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.

Grover's algorithm (a. k. a. @ quantum search process) is one of the most distinguished quantum algorithms, addressing the fundamental problem---how to find goal records from a huge but unstructured database efficiently. It can achieve a relatively optimal success probability after a few Grover iterations for amplitude amplification, which results in a quadratic speed-up in the whole process in terms of the size of database. However, it does not guarantee to achieve that probability within a user-specified error tolerance. So error-bounded quantum search process comes into being. The existing methods introduce extra qubits to meet that tolerance, or exploit high-precision (nonbasic) gates, each of which would be converted to a sequence of basic gates and thus costs much more computational units. In this paper, we employ the strategy of performing more Grover iterations expecting one of a series of local optima to meet the tolerance. To ensure it work rigorously, we identify and exclude three exceptional instances by algebraic number theory, which is reported for the first time. Then we analyze the theoretical complexity of the employed method. It turns out to be in time exponential in the encoding size of the tolerance using basic gates, comparable to the existing method's, while extra space consumption is saved. The experimental performance is validated by extensive examples from real-world data sets ASRS and public Amazon review.

The terrestrial ecosystem is the largest carbon pool in the world, and it is crucial to achieve China’s carbon neutrality goal by effectively removing carbon dioxide from the atmosphere. This study used provincial panel data from 2004 to 2020 and a spatial Durbin model to explore the influencing factors of China’s terrestrial ecosystem carbon sequestration capacity (TECSC) and their spatial spillover effects. The results demonstrate that China’s TECSC exhibits a spatially positively correlated development pattern. Furthermore, forest coverage, economic growth, industrial structure, and technological innovation promote the improvement of the regional TECSC. However, energy consumption hinders the growth of green vegetation, thus inhibiting the advancement of TECSC. Lastly, the study finds that environmental regulations may lead to the relocation of highly polluting firms, which could potentially harm the TECSC in the surrounding regions. The above conclusions can provide scientific decision-making basis for promoting China’s TECSC under the background of carbon neutrality.

Ever since Brockett, Clark and Mitter introduced the estimation algebra method, it becomes a powerful tool to classify finite-dimensional filtering systems. In this paper, we investigate estimation algebra on state dimension $n$ and linear rank $n-1$, especially the case of $n=4$. Mitter conjecture is always a key question on classification of estimation algebra. A weak form of Mitter conjecture states that observation functions in finite dimensional filters are affine functions. In this paper, we shall focus on the weak form of Mitter conjecture. In the first part, it will be shown that partially constant structure of Ω is a sufficient condition for weak form Mitter conjecture to be true. In the second part, we shall prove partially constant structure of Ω for $n = 4$ which implies the weak form Mitter conjecture for this case.

In this paper, we address the attitude regulation problem of uncertain flexible spacecraft with unknown control directions and input disturbances. The major challenges of the problem include the concurrence of the unknown actuation sign and the unknown parameters in both the plant and the external disturbances, along with the impact of vibrations from flexible appendages. To overcome these challenges, we transform the conventional mathematical model of a flexible spacecraft to a multivariable strict-feedback normal form and adopt a systematic approach within the framework of nonlinear output regulation. To solve the attitude regulation and disturbance rejection problem, we introduce a nonlinear internal model candidate to convert the problem into a stabilization problem for an augmented systems. Then, a Nussbaum function-based stabilizer is designed to handle unknown control directions and complete the design. Simulation results are provided to show the effectiveness of the proposed controller.

In this paper we first review the history of Hilbert's Tenth Problem, and then study mixed quantifier prefixes over Diophantine equations with integer variables. For example, we prove that $\forall^2\exists^4$ over $\mathbb Z$ is undecidable, that is, there is no algorithm to determine for any $P(x_1,\ldots,x_6)\in\mathbb Z[x_1,\ldots,x_6]$ whether $$\forall x_1\forall x_2\exists x_3\exists x_4\exists x_5\exists x_6(P(x_1,\ldots,x_6)=0),$$ where $x_1,\ldots,x_6$ are integer variables. We also have some similar undecidable results with universal quantifies bounded, for example, $\exists^2\forall^2\exists^2$ over $\mathbb Z$ with $\forall$ bounded is undecidable. We conjecture that $\forall^2\exists^2$ over $\mathbb Z$ is undecidable.

For functional data, the most popular dimension reduction methods are Functional Sliced Inverse Regression (FSIR) and Functional Sliced Average Variance Estimation (FSAVE). Both FSIR and FSAVE methods are based on the slice approach to estimate the conditional expectation $E[x(t)|y]$. While sliced-based methods are effective for scalar responses, they often perform poorly or even lead to failure for multivariate responses and small sample sizes as the so-called "curse of dimensionality". To avoid this problem, this study proposes a projective resampling method that first projects the multivariate response into a scalar-response and then uses SDR method for the univariate response to estimate the effective dimension reduction space(e.d.r space). The proposed projective resampling method is insensitive to the number of slices and the dimensionality of the response variable. In theory, the proposed resampling method can fully recover the effective dimension reduction space. Furthermore, this study investigates the performance of the proposed method through simulation studies and one real data analysis and compares the proposed method with other methods.

The purpose of this paper is to establish two algorithms for decomposing the radical of a polynomial ideal into an irredundant intersection of prime ideals, which are created by rational univariate representations. In the case of zero-dimensional polynomial sets, the calculation of Gr¨obner bases is not involved. In the case of arbitrary polynomial sets, the times of calculating Gr¨obner bases is less than r if a given set of polynomials is decomposed into r triangular chains.

This paper introduces a bivariate hysteretic integer-valued autoregressive (INAR) process driven by a bivariate Poisson innovation. It deals well with the buffered or hysteretic characteristics of the data. Model properties such as sationarity and ergodicity are studied in detail. Parameter estimation problem is also well address via methods of two-step conditional least squares (CLS) and conditional maximum likelihood (CML). The boundary parameters are estimated via triangular grid searching algorithm. The estimation effect is verified through simulations based on three scenarios. Finally, the new model is applied to the offence counts in New South Wales (NSW), Australia.

In this paper, we take Hubei carbon trading market prices as a sample, and select 27 variables from five aspects: international carbon market prices, energy prices, the macroeconomic situation, exchange rate factors and climate environment. We construct the elliptical approximate factor model and use a robust two step method based on multivariate Kendall’s Tau matrix to extract common factors, identify the influencing factors of carbon prices, make out-of-sample forecasting of carbon prices, and compare with the prediction based on the historical mean of carbon trading market prices. The results show that the prediction of carbon trading market prices using elliptical approximate factor model is more accurate than the prediction based on the historical mean of carbon trading market prices. Among them, fossil energy prices, international carbon prices and climate environment are important influencing factors of carbon trading prices.

This paper studies a dynamical system that models the free recall dynamics of working memory. This model is an attractor neural network with $n$ modules, named hypercolumns, and each module consists of $m$ minicolumns. Under mild conditions on the connection weights between minicolumns, we investigate the long-term evolution behavior of the model, namely the existence and stability of equilibria and limit cycles. We also give a critical value in which Hopf bifurcation happens. Finally, we give a sufficient condition under which this model has a globally asymptotically stable equilibrium consisting of synchronized minicolumn states in each hypercolumn, which implies that in this case recalling is impossible. Numerical simulations are provided to illustrate our theoretical results. Furthermore, a numerical example we give suggests that patterns can be stored in not only equilibria and limit cycles, but also strange attractors (or chaos).

Crowdfunding has experienced rapid development worldwide in recent years and has become a very important approach to raising money for some new-start companies and SMEs (small and medium-sized enterprises). This paper studies the optimal pricing and service strategies in a crowdfunding mechanism by which a project could be realized between a creator and a number of consumers only if the total funds committed by consumers reach the predetermined target within a certain time. Our model shows that the volume strategy is always dominated by the menu strategy, but the menu strategy is invalided when the fundraising target is relatively high. The creator can offer a certain level of services to attract more buyers to participate in the project, but any service is meaningless when the target exceeds the threshold. This paper also proposes suggestions for creators in setting targets and pricing when facing risk-averse buyers. Together, our findings benifit the crowdfunding project creators, making them more likely to succeed and obtain more funds.

Functional testing is key to fulfill quality control in laptop manufacturing and is with great economic value. However, due to the unavailability of practical data, mathematical model and systematic perspective, it has barely been touched from the academic community to date. For the first time, this work provides technical understanding of the key principles of functional testing, mathematically models the general framework, elucidates existing testing strategy under the proposed framework and model, and finally proposes a specified optimization strategy which outperforms existing strategies. This work lays the model foundation for the further optimization of functional testing, and can be regarded as a good example of how a systematic approach can solve practical industrial challenges. } % the abstract \Keywords{Modelling, Motherboard Functional Testing, Laptop Manufacturing, Optimization.

This paper studies sampled-data proportional-integral (PI) control for a basic class of nonlinear uncertain systems. We claim that a process with first-order dynamics can achieve zero steady-state error through a sampled-data PI controller whenever the sampling period $T＜T_0(k_p,k_i,L)$, where $T_0(k_p,k_i,L)$ is a number determined by the parameters $k_p,k_i$ and the Lipschitz constant $L$ of the system. On the other hand, once the sampling period $T$ is given, the two parameters $k_p$ and $k_i$ of the sampled-data PI controller are apparently restricted by $T$, or the setpoint tracking error diverges.

Clustering serves as a pivotal instrument in the realm of gene expression data analysis. This paper proposes a Biclustering Coefficient Estimation (BCE) method to identify groups in the individuals and genes. An alternating direction method of multipliers (ADMM) algorithm with a double fusion penalty is developed to solve the problem. We rigorously establish the oracle properties for the proposed penalized estimator. Numerical studies, including simulations and analysis of a lung adenocarcinoma dataset, suggest that the proposed method is expected to simultaneously recover reasonable potential groups of samples and covariates and provide satisfactory estimates of group coefficients.

We consider a two-period joint inventory and pricing decision problem for a retailer facing strategic customers with behavioral preferences such as reference dependence, loss aversion and risk preferences. We develop and analyze a model that accounts for customers’ behavioral preferences as well as value depreciation on the product, and makes predictions on the retailer’s optimal decisions. Moreover, we demonstrate how the presence of these behavioral preferences and primary parameters will leverage the retailer’s optimal decisions. It is revealed that strategic customers’ loss aversion behavior could benefit the retailer from pushing up the regular price, the stocking quantity and hence the expected profit. However, customer’s value depreciation on the product will drive down these aspects. To alleviate the negative effect of the strategic customers’ behavioral preferences, we suggest the retailer applying inventory commitment strategy and price guarantee policy, which could increase the retailer’s profit beyond the rational expectation equilibrium level in some situations.

Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(n)$ and show the denominator of $r(n)$ can be read from annihilators of $F(n)$. This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones.

Please make sure NO reference number in your Abstract since it is misunderstood independent of full text.

Space-filling designs are popular for computer experiments. Therein space-filling designs with good two-dimensional projection are preferred as two-factor interactions are more likely to be important than three- or higher-order interactions in practice. Considering two-dimensional projection, we propose a new class of designs called group strong orthogonal arrays. A group strong orthogonal array enjoys attractive two-dimensional space-filling property in the sense that it can be partitioned into groups, where any two columns can achieve stratifications on $s^{u_1}times s^{u_2}$ grids for any positive integers $u_1,u_2$ with $u_1+u_2=3$, and any two columns from different groups can achieve stratifications on $s^{v_1}times s^{v_2}$ grids for any positive integers $v_1,v_2$ with $v_1+v_2=4.$ Few existing designs enjoy such appealing two-dimensional stratification property in the literature. And the level numbers of the obtained designs can be $s^3$ or $s^4$. In addition to the attractive stratification property, the proposed designs perform very well under orthogonality and uniform projection criteria, and are flexible in run sizes, rendering them highly suitable for computer experiments.

With the widespread application of model averaging across various fields, the post-averaging inference for model averaging estimators has attracted more and more attention. In this article, we study the asymptotic properties of the parsimonious model averaging estimator in the case of heteroskedasticity, confirming the suitability of the estimator for statistical inference. When a correctly specified model exists in the candidate model set, it is proven that the method can assign the weight to the smallest correct model tending to 1, which further yields its consistency in variable selection and asymptotic normality. Simulation results show that the coverage of the confidence intervals constructed based on the parsimonious model averaging estimator can converge to the nominal level in both homoskedasticity and heteroskedasticity cases. As an illustrative example, we apply the method to the carbon emission data of prefecture-level cities in China for the year 2019.

In this paper, we propose a distributed gradient tracking algorithm with compressed communication to address an aggregative optimization problem under communication constraints. The problem involves minimizing the sum of local cost functions, where each cost function depends on both local and global state variables. We aim to solve this optimization problem through local computation and efficient communication among agents in a network, without the need for a central coordinator. The proposed algorithm combines the variable tracking method to estimate global state variables and a compressed communication scheme to reduce communication costs during the optimization process. Among which, the compressed scheme can encompass both biased and unbiased compressors. Despite the loss of some transmitting information due to quantization, our algorithm can still achieve the exact optimal solution with a linear convergence rate. We validate the theoretical results through simulation experiments on an optimal placement problem.

The fluctuations in weather conditions, such as temperature and wind speed, can impact the process of solar and wind power generation, thereby influencing electricity prices. Real-time price settlement requires a higher resolution than daily frequency to forecast electricity prices. This research proposes a novel mixed-frequency model to address the issue of frequency inconsistency problem between electricity prices and related factors, and successfully applies it to Belgium electricity price forecasting. Firstly, the RU-MIDAS method is used to analyze the dynamic impact of weather conditions on prices. Then, RU-MIDAS is combined with machine learning algorithms to predict the prices. The results of error metrics and MCS test indicate that humidity can improve the prediction accuracy of all four sequences. The prediction ability of wind gusts is comparable to that of the highest price; the former helps predict the last two subsequences, while the latter improves the prediction accuracy of the first two subsequences. Temperature can only help predict the fourth electricity price series, and the forecasting ability of weather factors is consistent with the order of feature importance.}

This paper studies the distributed consensus control for linear multiagent systems under discontinuous communication and control updating. A fully distributed event-triggered adaptive control protocol with strictly positive minimum interevent time (MIET) guarantees is proposed. First,~an event-triggered distributed adaptive control law without using prior global information of network topologies is presented, which achieves asymptotic consensus via discrete control updating and intermittent communication. Then, a hybrid adaptive event-triggering scheme with an internal timer~is~designed that is activated only when the timer decreases to zero from a specified positive value. Under the proposed triggering scheme, not only Zeno behavior is excluded but also a strictly positive MIET between any two consecutive events is guaranteed, which facilitates the physical implementation. In contrast to the existing related results, the proposed fully distributed protocol only needs low-frequency communication and control updating, while ensuring the strictly positive MIET property. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.

In this paper, the singularity-free predefined-time fuzzy adaptive tracking control problem is studied for non-strict feedback (NSF) nonlinear systems considering mismatched external disturbances. An innovative practical predefined-time stability (PPTS) criterion is proposed to provide the theoretical basis for subsequent control design. Compared to the existing predefined-time stability (PTS) criterion, this criterion has a broader application range and can solve the control design issues of nonlinear systems with system uncertainties. Fuzzy logic systems (FLSs) are employed to identify unknown nonlinear functions. Based on the backstepping control technology, a singularity-free predefined-time control (PTC) design method is proposed, in which the hyperbolic tangent function is utilized to avoid the singular problem, and the nature of fuzzy basis function is adopted to resolve the algebraic loop problem. The PPTS of the closed-loop NSF nonlinear system is proven with the Lyapunov theory and the proposed PPTS criterion. Ultimately, the efficiency of the presented PTC design method is verified by several sets of simulations on a single link manipulator system.

In this article, attitude tracking control with arbitrary convergence time for rigid spacecraft is considered. First, a novel time-varying sliding function is proposed to achieve free-will arbitrary time convergence when the system states reside on the sliding surface. With such a sliding function, an attitude tracking controller is designed to guarantee that the states of the closed-loop system converge to the sliding surface within a predetermined time in the presence of external disturbances. The free-will arbitrary time convergences of the closed-loop system and sliding function are illustrated by numerical simulations.

This paper develops distributed algorithms for solving Sylvester equations. We transform solving Sylvester equations into a distributed optimization problem, unifying all eight standard distributed matrix structures. Then we propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence rate. These results are obtained by carefully choosing the step-size of the algorithm, which requires particular information of data and Laplacian matrices. To avoid these centralized quantities, we further develop a distributed scaling technique by using local information only. As a result, our distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable intervals. Finally, we provide three examples to illustrate the effectiveness of the proposed algorithms.