The factorial design within a conditional model is utilized when the effects of one factor in a factorial experiment hold greater significance under each fixed level of another factor. This paper investigates the generalized minimum aberration $(N,s^p)$-design, where each factor is $s$-level, with $s$ being any prime or prime power. Via utilizing the method of complementary designs, we explore the design with a pair of conditional and conditioning factors. The proposed approach applies not only to regular designs but also to nonregular designs. Additionally, the findings can be extrapolated to encompass designs under the two pairs conditional model. The findings presented in this paper not only strengthen but also generalize the existing knowledge in this field.

Visual-based defect detection efficiently monitors the health and quality of construction and industrial products. However, current defect detection methods often improve detection accuracy at the cost of lower inference speeds or more parameters, struggle with complex data representation, emphasize target features while neglecting environmental information importance, and utilize convolutional or max pooling operations for downsampling, leading to more feature loss. To address these issues, this work presents a low complexity, accurate defect detection network augmented by environmental information-assisted and flexible activation functions to enhance the neural network performance on complex data representation. Environmental information-assisted module is designed for defect detection tasks to assist in accurately locating and predicting defects. Moreover, this work restructure features post-downsampling to mitigate feature loss and design a simple feature module called deep-global fusion that integrates deep and global features to enhance detection performance. Extensive experiments validate the superiority of our detection network. The deployment of our network on edge computing devices confirms its competitive advantage in portability and reliability.

For $k$-valued (control) networks, two types of (control) invariant subspaces are proposed, namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual-(control) invariant{, and to construct state feedback controls}. The bearing space of $k$-valued (control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is introduced, which is independent of the dynamics of particular networks. Finally, the relationship between the state-invariant subspaces and the dual-invariant subspaces of a network is investigated. A duality property shows that if a dual subspace is invariant, then its perpendicular state subspace is also invariant, and vice versa.

This paper proposes a trajectory generation method utilizing the Bézier curve for mobile robots and employs it in the cooperative transportation task. In contrast to the approach of predefining spatial features and then allocating time accordingly, the proposed method expresses the spatial characteristics through duration on the basis of ensuring the continuity of dynamics, and then concurrent planning of spatial and temporal characteristics, thereby leading to a trade-off between time efficiency and optimizing spatial features. Furthermore, the proposed method is combined with formation control and applied to a cooperative transportation task. The effectiveness and practicability of the proposed trajectory generation method are verified through both simulation and experiment.

The Proportional-Integral-Derivative (PID) control has enjoyed significant success and widespread adoption in aviation, automotive, robotics, and various other domains. However, to align with the current trend of networked control systems and optimize communication resource utilization, we introduce an extended PID (EPID) control framework that leverages an event-triggered mechanism. This controller is designed for single-input single-output (SISO) high-order affine nonlinear systems, overcoming the limitation of traditional PID control, which typically guarantees stability only for second-order systems. Leveraging the open unbounded parameter manifold and event-triggered conditions of the controller parameters, we prove through the Lyapunov method that our proposed controller achieves uniformly ultimately bounded stability and guarantees the absence of the Zeno phenomenon in the event-triggered EPID (ET-EPID) system. The efficacy of the ET-EPID control system approach is exhibited through simulation of a third-order system as well as practical experiment conducted on a second-order direct current motor.

This paper investigates the prescribed-time leader-follower consensus problem of second-order multi-agent systems (MASs) with stochastic switching directed topologies. For unknown external disturbances, a prescribed-time disturbance observer is designed to accurately estimate disturbances within a prescribed time, and a fuzzy logic system (FLS) is used to approximate the unknown nonlinear functions, which reduces the conservativeness of the control scheme. The information exchange between agents is modeled using a Bernoulli random process due to various factors influencing the communication layer. Meanwhile, a prescribed-time distributed sliding mode control (SMC) scheme is designed, ensuring that the convergence time of the MASs is independent from the initial values and other parameters of the system. Finally, the effectiveness of the proposed method is verified by a real single link robot arm system.

With advances in network control systems, new applications such as the analysis of opinion dynamics have emerged. Using mathematical tools, various dynamic models have been developed to study how people change opinions in social settings. One such model is the DeGroot-Friedkin model, a two-stage approach for sequential discussion of multiple issues. For each issue, the classical DeGroot model, closely related to the consensus problem, is used to analyze opinion dynamics. This model incorporates the theory of self-appraisal to study the evolution of an individual's self-esteem, where individuals evaluate their contributions to the issues being discussed. However, the question "How does the social network affect one's self-esteem?" remains unaddressed. In this paper, we propose a new self-esteem evolution model that examines the effects of social relationships on individuals' self-esteem by considering changes in opinion as an indicator of the social network's impact. We also introduce a convergence criterion for the new model and provide analytical proofs of the results.

Direct modeling in CAD offers a promising avenue for model modification through direct interaction. However, a critical impediment to the advancement of direct modeling technology is the inconsistency between modified geometry and unaltered constraints. While several methods have been proposed to address this challenge, they often fail to provide effective solutions, particularly in contexts demanding high model precision. In this paper, we introduce a novel approach by integrating tolerance analysis into the constraint update system, followed by the proposal of a constraint update scheme utilizing the extreme value tolerance model and the probability tolerance model. This innovative tolerance-based scheme adeptly resolves the inconsistency problem prevalent in direct modeling while satisfying the requisites of high-precision modeling. A comparative analysis against established methodologies is conducted to demonstrate the advantages of our proposed approach.

Contingent free shipping can improve purchase motivation and increase sales, and is an important promotional means for e-commerce platforms. Among them, it is particularly common for e-commerce platforms to provide free shipping coupons to paid members. How much cost does it take to provide free shipping coupons and how much revenue does it bring, causing confusion to ecommerce platforms. We build pricing decision models based on consumers’ shopping frequency and their sensitivity to shipping costs when e-commerce platforms offering single, multiple and unlimited number of free shipping coupon services. Through the analysis, we find that high-sensitivity consumers dislike paying for shipping and prefer to purchase free shipping coupons. We also find that when adopting multiple free shipping coupons strategy, the optimal number of free shipping coupons to offer is associated with the frequency of consumers’ small order purchases. However, if unlimited number of free shipping coupons is offered, online retailers need to increase membership fees to make more profit. This study brings practical insights for e-commerce platforms as well as online retailers to determine reasonable pricing under different free shipping coupon service strategies and provide consumers with a more convenient shopping experience.

Riemman metric tensor (Rmt) plays a significant role in deducing basic formulas and equations arising in differential geometry and (pseudo-)Riemannian manifolds. It is a fundamental and challenging problem to determine the equivalence of indexed differential Rmt polynomials. This paper solves the problem by extending Gröbner basis theory and the previous work on the computational theory for indexed differentials. L-expansion of an indexed differential Rmt polynomial is defined. Then a decomposed form of the Gröbner basis of defining syzygies of the polynomial ring is presented, based on a partition of elementary indexed monomials. Meanwhile, the upper bound of the dummy index numbers of sim-monomials of the elements in each disjoint elementary indexed monomial subset is found. Finally, a DST-fundamental restricted ring is constructed, and the canonical form of a polynomial is confirmed to be the normal form with respect to the Gröbner basis in the DST-fundamental restricted ring.

This paper tackles the problem of constructing Bézout matrices for Newton polynomials in a basis-preserving approach that operates directly with the given Newton basis, thus avoiding the need for transformation from Newton basis to monomial basis. This approach significantly reduces the computational cost and also mitigates numerical instability caused by basis transformation. For this purpose, we investigate the internal structure of Bézout matrices in Newton basis and design a basis-preserving algorithm that generates the Bézout matrix in the specified basis used to formulate the input polynomials. Furthermore, we show an application of the proposed algorithm on constructing confederate resultant matrices for Newton polynomials. Experimental results demonstrate that the proposed methods perform superior to the basis-transformation-based ones.

Leveraging the principal-agent theory, this study incorporates reputational capital into a continuous-time framework for analyzing venture capital exit decisions. We explore how the principal-agent relationships influence the decision to take capital public by synthesizing optimal incentive alignment and IPO timing within a unified model. Our results uncover an intriguing aspect of reputational capital: despite entrepreneurial efforts to augment this capital, its growth is not linear but tends to reach the highest level before the IPO event. Furthermore, the accumulation of reputational capital expedites the capital exit process and enhances the returns from such exits. Subsequently, as the exit timeline extends, the proportion of exit returns allocated to entrepreneurs escalates to a full share, imposing a constrained decision window for investors on exit timing. Our findings suggest that the timing for maximizing investor returns at an IPO is later than the timing that maximizes company revenue. Moreover, excessive IPO costs further delay this exit decision for investors. These findings offer fresh insights into the languishing IPO market observed over the last two decades.

Extreme risk plays an important role in financial supervision and financial investment, which can cause substantial loss in the financial market. To better manage the severe risks resulting from extreme events, we propose a novel fixed-$k$ autoregressive conditional Fréchet ($k$-AcF) model. The proposed model incorporates the $k$-dimensional extremal distribution and an observation-driven evolution scheme for the key parameters, which accommodates well with the time-varying tail behavior of financial data. Compared to the existing dynamic methods under the extreme value theory framework that focus solely on maximum observations, the $k$-AcF model employs the largest $k$ observations, which enhances the utilization of tail information and obtains a more accurate extreme risk estimation. Furthermore, this paper uses the maximum likelihood estimators to conduct the model estimation and investigates their statistical properties. Simulation studies validate the reliability of the estimators and confirm the theoretical properties of $k$-AcF. Empirical applications to the constituent stocks of two major stock indices in the U.S. demonstrate that the $k$-AcF model accurately captures the clustering and dynamics of extreme risk in the stock market. Moreover, the results show that our model is more responsive and sensitive to a financial crisis than the benchmark model considering only the maximum observations.

Using a sample of Chinese listed firms for the period 2006-2021, this paper constructs dynamic stock networks annually using symbolization and mutual information methods, and investigates the impact of stock network centrality on one-year-ahead stock price crash risk with the help of the bad news hoarding mechanism. We find robust evidence that firms with higher centrality are less likely to experience stock price crashes in the future. An examination of underlying mechanisms suggests that being at the center of the stock network enhances firms’ investment efficiency and managers’ cost of engaging in earnings management, thereby reducing the likelihood of such firms forming and hoarding bad news, and hence their crash risk. Further analysis reveals that the mitigating effect of network centrality on stock price crashes is more salient for firms with weaker external monitoring and less conservative accounting policies. Overall, this paper sheds light on a novel benefit of being at the center of the stock network, namely that central firms are less prone to crash risk, which provides practical insights for risk-management applications related to asset pricing and tail events.

This paper presents a new proportional-integral-derivative control approach for positive switched systems based on a positive proportional-integral observer. First, a positive proportional-integral observer is constructed. By using the observer state, the proportional-integral-derivative control and the corresponding integral part are designed, respectively. Using $1$-norm inequality, two dynamic event-triggering conditions are established for the proportional-integral observer and proportional-integral-derivative controller, respectively. A dynamic event-triggered proportional-integral observer-based dynamic event-triggered proportional-integral-derivative controller is proposed by combining the sample state and the integral of the weighted sample output estimation error. Under the designed event-triggering conditions, an interval system with upper and lower bounds is introduced. The positivity and $\ell_1$-gain stability are achieved by realizing the according properties of the lower and upper bound systems in terms of multiple copositive Lyapunov function, respectively. All gain matrices are designed by a matrix decomposition approach and the corresponding conditions are solved by linear programming. Finally, two examples are provided to illustrate the validity of the results.

In this paper, fully actuated system approaches are utilized to synthesize feedback linearizable nonlinear systems. First, a simple transformation is introduced to convert feedback linearizable nonlinear systems into fully actuated system models for both single-input and multi-input scenarios. Once the fully actuated system model is established, a nonlinear state feedback controller can be derived to achieve a constant linear closed-loop system with an assignable eigenstructure. All degrees of freedom present in the closed-loop system can be leveraged to enhance overall system performance. In comparison to feedback linearization, the proposed method places greater emphasis on the control variables, making it more convenient to address control challenges in dynamic systems. Finally, two numerical examples are presented to illustrate the design procedure for both single-input and multi-input cases, and to validate the effectiveness of the proposed approach.

The allocation of heterogeneous battlefield resources is crucial in Command and Control (C2). Balancing multiple competing objectives under complex constraints so as to provide decision-makers with diverse feasible candidate decision schemes remains an urgent challenge. Based on these requirements, a constrained multi-objective multi-stage weapon-target assignment (CMOMWTA) model is established in this paper. To solve this problem, three constraint-feature-guided multi-objective evolutionary algorithms (CFG-MOEAs) are proposed under three typical multi-objective evolutionary frameworks (i.e., NSGA-II, NSGA-III, and MOEA/D) to obtain various high-quality candidate decision schemes. Firstly, a constraint-feature-guided reproduction strategy incorporating crossover, mutation, and repair is developed to handle complex constraints. It extracts common row and column features from different linear constraints to generate the feasible offspring population. Then, a variable-length integer encoding method is adopted to concisely denote the decision schemes. Moreover, a hybrid initialization method incorporating both heuristic methods and random sampling is designed to better guide the population. Systemic experiments are conducted on three CFG-MOEAs to verify their effectiveness. The superior algorithm CFG-NSGA-II among three CFG-MOEAs is compared with two state-of-the-art CMOMWTA algorithms, and extensive experimental results demonstrate the effectiveness and superiority of CFG-NSGA-II.

This paper investigates a security problem of simultaneously addressing two types of attacks: eavesdropping and infiltration. We model the target system as a discrete-event system (DES) with subsets of concealable events and protectable events, in order to make our methodology applicable to various practical systems and employ two existing works of DES security: degree of opacity and state protection. Specifically, we consider that all protectable events are observable, and some observable events are concealable. In addition, protectable events cannot be protected once they are concealed. Given such a constraint, our goal is to figure out which events to conceal and which transitions to protect so that the prescribed requirements of degree of opacity and state protection are satisfied. In this work we decide which events to conceal as all transitions of a given event label are concealed or not concealed. Our problem formulation also requires a solution to only involve absolutely necessary protectable events in order for the system to avoid superfluous protection costs. We first examine a general version of our security problem with an intuitive algorithm to compute acceptable solutions, and then present a special version which results in a reduced computation time compared to the general version.

In this paper, we study the problem of distributed Nash equilibrium seeking of $N$-player games with high-order integrator dynamics subject to disturbances generated by an uncertain exosystem. Similar problems have been studied for disturbances with an exactly known exosystem. Compared with the existing results of high-order integrator dynamics, which can only handle sinusoidal disturbances with known frequencies, this paper aims to handle multi-tone disturbances with unknown frequencies by introducing an adaptive control technique to estimate the unknown frequencies. Technically, when the exosystem is known, the disturbance can be dealt with by the Luenburger observer. In contrast, the Luenburger observer cannot deal with an uncertain exosystem. We have combined the internal model design and some adaptive control technique to solve our problem. Further, we also establish the sufficient condition to guarantee the convergence of the estimated unknown frequencies to the actual values of these frequencies. Two examples are given to verify the proposed algorithm.

In clinical and observational research, multivariate recurrent event data are commonplace, as people may encounter several kinds of repeating occurrences. While event times are consistently recorded, there are instances where the corresponding event types might not be observed. For multivariate recurrent event data, we introduce a time-varying coefficients additive rate model which takes into consideration scenarios in which event types are missing at random (MAR). We employ an inverse probability-weighted estimating equation to derive inferences for the time-independent and time-dependent effects, with proofs for the estimators' asymptotic behavior. Moreover, we offer statistical tests to assess the temporal variation of covariate effects. The estimators' performance is evaluated by simulation experiments, and we apply this method to a platelet transfusion reactions dataset.

In the context of global value chain restructuring, developing countries involved in processing trade face severe challenges in industrial upgrading. The development of transportation can accelerate the flow of knowledge resources and promote regional technology upgrading. This study aims to investigate whether the development of air capacity can alleviate the regional demand for technologically sophisticated trade, incorporate the factor of international air capacity into the influencing factors of product technology sophistication, explore the relationship between regional transportation development and the technical level of trade products from the perspective of enterprises, so as to fill the gap in relevant research. By combining OAG databases with customs data, the study matches the import and export data of 1302 listed companies from 2010 to 2016, along with corresponding regional air transport data. The empirical results demonstrate that increasing air capacity reduces the regional demand for trade technology sophistication. Moreover, internal factors such as enterprise R&D expenditure and capital-intensive negatively moderate the influence of air capacity growth on the trade technology sophistication. Additionally, external institutional factors, such as government effectiveness and the business environment across various countries negatively regulate the impact of the air capacity expansion on trade technology sophistication.

Cohesive players are a generalization of necessary players, where a player being a cohesive player means that his absence would result in the coalition's worth being equal to the sum of the individual worths of its members. This paper proposes axioms on cohesive players to characterize the positively weighted Shapley values. We first suggest (weak) differential invariance for cohesive players and equal surplus of cohesive players to axiomatize the Shapley value. Then, using weak versions of these two axioms, we provide axiomatizations of the class of positively weighted Shapley values.

This paper analyses problems in the price of anarchy (PoA) for a mixed traffic network with stochastic demands. We focus on two types of users with distinct path-selection principles, self-interested users (SU) and altruistic users (AU). A variational inequality model for the SU-AU mixed traffic equilibrium assignment with stochastic demands is proposed. We develop an upper bound formulation for monomial link travel cost functions by the nonlinear programming approach and analyze the log-normal demand distribution. Additionally, an extended study on the PoA with road pricing for this mixed traffic network is presented and justified. Emphasis is placed on scenarios where road pricing is not included in the total system cost and the other where road pricing is included. The numerical results illustrate that the upper bounds on the PoA are contingent on the degree of the link travel cost function, as well as the maximum/minimum altruism coefficients for both non-road pricing and road pricing implementation. Notably, these bounds are also related to the maximum variation coefficient of the demand and the highest degree of the link travel cost function when the travel demand follows the log-normal distribution.

Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and ternary LCD codes leveraging curiosity-driven reinforcement learning (RL). By establishing reward and devising well-reasoned mappings from actions to states, it aims to facilitate the successful synthesis of binary or ternary LCD codes. Experimental results indicate that LCD codes constructed using RL exhibit slightly superior error-correction performance compared to those conventionally constructed LCD codes and those developed via standard RL methodologies. The paper introduces novel binary and ternary LCD codes with enhanced minimum distance bounds. Finally, it showcases how Random Network Distillation aids agents in exploring beyond local optima, enhancing the overall performance of the models without compromising convergence.

The formalization of geometry theorems in a proof assistant such as Coq poses significant challenges, especially when dealing with higher dimensions. The complexity increases due to the numerous technical lemmas arising from the multitude of incidence relations. This difficulty is particularly pronounced when considering higher-dimensions, as the multitude of incidence relations gives rise to numerous technical lemmas. This paper explores the formalization of the ordered geometry derived from Hilbert's Foundations of Geometry, a system that notably lacks any space order axioms. Our primary focus centers on a vital theorem: "A plane distinctly partitions space into two regions with specific properties." Utilizing the Coq theorem prover, we establish order on both lines and planes. Our key contribution lies in extending these results to three-dimensional (3D) space. Remarkably, our work verifies the redundancy of additional space order axioms in Hilbert's axiom system. This not only bridges a gap in existing research but also highlights the potency of computer proof assistants in ensuring mathematical rigor.

This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations, while considering actuator saturation and external disturbances. Different with the traditional consensus methods, the proposed observer-based boundary control relies on non-collocated and incomplete local measurements rather than idealistic global spatiotemporal dynamics. First, the discrete agents with a chain topology are regarded as a continuum, resulting in the derivation of a reaction-diffusion equation to replace the cumbersome ordinary differential equations (ODEs). Subsequently, an observer is constructed based on the non-collocated measurements to estimate the errors between leader-following agent clusters. Then, a sufficient condition for the consensus controller is derived by improving the Lyapunov direct method, mean value theorem of integrals and a variation of Wirtinger’s inequality. Furthermore, an optimization problem is proposed to effectively enhance the $H_\infty$ disturbance attenuation performance in the presence of actuator saturation. Finally, the comparison simulation is given to illustrate the superiority of proposed methodology.

This paper focuses on studying the problem of robust output practical stability of time-varying nonlinear control systems. The main innovation lies in the fact that the proposed approach for stability analysis allows for the computation of bounds that characterize the asymptotic convergence of solutions to a small ball centered at the origin using a Lyapunov method with a definite derivative. Under different conditions on the perturbation, we demonstrate that the system can be globally robustly asymptotically output stable by designing a candidate feedback controller. Finally, three examples are given to illustrate the practical implications and significance of the theoretical results.

This research addresses existing shortcomings in epidemic-logistics studies by emphasizing the integration of multiple models to determine optimal strategies for medical resource allocation during public health emergencies, such as the COVID-19 outbreak. We develop a multi-model integrated epidemic-logistics model that seamlessly merges three specific sub-models: optimal allocation, epidemic dynamics, and production-inventory. This model dynamically tracks the real-time varying in resource inventory levels at supply nodes and the storage capacities at transit hubs within a logistics network. Unique to our research is the embedding of both the production-inventory mechanism and the impact of a social intervention (Traditional Chinese medicine as the background) within a logistics framework of resource allocation. Moreover, we also introduce an adaptive demand function that possesses learning ability and a probabilistic understanding, crucial for gauging real-time resource demands in affected regions. Our innovation extends to designing a recursive and linearizable structure, transforming the intricate multi-model system into solvable sub-models, while also offering a standardized method for creating demand functions. The numerical simulations and sensitivity analysis demonstrate the efficiency and robustness of the proposed model. Our framework not only enhances theoretical understandings of epidemic resource management but also provides policymakers with actionable strategies for future pandemics.

This paper is concerned with the relationship between general maximum principle and dynamic programming principle for the stochastic recursive optimal control problem with jumps, where the control domain is not necessarily convex. Relations among the adjoint processes, the generalized Hamiltonian function and the value function are proved, under the assumption of a smooth value function and within the framework of viscosity solutions, respectively. Some examples are given to illustrate the theoretical results.

The overuse and misuse of antibiotics has become a major problem for public health. People become resistant to antibiotics and because of this the anticipated therapeutic effect is never reached. In-hospital infections are often aggravated and large amounts of money are spent for treating complications in the patients' condition. In this article a nonlinear optimal (H-infinity) control method is developed for the dynamic model of bacterial infections exhibiting resistance to antibiotics. First, differential flatness properties are proven for the associated state-space model. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed method achieves stabilization and remedy for the bacterial infection under moderate use of antibiotics.

In recent years, there has been considerable research on testing alphas in high-dimensional linear factor pricing models. In our study, we introduce a novel max-type test procedure that performs well under sparse alternatives. Furthermore, we demonstrate that this new max-type test procedure is asymptotically independent from the sum-type test procedure proposed by Pesaran and Yamagata (2023). Building on this, we propose a Fisher combination test procedure that exhibits good performance for both dense and sparse alternatives.

In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of $n$ distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to purchase to complete the whole collection. In this work, we extend the classical problem to $k$ players who compete with one another to be the first to collect the whole collection. We find the expected numbers of boxes required for the slowest and fastest players to finish the game. The odds of a particular player being the slowest or fastest player will also be touched upon. Using the law of total expectation, the solutions will be discussed from both the tractable recurrence relation as well as the probability point of views.

In recent decades, significant advancements have been made in the rigorous runtime analysis of Evolutionary Algorithms (EAs). However, in the context of non-elitist EAs and the use of crossover, it is challenging to engage in any meaningful theoretical discussion due to the increasing complexity of the EA's population distribution as the EA runs. This paper aims to gain insight into the rigorous runtime analysis of the $(\mu,\lambda)$ EA with crossover, focusing on its optimization of the JUMP test function, by investigating the population distribution during the optimization process. It is proposed that, under typical circumstances, the population distribution will first reach a stable and fully-diverged state before attaining the global optimum. Consequently, the optimization process is divided into two parts, based on whether the population distribution has reached this state. By investigating this state, we are able to provide a better upper bound on the runtime of the EA. Furthermore, a series of experiments were conducted to validate our theoretical results, which also offered insights into the impact of different parameters on this state.

This paper investigates a dynamic mean variance investment decision problem with partial information, where the stock return is assumed to consist of an observable factor and an unobservable factor, which both follow mean reversion processes. Through the Bayesian learning mechanism, the unobservable components of stock returns can be learned by investors from available information, including stock prices and observable returns. Due to lack of time consistency in dynamic investment decision problem with mean-variance criterion, we solve this problem by using a game theory approach and characterize the equilibrium investment strategy through the extended Hamilton-Jacobi-Bellman equation (HJB) equations system. we obtain the analytic solution of the dynamic mean-variance model. By solving the extended HJB equations system, the semi-analytical solutions of the equilibrium strategy and the corresponding value function are obtained. In addition, the influence of unobserved predictor and learning mechanism on the equilibrium investment strategy is also analyzed by utilizing numerical examples.

This study addresses the fault detection problem in multi-agent systems (MASs) with additive faults and stochastic uncertainties. The main focus is on enhancing the fault detection capability of each agent through a cooperative fault detection scheme, fostering cooperation between agents in two scenarios. For Gaussian uncertainties, one scheme is developed using the maximum likelihood estimation (MLE) matching expectation maximization (EM) algorithm. Additionally, a novel cooperative fault detection scheme is introduced to handle non-Gaussian uncertainties, where the cooperation mechanism among agents is determined by approximating non-Gaussian uncertainties using the Gaussian mixture model (GMM). The effectiveness and improvements of the proposed cooperative fault detection method are validated through numerical simulations.

This paper focuses on the trajectory tracking control problem of unmanned underwater vehicles (UUVs) with unknown dead-zone inputs. The primary objective is to design an adaptive trajectory tracking error constraint controller using the fully actuated systems (FAs) approach to enable UUVs to asymptotically track target signals. Firstly, a novel error constraint fully actuated systems (ECFAs) approach is proposed by incorporating the tracking error dependent normalized function and barrier function along with time-varying scaling. Secondly, in order to deal with the model uncertainties of the UUVs, adaptive radial basis function neural networks (RBFNNs) is combined with the ECFAs approach. Then, a positive time-varying integral function is introduced to completely eliminate the effect of the residual effect caused by unknown dead-zone inputs, and it is proved that the trajectory tracking error converges to zero asymptotically based on the Lyapunov functions. Finally, the simulation results demonstrate the effectiveness of the designed adaptive controller.

In this paper, a cross-sensor generative self-supervised learning network is proposed for fault detection of multi-sensor. By modeling the sensor signals in multiple dimensions to achieve correlation information mining between channels to deal with the pretext task, the shared features between multi-sensor data can be captured, and the gap between channel data features will be reduced. Meanwhile, in order to model fault features in the downstream task, the salience module is developed to optimize cross-sensor data features based on a small amount of labeled data to make warning feature information prominent for improving the separator accuracy. Finally, experimental results on the public datasets FEMTO-ST dataset and the private datasets SMT shock absorber dataset(SMT-SA dataset) show that the proposed method performs favorably against other STATE-of-the-art methods.

Existing structural analysis methods may fail to identify all hidden constraints in systems of differential-algebraic equations with parameters, particularly when the system is structurally unamenable for certain parameter values. In this paper, we address numerical methods for polynomial systems of differential-algebraic equations using numerical real algebraic geometry to resolve such issues. Initially, we propose an embedding method that constructs an equivalent system with a full-rank Jacobian matrix for any given real analytic system. Secondly, we introduce a witness point method, which assists in detecting the constant rank of a component of the constraints in such systems. Finally, these two methods lead to a comprehensive numerical global structural analysis method for polynomial differential-algebraic equations across all components of constraints.

The safety of vehicle travel relies on good stability performance, making vehicle motion control a vital technology in vehicles. This paper focuses on investigating the impact of roll control on vehicle performance, particularly in terms of avoiding rollover and ensuring lateral stability. By introducing a feedback roll moment, the roll motion can be effectively controlled. The paper considers two roll reference generators: a static one aimed at zero roll, and a dynamic one based on the vehicle's lateral acceleration. The static roll reference generator enhances stability by employing a fixed reference, particularly beneficial during routine driving conditions. In contrast, the dynamic roll reference generator continually adapts the roll angle reference in response to real-time vehicle dynamics and driving conditions. These proposed reference generators can be paired with varying suspension systems — static reference could be achieved using semi-active suspensions, while the dynamic one is integrated into advanced active suspension systems, offering heightened adaptability and performance.} To address the roll control objectives, this paper proposes a novel Sum Of Squares (SOS) integral polynomial tracking control. The proposed controller satisfies control bounds and considers control constraints during the design phase. The effectiveness and robustness of the proposed control scheme are evaluated through numerical simulations using a full vehicle nonlinear model in MATLAB/Simulink. The results of these simulations are compared to super-twisting sliding mode and Lyapunov-based controllers.