This paper presents a systematic comparative study of three major axiomatic set theory systems: Zermelo-Fraenkel system with "the Axiom of Choice" (ZFC), von Neumann-Bernays-G?del system (NBG), and Morse-Kelley system (MK). The research begins by tracing the historical development and motivations behind these three axiomatic frameworks, followed by a detailed analysis of their axiom structures and fundamental concepts. The systems are then compared across several dimensions: expressive power, metamathematical properties, and practical applications. The significant contribution of this study lies in introducing the Coq proof assistant as a formal verification tool to implement and compare MK, NBG, and ZFC, systematically investigating their differences within a formalized environment. Research findings indicate that the three axiomatic systems present distinct advantages and challenges during formalization, providing new perspectives for understanding the essential characteristics of axiomatic set theory and its position in mathematical foundations. This comparative analysis helps clarify the relationships between these three axiomatic systems and provides a theoretical reference for future formal verification work in set theory.

We extend the marginal coordinate test for predictor contribution (Cook, 2004) to the case with multivariate responses. Instead of explicitly specifying the link functions between the responses and the predictors, an asymptotic test is proposed under the normality assumption of the predictors as well as an asymmetry assumption about the unknown regression mean function. When these assumptions are violated, the asymptotic test with elliptical trimming and clustering is still valid with desirable numerical performances.

We consider the issue of hypothesis testing in varying-coefficient regression models with high-dimensional data. Utilizing kernel smoothing techniques, we propose a locally concerned U-statistic method to assess the overall significance of the coefficients. We establish that the proposed test is asymptotically normal under both the null hypothesis and local alternatives. Based on the locally concerned U-statistic, we further develop a globally concerned U-statistic to test whether the coefficient function is zero. A stochastic perturbation method is employed to approximate the distribution of the globally concerned test statistic. Monte Carlo simulations demonstrate the validity of the proposed test in finite samples.

This note aims at conducting the switched-filter-based adaptive neural fast tracking control design for networked multi-delay switched systems involving time-varying network-induced input delays. Different from the traditional Luenberger-based state observers, the designed switched K-filters, in cooperation with the coordinate transformation in backstepping design, not only address the unknown states problem, but also avoid the design difficulties caused by the unknown switched control gains. By constructing the auxiliary functions and specific Lyapunov-Krasovskii functions, and using neural networks (NN) approximation, the delayed coupling functions can be processed. Meanwhile, the auxiliary switched systems are devised to compensate for the impact of switched input delay. To guarantee the superior tracking performance of time-delay switched nonlinear systems, an improved fast tracking control method with tight error constraints is proposed. In contrast to existing adaptive tracking control methods, the proposed method not only ensures the fast fixed-time convergence property without strict initial conditions, but also achieves transient performance without significant overshoot. The designed controllers ensure that tracking error converges to a specified convergence region in a preset time and the semi-global uniform ultimate boundedness (SUUB) of all signals of the overall controlled systems is realized for switching signals with average dwell time (ADT). Synthetic simulation results confirm the feasibleness and superiority of the control scheme.

This study focuses on the finite-time output feedback stabilization of a one-dimensional wave equation with velocity recirculation (nonlocal term) and matched disturbance. Initially, the sliding mode control (SMC) method is used to design a finite-time state feedback controller. Subsequently, the active disturbance rejection control (ADRC) approach is employed to accurately estimate the disturbance in finite time. A finite-time observer is then constructed, facilitating the design of an output feedback controller. Furthermore, we establish the well-posedness and finite-time stability (FTS) of the resulting closed-loop system. Finally, some simulation examples are presented to validate the theoretical findings.

This paper focuses on the problem of distributed online convex optimization with nonlinear switching costs in a multi-agent network. In this problem, each agent has its own time-varying private loss function, which is either convex or convex and smooth, and is restricted to partial access to information about the global time-varying loss functions. Consequently, agents need to engage in local information exchange with their neighbors to make decisions, and any changes in decisions will incur additional costs in a nonlinear manner. To address this problem, two algorithms are proposed: the distributed online gradient descent algorithm (DOGD) for general convex loss functions and the distributed online gradient tracking algorithm (DOGT) for convex and smooth loss functions. It is shown that both the proposed algorithms have sublinear dynamic regret bounds when the environment undergoes sublinear changes. In the end, a numerical simulation of a distributed online learning example is conducted to validate the theoretical results.

The notion of generalized almost perfect nonlinear (GAPN) functions extends the classical concept of almost perfect nonlinear (APN) functions, which are optimal with respect to differential uniformity over finite fields of even characteristic. Since its introduction, the study of GAPN functions has primarily concentrated on monomial and binomial GAPN functions over the finite field $\mathbb{F}_{p^n}$. In this paper, we focus on characterizing GAPN functions over $\mathbb{F}_{p^n}$ from the Dickson polynomials and reversed Dickson polynomials. Additionally, we present one class of GAPN functions derived from known GAPN functions.

The ACC/DEC method to schedule the feedrate is widely used in 3-axis CNC machining due to its simplicity and effectiveness. However, for most of the existing methods, the chord error is computed by an approximate way, which can not strictly control the chord error. In this paper, the feedrate scheduling for a NURBS toolpath is considered and it is transformed to construct an information matrix, with the help of which it can be found that the key issue of feedrate scheduling is to update the matrix by three kinds of basic operation. To control the chord error strictly, it is proved that the calculation of chord error can be transformed into finding the real roots of algebraic equations. Then, the feasibility of the feedrate can be guaranteed by adjusting the information matrix. To improve the efficiency of the machining, several optimal strategies are proposed. The simulation results show that the proposed method can strictly control the chord error with relatively shorter machining time compared with other ACC/DEC methods.

Estimating the sample mean and standard deviation from summary statistics such as the median, range and quartiles is an important problem in medical research. The established methods relying on normality assumptions and linear approximation yields the inaccurate results for the skewed distributions. We propose a supervised learning framework using a hierarchical neural network trained on a diverse synthetic data. This data-driven approach is theoretically well-founded and substantially outperforms the existing methods, particularly in non-normal scenarios. To facilitate broad adoption, we provide a user-friendly online calculator and a Python package, both of which ensure data privacy by performing all computations locally on the user's machine.

Convolutional neural networks (CNNs) have been widely utilized in hyperspectral image (HSI) classification tasks, achieving remarkable performance. However, in existing HSI-CNN methods, the cubic information in HSI is often vectorized, which can compromise the geometric structure of the data. Meanwhile, how to break through the bottleneck of parameter redundancy and immense computation consumption is a hot topic in CNN-based methods. Inspired by these, a stand-alone tensor neural network (SATNN) is proposed, which uses tensor algebra to construct a deep learning framework to replace the convolutional, pooling, and fully connected layers typically found in CNNs. Feature extraction is carried out among the tensor contraction layer (TCOL), tensor pattern product layer (TMPL), tensor replacing the flatten operation, and the fully-connected layer (TRFFC), which can capture the geometric structure and multilinear structure of high-dimensional data. What is important, TCOL can reduce the parameters of LeNet-5 and the hybrid spectral convolution neural network (HybridSN) by 64.46% and 98.24% with little effect on precision. Experiment results on three commonly used hyperspectral imagery datasets demonstrate the effectiveness of HSI-SATNN, with its classification accuracy surpassing that of several CNN-based and tensor-based approaches.

In this study, we introduce three distinct testing methods for testing alpha in high dimensional linear factor pricing model that deals with dependent data. The first method is a sum-type test procedure, which exhibits high performance when dealing with dense alternatives. The second method is a max-type test procedure, which is particularly effective for sparse alternatives. For a broader range of alternatives, we suggest a Cauchy combination test procedure. This is predicated on the asymptotic independence of the sum-type and max-type test statistics. Both simulation studies and practical data application demonstrate the effectiveness of our proposed methods when handling dependent observations.

In this paper, we define the weighted skew symmetric game (WSSG) according to the definitions of the weighted symmetric game (WSG) and the skew symmetric game. Based on the vector space structure of finite games and the semi-tensor product (STP) of matrices, we provide the basis and orthogonal complements of the weighted symmetric game and weighted skew symmetric game. Finally, we provide a weighted symmetry-based decomposition of finite games, which consists of weighted symmetric subspace, weighted skew symmetric subspace and non-symmetric subspace. Some examples are provided as the verification of the proposed results.

To tackle the overshoot phenomenon in linear active disturbance rejection control (LADRC), this paper proposes a composite saturation-enhanced control strategy. Firstly, an error-based extended state observer (ESO) is designed to estimate the total disturbances in real time eliminating the need for high-order derivatives of reference signals. Secondly, a saturation-constrained control strategy is proposed to mitigate the overshoot phenomenon in the initial phase. Thirdly, the global exponential convergence of the closed-loop system with nonlinear disturbances is rigorously analyzed via Lyapunov stability theory. Finally, two sets of comparative experiments are conducted to demonstrate the control performance of the proposed method. The first set is performed with additional disturbances, while the second set is conducted without additional disturbances. Both results demonstrate that compared to LADRC and PID control, the saturated ADRC can effectively suppress overshoot phenomena.

The cooperative output regulation problem for unknown linear multi-agent systems has been studied by both policy-iteration method and value-iteration method via distributed internal model approach. However, the original results were limited to single-input single-output linear multi-agent systems under the assumption that the communication digraph is acyclic. Recently, we have extended the existing result to multi-input multi-output linear multi-agent systems over a general static and connected digraph by a more efficient value-iteration method. Since the policy-iteration method is simpler and has a much faster convergence rate than the value-iteration method, in this paper, we further apply the policy-iteration method to the cooperative output regulation problem of unknown multi-input multi-output multi-agent systems over a general static and connected digraph. Compared with the existing policy-iteration method, our policy-iteration approach not only drastically reduces the computational cost, but also significantly weakens the solvability conditions. Moreover, by introducing a virtual exosystem, our policy-iteration approach eliminates the need for employing a distributed observer. As a result, the data collection can start at any time, and the computing cost for each agent is also reduced.

High-dimensional linear mixed models are widely used for longitudinal data analysis, yet their reliance on normality assumptions often limits applicability in psychometric and biomedical settings. To address this, we propose a high-dimensional skew-normal linear mixed model and develop a novel variational Baysian method that integrates spike-and-slab Lasso priors for simultaneous parameter estimation and variable selection. To handle dependencies in the joint posterior, we propose a variational auto-encoders to extract latent features, and employ a coordinate ascent algorithm to optimize the evidence lower bound (ELBO), circumventing intractable integrals. Model comparison is conducted using the Bayes factor, approximated via the ELBO. The effectiveness of the proposed methodologies is demonstrated through simulation studies and a real-data application.

Space-filling designs are widely used in computer experiments to build effective metamodels with limited prior information, as they enable thorough exploration of the design space by uniformly distributing points. However, many existing designs perform poorly in low-dimensional projections, particularly when only a few factors are active. Uniform projection designs address this limitation by optimizing point distribution across low-dimensional subspaces, ensuring uniformity in all dimensions while maintaining desirable distance and column-orthogonality properties. Existing methods for constructing such designs often rely on complex algorithms or can only generate designs with large factor-to-run ratios. In this work, we propose a simple approach for constructing uniform projection Latin hypercube designs by employing orthogonal arrays. Our method is particularly effective when the number of factors is much smaller than the number of runs. Both theoretical and numerical results demonstrate that the designs produced by our method perform well with respect to the uniform projection, low-dimensional stratification, maximin distance, and column-orthogonality criteria.

We formalize a proof of the irrationality of ζ(3) in Lean 4, using Beukers’ method. To support this, we extend the Lean mathematical library (Mathlib) by formalizing shifted Legendre polynomials and important results in analytic number theory that were previously missing. As part of the Lean 4 PrimeNumberTheoremAnd project, we also formalize the asymptotic behavior of the prime counting function, giving the first formal proof in Lean 4 of a version of the Prime Number Theorem with an error term which is stronger than what had previously been formalized. This result is a crucial ingredient in proving the irrationality of ζ(3). Our complete Lean 4 formalization is publicly available on GitHub.

This paper studies the equivalence theory between bivariate polynomial matrices and their Smith forms. For a class of bivariate polynomial matrices, by leveraging the special form of the greatest common divisor of the maximal minors of the matrix, we construct a homomorphism from the bivariate polynomial ring to a Euclidean domain. Subsequently, by applying Gaussian elimination, the matrix can be reduced to its Smith form. Consequently, we establish that the necessary and sufficient condition for such a type of matrix to be equivalent to its Smith form is that the reduced minors of each order generate the unit ideal.

Hotel occupancy rate forecasting is crucial for hotel management, impacting resource allocation, pricing, and revenue strategies. However, traditional methods often fail due to complex factors like seasonality, unforeseen events, and market dynamics, especially in multi-step and probabilistic interval predictions. This study proposes a novel hybrid forecasting model, NHITS-GMM, designed to improve the accuracy and reliability of occupancy rate predictions. By combining the multi-scale feature extraction of NHITS with the probabilistic modeling strength of Gaussian Mixture Models (GMM), the model decomposes time-series data using hierarchical interpolation and generates dynamic Gaussian mixture parameters. This enables both point and probabilistic interval forecasts for single-variable occupancy rates. Experimental results across four typical hotel scenarios show that NHITS-GMM significantly outperforms traditional and deep learning models in terms of stability and accuracy, particularly for multi-step and probabilistic interval forecasts. The proposed model offers hotel managers a more reliable tool for optimizing resource allocation and revenue management.

This paper investigates the inverse optimal control problems for continuous-time linear quadratic regulators over finite-time horizons, aiming to reconstruct the control, state, and terminal cost matrices in the objective function from observed optimal inputs. Previous studies have mainly explored the recovery of state cost matrices under the assumptions that the system is controllable and the control cost matrix is given. Motivated by various applications in which the control cost matrix is unknown and needs to be identified, we present two reconstruction methods. The first exploits the full trajectory of the feedback matrix and establishes the necessary and sufficient condition for unique recovery. To further reduce the computational complexity, the second method utilizes the feedback matrix at some time points, where sufficient conditions for uniqueness are provided. Moreover, we study the recovery of the state and terminal cost matrices in a more general manner. Unlike prior works that assume system controllability, we analyse its impact on well-posedness, and derive expressions for unknown matrices for both controllable and uncontrollable cases. Finally, we characterize the structural connection between the inverse problems with the control cost matrix either to be reconstructed or given as a prior.

Rumor propagation in social networks poses severe challenges to social stability. This study proposes a novel ILSDR rumor propagation model by introducing latents and debunkers within homogeneous networks, systematically elucidating dissemination mechanisms. First, theoretical stability proof is established through Lyapunov functions and the Poincaré-Bendixson property. Subsequently, to counteract rumor dissemination, a PID control strategy optimized via BP neural networks is developed, effectively mitigating rumor diffusion through intelligent control pathways. Compared with traditional static control models, this strategy provides an innovative technological pathway for rumor governance. Finally, leveraging Facebook data to construct network topology and the Erdős-Rényi algorithm to quantify average degree, three practical control strategies are proposed. Simulations validate their efficacy in curbing rumor diffusion. Overall, this work establishes a unified framework integrating dynamic modeling with intelligent control, laying methodological foundations for disinformation governance.

This paper addresses the leader-follower consensus control problem for multi-agent systems (MASs) with uncertainties. First, a fixed-time integral sliding mode (ISM) controller is developed to suppress uncertainties and achieve fixed-time consensus. Subsequently, a dynamic event-triggered mechanism (DETM) with an improved internal dynamic factor is proposed to dynamically adjust the triggering times. By incorporating full-state consensus errors into the error function, the DETM ensures the desired control performance while reducing the triggering times. Finally, a leader-follower consensus control strategy based on the fixed-time ISM control and the DETM is proposed to ensure that the system reaches the real sliding mode surface within a fixed time while reducing communication resource consumption. Theoretical analysis and comparative simulations validate the effectiveness of the proposed control scheme.

In this paper, a classical topic from computer science is reexamined from the perspective of modern control theory. Vector addition systems, first introduced in 1969, saw their first major results published in 1976. More recently, new developments have appeared in the computer science literature. Here, we study controllability, positive controllability, and reachability in detail, and establish necessary and sufficient conditions for each of these three concepts. While reachability has been the primary focus of the computer science works, those studies emphasize decidability-a topic not addressed in this paper. Instead, the main contribution of this work is the derivation of necessary and sufficient conditions for reachability expressed in terms of the system matrix.

This paper aims to investigate the secure synchronization control for complex dynamic networks (CDNs) under multi-channel deceptive attacks. Deceptive attacks compromise system synchronization by injecting false information to manipulate node states. Unlike existing related research, cyber attacks may exist in both the sensor and controller channels. To address the impact of cyber attacks on the detection channel, the purpose of an observer is to estimate the state information. Meanwhile, to ensure the dynamic performance of CDNs, an observer-based secure synchronization control method under deception attacks is proposed. By applying the comparison theory and Lyapunov stability theorem, some conditions for secure synchronization are derived, and an estimate is made of the maximum permitted synchronization error. Lastly, two computational simulation examples are provided to confirm the precision and potency of the suggested conceptual framework.

This study proposes a novel methodology for detecting change-points in time series risk measures based on support vector regression (SVR). For this, we first employ the FZ loss function to jointly model two key risk measures Value-at-Risk (VaR) and Expected Shortfall (ES), and then construct a LS-CUSUM statistic to test structural breaks in the resulting loss series. This can help us capture simultaneous changes both in VaR and ES. The asymptotic distribution of the LS-CUSUM statistic under the no change-point null hypothesis as well as its consistency under the alternative hypothesis are proved. To address the limitations of conventional parametric method in risk measurement estimation, we introduce a new SVR based estimation technique to estimate VaR and ES. This data-driven method effectively models the volatility processes in financial risk measures, overcoming the biases and underestimation issues inherent in parameter estimation. Simulation studies demonstrate the enhanced robustness of our proposed method when handling highly nonlinear time series, and show superior power performances when detecting change-point in high-frequency time series. Finally, we illustrate our method by a set of S&P 500 index data.

An off-policy reinforcement learning algorithm is proposed to solve the optimal control problem for discrete-time switched linear systems with both infinite and finite time horizons. The proposed algorithm does not require access to system dynamics and requires less computational effort to obtain the optimal policy for discrete-time switched linear systems while minimizing the performance function. In this work, reinforcement learning is used to fit the switched Riccati set and Q-functions via a least-squares algorithm. The complexity of the Q-function is reduced by combining it with the matrix pruning algorithm. It can be guaranteed that the algorithm will obtain the optimal solution with sufficient training data. Finally, the effectiveness of the algorithm is verified via simulation.

The Smith form of matrices plays a significant role in the reduction of multidimensional systems and the equivalence of matrices. In this paper, we investigate the equivalence problem for two classes of multivariate polynomial matrices and their Smith forms. We derive some criteria on reducing these matrices to their Smith forms. Additionally, we provide an example to illustrate the main results.

Although considerable progresses have been made in fuzzy or neural decentralized adaptive control, most of them only guarantee the closed-loop system to be semi-globally stable. This article concentrates on the globally fuzzy decentralized adaptive fault compensation control problem for a class of large-scale stochastic nonlinear time-delay systems subject to input nonlinearities. Compared with the existing results, the main features of this study include three aspects: (i) By virtue of a function replacement strategy, the input of the fuzzy logic systems becomes bounded reference signals, thereby ensuring that the closed-loop large-scale system is globally stochastically stable. (ii) The mismatched delayed interactions are not assumed to be upper bounded by any specific functions, and no extra growth assumption is imposed on them except for the global Lipschitz condition. (iii) Markovian jump faults of multiple nonlinear actuators are compensated in each control loop, in which the control gains are state-dependent functions rather than constants. By means of a novel Lyapunov-Krasovskii functional, it is shown that the closed-loop large-scale system is globally stable in probability, and the tracking error can converge into a tunable residual set in the sense of mean quartic value. Simulation studies are provided to demonstrate the validity and superiority of our proposed method.

This paper studies consensus of linear multi-agent systems with binary-valued measurements and switching topologies. Unlike the existing consensus of multi-agent systems with binary-valued measurements, Markovian switching topology is considered in this paper. A new algorithm is proposed to improve the consensus speed of multi-agent systems, with constant gains in both estimation and control, instead of time-varying gains. By analyzing the estimation error and the expected consensus error simultaneously, we prove that the proposed algorithm can make agents achieve consensus in a bounded range, and the consensus speed is negative exponential under certain conditions, which is faster than that in existing literature. Finally, simulation results are given to demonstrate the theoretical results.

Network data typically contain sensitive relational information, where direct release or sharing may lead to non-negligible privacy violations without proper statistical safeguards. While differential privacy has emerged as a powerful framework for privacy-preserving network data analysis, theoretical understanding remains limited particularly for models incorporating both network structure and nodal attributes. This paper bridges this gap by investigating a directed β-model with covariates under differential privacy constraints. Our model accounts for both node-level heterogeneity (via 2n-dimensional degree parameters θ) and covariate-driven homogeneity (via a p-dimensional parameter γ). To protect privacy, we introduce a joint Laplace mechanism for releasing network statistics while satisfying differential privacy constraints. Leveraging moment-based estimation techniques, we estimate the parameters of both degree heterogeneity and homogeneity and derive the consistency and asymptotic normality of the differentially private estimators as the network size tends to infinity. Our theoretical findings are validated through numerical simulations and real-world case studies, demonstrating the validity of our theoretical results.

This work investigates prescribed-time flocking control with collision avoidance for Cucker-Smale systems. We propose a novel control framework that guarantees prescribed-time flocking, with convergence time that are both independent of initial conditions and control parameters. Within the framework of Lyapunov stability theory, we derive sufficient conditions guaranteeing both flocking convergence and collision avoidance in Cucker-Smale systems. In addition, an upper bound for the energy required to achieve flocking is theoretically derived. The results indicate that parameters α and β significantly affect the system’s flocking dynamics. Specifically, parameter α exhibits a nonmonotonic relationship with convergence speed and energy cost, revealing a fundamental performance trade-off. In contrast, reducing parameter β simultaneously improves convergence speed and decreases energy cost. Furthermore, the prescribed time T_p and system size N are critical factors that substantially affect energy consumption. The results provide theoretical foundations for designing efficient flocking controllers and balancing the trade-off between convergence speed and energy cost.

In the real world, interactions are often subject to disruption due to imperfections and uncertainties. In this paper, we investigate the designing method of zero-determinant (ZD) strategies for repeated games on homogeneous networks. First, for each player, the set of his neighbors is regarded as a whole player, called the fictitious opponent player, then the corresponding algebraic model is proposed for repeated prisoner’s dilemma game on homogeneous networks. Moreover, the influence of implementation errors on designing ZD strategies is explored. Finally, the 3-degree homogeneous networked game is given to illustrate the theoretical results.

In this article, we demonstrate the construction of a small-disturbance input-to-state stabilizing output feedback saturation controller for a chain of integrators subject to measurement and external disturbances. More generally, we demonstrate that the saturation controller for a chain of perturbed integrators remains robust even when the measurement disturbances are eventually bounded. Futhermore, as an application, the proposed robust controller design approach is used as a design tool in solving robust output-feedback event-triggered saturation control problems in chains of integrators.

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.

This article studies attack detection problems for the secure distributed state estimation of multi-sensor networks with intermittent observation. The Kalman consensus filter is equipped to develop the minimum mean-square error estimation of the process. Due to the vulnerability of the communication network, an attack scenario is considered where both the sensor-to-estimator channels and the estimator-to-estimator channels are attacked. The attackers would intercept and modify the measurement based on a linear attack strategy. Meanwhile, the false data is injected into the prior state estimates sent to other nodes. The χ² detectors fail to identify the well-designed linear and false data injection attacks. To overcome this drawback, the watermarking-based attack detection strategy is proposed. The effectiveness of the proposed scheme for stealthy attacks is analyzed. Furthermore, the presence of intermittent observations prevents the residuals from reflecting false data injection attacks in estimator-to-estimator channels. This problem is effectively addressed by employing a stochastic detection strategy integrated with watermarking. Based on effective attack detection, the malicious data can be mitigated by using the Kalman consensus filter to avoid performance degradation. Finally, a numerical simulation validates the effectiveness 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.