundedness under time-varying actuator attacks. Finally, the effectiveness of the proposed adaptive control algorithms is validated through simulation results based on numerical examples, underscoring their practical applicability.

This paper studies the consensus tracking control of networked stochastic leader-following multi-agent systems (MASs) with multiplicative and additive time-varying actuator failures under random communication topology switching. Considering the measurement noise generated by information transmission in networked systems, the stochastic MASs model with multiplicative noise is established. Meanwhile, the random time-varying loss of actuator effectiveness failure and bias faults are taken into account. Based on the neighbors’ and leaders’ state, the distributed adaptive fault-tolerant consensus tracking control protocols are proposed under the case of Markovian and semi-Markovian switching topology. Using stochastic system theory and Lyapunov theorem, sufficient conditions of the meansquare practical stability for leader-following consensus tracking are obtained. Results show that under the proposed distributed adaptive fault-tolerant control (DAFTC) protocols, the follower agents can track the leader under actuator constrains and random switching topology. Finally, the effectiveness of the mentioned control protocols are verified the numerical simulations.

Model checking is crucial in statistical analyses and has garnered significant attention in the academic literature. However, certain challenges persist in scenarios that involve large-scale datasets and limited resource allocations. This research introduces a novel subsampling methodology for testing regression models with continuous and categorical predictors, referred to as the Subsampling Adaptive Projection-Test (SAPT). This innovative approach demonstrates substantial improvements in test power for both local and global alternatives, outperforming conventional uniform subsampling mechanisms. We rigorously establish the asymptotic properties of SAPT and delineate its maximum achievable power under asymptotic conditions. Comprehensive simulations and real-world dataset applications provide robust validation of the proposed theoretical propositions.

This paper investigates the problems of partial state consensus and output consensus for heterogeneous linear multi-agent systems (MASs). Firstly, the partial state consensus problem of parameter heterogeneous linear MASs is solved by converting it to a corresponding partial stability problem via the linear transformation approach, a necessary and sufficient condition for achieving partial state consensus is obtained utilizing the partial variable stability theory and a bilinear matrix inequality (BMI) -based algorithm for finding the gain matrices in the control protocols is presented. Secondly, the partial state consensus problem of structural heterogeneous linear MASs with distinct state dimensions is dealt with, and a necessary and sufficient condition is derived by a similar technical route. Finally, the output consensus problem of heterogeneous linear MASs is considered and a necessary and sufficient condition is derived by a linear transformation to convert the output consensus problem to the partial state consensus problem. The obtained results are verified through several numerical examples.

Both actuator faults and time delays degrade the performance of control systems. Although fault-tolerant mechanisms are commonly used in advanced control systems, no result is available in investigating the adaptive tracking problem of stochastic nonlinear time-delay systems in the presence of Markovian jump actuator faults. After establishing some mathematical fundamentals for stochastic differential delayed equations with multi-Markovian switching, this issue is tackled in this article, by proposing a novel adaptive backstepping fault-tolerant controller. Uncertainties caused by random actuator faults, unknown time-varying delays, the Wiener noise of unknown covariance as well as the unknown plant parameter are handled skillfully in a unified stochastic framework. By constructing a suitable Lyapunov-Krasovskii functional, it is proved that all closed-loop signals are bounded in probability, and the tracking error can converge into an arbitrarily small residual set in the sense of mean quartic value. In addition, the range of reference signals is greatly enlarged by comparison with the conventional backstepping controller. Two simulation examples are presented to illustrate our theoretical findings.

How to evaluate the system reliability through the test data of components is one of the key challenges in the field of reliability. In this study, we focus on calculating the Bayesian lower credible limit. Although the approximation methods are widely used in reliability evaluation, how to apply them to the Bayesian context remains to be solved. Some previous studies have attempted to address this issue. However, their approaches might result in instability, and they have imposed significant constraints on component and system structures. A high-order saddlepoint approximation method for high accuracy is proposed, as well as a feasible procedure for determining the saddlepoint method’s asymptotic variable. Our framework allows us to analyze the components following various posterior distributions without limiting the system structure. Numerical experiments on various systems are presented to demonstrate the effectiveness and accuracy of our method. In comparison, it consistently outperforms other commonly used approximation approaches.

For copula models with unknown marginal distributions and an unspecified Euclidean parameter, a natural way to get a rank-based semiparametric efficient estimator for the Euclidean parameter is to solve the estimating equation constructed using the efficient score, with the unknown marginal distribution functions substituted by empirical versions. However, the solution may lack a closed form and may only be approximate. At present, it is not known how a rank-based semiparametric efficient estimator can be found for general copula models. By using a given arbitrary consistent rank-based estimator as the initial point, we propose a K-step estimator based on the initial point and make it more efficient, where K is related to the convergence rate of the initial point. We show that, under regularity conditions, the K-step estimator can achieve semiparametric efficiency for general copula models, and we present some numerical calculation methods. We conduct simulations to explain our theoretical results and confirm that the proposed method performs very well.

To explore the impact of various groups and methods on rumor propagation, we propose a ‘Double-Refutation (DR) and Double-Blocking (DB) ’ rumor control strategy. This strategy combines external refutation via media reports, internal refutation by counteracting individuals, and both continuous and impulse blocking methods. By leveraging multi-synergy and aiming to minimize control costs, we propose stochastic optimal hybrid control strategies for rumor containment. Additionally, to enhance the response speed of the control strategy, we introduce an ensemble learning algorithm as a substitute for theoretical solutions. Numerical simulations demonstrate that the trained ensemble learning control algorithm can quickly identify sub-optimal control strategies for rumor spreading, with costs only 4.1% higher than those of the optimal control theory.

This paper addresses the control problem of continuous-time network control systems (NCSs) subject to aperiodic denial-of-service (DoS) attacks and actuator saturation. By considering the minimum communication security duration and the maximum attack duration, an aperiodic DoS attack model is proposed. This model facilitates system performance analysis by linking two general hypothetical models. For NCSs experiencing both aperiodic DoS attacks and actuator saturation, a dynamic memory-based event-triggered mechanism (DMETM) is designed to operate during the attack dormant periods. Based on the aperiodic DoS attack signal, a set of memory-based controllers and auxiliary controllers are designed to linearize the actuator’s saturation effect. Using the obtained switching system model and a piecewise Lyapunov-Krasovskii functional (LKF), suffcient conditions are derived for the system to achieve local asymptotic stabilization and weighted perturbation attenuation H_∞ performance. Additionally, a method for estimating the attraction domain is provided. The co-design of the event-triggered weighting matrix and controller gains is presented using linear matrix inequalities (LMIs). Finally, the effectiveness and superiority of the proposed method are demonstrated through a practical application example.

In this paper, we investigate the consensus control problems of multiagent systems in undirected network settings where all agents obey by third-order fractional-order dynamics. Three types of consensus are discussed: the typical consensus, the scaled consensus and the scaled group consensus. For realizing these agents’ consensus control, we design distributed consensus protocols, and derive accurate consensus states and explicit convergence criterion based on matrix theory and the basic properties of both fractional-order derivatives and fractional-order integrals. Finally, several simulations are presented to guarantee the effectiveness of the theoretical results.

In this note, we revisit the envelope dimension reduction, which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance. Motivated by the recent developments in envelope methods and algorithms, we refresh the envelope inverse regression as a flexible alternative to the existing inverse regression methods in dimension reduction. We discuss the versatility of the envelope approach and demonstrate the advantages of the envelope dimension reduction through simulation studies.

This paper investigates the adaptive tracking control problem for AutoRegressive Moving Average (ARMA) systems with quantized observations, explicitly focusing on reference signals composed of non-periodic sequences. We propose an adaptive tracking control scheme integrating an adaptive controller with a stochastic approximation-type estimation algorithm. Different from the control scheme for Finite Impulse Response (FIR) systems, the estimation part not only estimates the unknown system parameters but also the unknown system outputs. Next, based on the certainty equivalent principle, the adaptive controller is designed using the above two estimates instead of the actual parameters and system outputs. To tackle the inherent coupling between the two estimates, we introduce a novel approach that combines the Lyapunov function method with a backward-shifted polynomial method featuring time-varying coefficients. This approach assists in establishing the mean square convergence of the estimates with a convergence rate of $O\left(\frac{1}{k}\right)$ under suitable conditions of the step size coefficient. Additionally, this paper shows that the designed adaptive control law can achieve asymptotically optimal tracking of non-periodic reference signals in the mean square sense. Finally, a numerical simulation is presented to validate the theoretical results obtained in this paper.