查看更多>>摘要：In this article we propose an adaptive algorithm for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel- based method of lines that allows us to split the spatial and time derivatives, dealing with each separately. This adaptive scheme is based on a leave-one-out cross validation (LOOCV) procedure, which is employed as an error indicator. By this technique, we can first detect the domain areas where the error is estimated to be too large - generally due to steep variations or quick changes in the solution - and then accordingly enhance the numerical solution by applying a two-point refinement strategy. Numerical experiments show the efficacy and performance of our adaptive refinement method. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper investigates the bipartite consensus problem in mean square sense for multi-agent systems subject to multiplicative and additive noises using the event-triggered strategy. Since the control gain is time-varying and agent-dependent, the implementation of event-triggered control may cause desynchrony of the control gain and the time-variation of Laplacian matrix. Moreover, the coexistence of antagonistic information and multiplicative noise gives rise to the difficulty of regarding the error system as the deterministic counterpart. To cope with these challenges, the boundedness of each agent's states is first formulated. Based on it, a criteria for mean square bipartite consensus with event-triggered mechanism is derived by utilizing the semi-decomposition method. Finally, one example is given to show the validity of the event-triggered control protocol. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The Quickhull algorithm for determining the convex hull of a finite set of points was independently conducted by Eddy in 1977 and Bykat in 1978. Inspired by the idea of this algorithm, we present a new efficient algorithm, for determining the connected orthogonal convex hull of a finite set of points through extreme points of the hull, that still keeps advantages of the Quickhull algorithm. Consequently, our algorithm runs faster than the others (the algorithms introduced by Montuno and Fournier in 1982 and by An, Huyen and Le in 2020). We also show that the expected complexity of the algorithm is O(n log n), where n is the number of points. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The impulsive synchronization of fractional-order coupled neural networks (FOCNNs) via an event-triggered law is investigated in this paper. For the objective of conserving computing resources and decreasing network load, an event-triggered impulsive control (ETIC) mechanism depending on state errors is introduced. The event-triggered controller updates only at impulsive instants, which are defined by some certain triggering conditions and not predetermined. Then, by means of fractional Lyapunov theory, the Kronecker product together with the comparison principle and Laplace transform, sufficient conditions depending on fractional order are obtained to achieve event-triggered impulsive synchronization of FOCNNs. Furthermore, it is also proved that there exists a positive constant less than the time interval between arbitrary two consecutive impulsive instants, which means the Zeno phenomenon is eliminated. At last, a numerical simulation of the typical chaotic system is presented to indicate the feasibility of the developed ETIC mechanism and the correctness of the obtained results. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We propose a direct arbitrary Lagrangian-Eulerian (ALE) variant of the previously developed discrete velocity method to solve the kinetic equation with the Bhatnagar-Gross- Krook (BGK) model collision integral. The effectiveness and robustness of the new scheme are demonstrated by computing the axisymmetric plume expansion into a low pressure gas due to evaporation from the solid surface caused by a nanosecond laser pulse. The numerical studies show that the new numerical scheme provides a very significant reduction of the required computing time as compared to the discrete velocity method on a fixed mesh. Cross-comparisons with the direct simulation Monte Carlo (DSMC) approach further confirm the accuracy of the new scheme and model kinetic equations as applied to plume expansion studies. Finally, the good parallel scalability of the new ALE scheme as implemented into the in-house code Nesvetay is demonstrated. The use of two very different approaches to numerical prediction of the transient flow pattern allows us to obtain a reliable numerical solution, which can be regarded as a new transient benchmark test. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this research study, we present an efficient method based on the generalized hat functions for solving nonlinear stochastic differential equations driven by the multi-fractional Gaussian noise. Based on the generalized hat functions, we derive a stochastic operational matrix of the integral operator with respect to the variable order fractional Brownian motion, for the first time so far. Also, we establish a procedure to generate the variable order fractional Brownian motion. Then, we use them to provide numerical solutions for the proposed problems. In addition, the convergence of the new method is theoretically analyzed. Moreover, we solve the stochastic logistic equation, stochastic population growth model, and three test problems to confirm the efficiency of the new method. The obtained results are compared with other existing methods used for solving these problems. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In a recent paper, extreme points (in the Krein-Milman sense) of the class of semilinear copulas were introduced, motivated by the lack of known extreme copulas such as shuffles of M. We propose an extension of this concept to the class of all bivariate shock induced copulas, the most well-known part of them being the Marshall-Olkin copulas. This class properly contains semilinear copulas. Our technique coincides with the existing notion on them and has some advantages. First, it is defined on a wider family of copulas, which is helpful in finding more examples of extreme copulas. Second, we show that they are dense in each class they belong to (including the class of semilinear copulas) in a stronger sense than in the Krein-Milman approach; actually, they are dense in a similar way as shuffles of M are dense in the set of all copulas. Third, this definition enables practitioners to give stochastic interpretation of extremality. Roughly speaking, a shock induced copula is extreme whenever the inducing shocks have pairwise disjoint supports. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The issue of asynchronous mixed H-infinity and passive control for Takagi-Sugeno fuzzy singular delayed Markovian jump system is investigated in this paper. The modes of designed fuzzy controller operate asynchronously with the modes of original system, which can be represented by a hidden Markovian model (HMM). By constructing a delay-dependent and mode-dependent stochastic Lyapunov-Krasovskii functional, new criteria are derived to guarantee that the fuzzy singular delayed Markovian jump system is stochastically admissible with a mixed H-infinity and passivity performance. Then, an asynchronous fuzzy controller is designed successfully via parallel distributed compensation technique and HMM principle based on these criteria. Finally, two simulation examples including a DC motor device are presented to verify the correctness and effectiveness of the derived results. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper addresses the fault detection of Boolean networks (BNs) using semi-tensor product (STP) of matrices. We first introduce the concept of meaningful faults, and give an equivalent condition for fault sequence to be detectable. Next, an algorithm is presented to determine whether it occurs a fault and identify the specific location of the fault. Further, structure matrix of the faulty BNs can be derived. In order to estimate or reduce the impact of the fault on the BN, the global stabilization of BNs is investigated through partial pinning control. Finally, examples are given to illustrate the validity of the given results. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper is concerned with the problem of sampled-data distributed state estimation for a linear continuous-time system with multiple transmission channels under denial-of-service attacks. To solve this problem, sampled-data distributed observers, which only have access to their respective measurable output variables and the information obtained from their neighbors, are designed, where a decomposition form of the coefficient matrices of the system and a time interval division-based method are proposed to deal with the complex interaction of the sampled-data schemes and the attack schemes among different transmission channels. Different from the previous results, the transmission channels from the sensors to the remote observers do not share the same sampled-data scheme and are allowed to be compromised by different adversaries. An example is provided to validate the effectiveness of the proposed method. (C) 2022 Elsevier Inc. All rights reserved.
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