查看更多>>摘要：This paper deals with the stabilization problem for non-smooth variable-order Riemann-Liouville fractional switched systems with all modes unstable in the presence of unknown nonlinearity. A controller containing the discontinuous switching item and Riemann-Liouville fractional-order derivative term is firstly designed. By applying fractional order calculation, non-smooth analysis theory and Lyapunov stability theory, some criteria are established under the joint design of controller and state-dependent switching law. An application to variable-order fractional switched permanent magnet synchronous motors is demonstrated and relevant numerical simulations for considered system are given to verify the validity of our designed scheme. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Weight initialization plays an important role in training neural networks and also affects tremendous deep learning applications. Various weight initialization strategies have already been developed for different activation functions with different neural networks. These initialization algorithms are based on minimizing the variance of the parameters between layers and might still fail when neural networks are deep, e.g., dying ReLU. To address this challenge, we study neural networks from a nonlinear computation point of view and propose a novel weight initialization strategy that is based on the linear product structure (LPS) of neural networks. The proposed strategy is derived from the polynomial approximation of activation functions by using theories of numerical algebraic geometry to guarantee to find all the local minima. We also provide a theoretical analysis that the LPS initialization has a lower probability of dying ReLU comparing to other existing initialization strategies. Finally, we test the LPS initialization algorithm on both fully connected neural networks and convolutional neural networks to show its feasibility, efficiency, and robustness on public datasets. (C) 2021 Published by Elsevier Inc.
查看更多>>摘要：Given a set of n red and n blue points in the plane, we are interested in matching red points with blue points by straight line segments so that the segments do not cross. We develop a range of tools for dealing with the non-crossing matchings of points in convex position. It turns out that the points naturally partition into groups that we refer to as orbits, with a number of properties that prove useful for studying and efficiently processing the non-crossing matchings. Bottleneck matching is a matching that minimizes the length of the longest segment. Illustrating the use of the developed tools, we solve the problem of finding bottleneck matchings of points in convex position in O(n(2)) time. Subsequently, combining our tools with a geometric analysis we design an O(n)-time algorithm for the case where the given points lie on a circle. The best previously known running times were O(n(3)) for points in convex position, and O(n log n) for points on a circle. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The main aim of this paper is to propose a Galerkin finite element method (FEM) for solving the Klein-Gordon-Zakharov (KGZ) equations with power law nonlinearity, and to give the error estimations of approximate solutions about the electronic fast time scale component q and the ion density deviation r. In which, the bilinear element is used for spatial discretization, and a second order difference scheme is implemented for temporal discretization. Moreover, by use of the combination of the interpolation and Ritz projection technique, and the interpolated postprocessing approach, for weaker regularity requirements of the exact solution, the superclose and global superconvergence estimations of q in H-1 - norm are deduced. At the same time, the superconvergence of the auxiliary variable phi (-Delta phi = r(t)) in H-1-norm and optimal error estimation of rin L-2-norm are derived. Meanwhile, we also discuss the extensions of our scheme to more general finite elements. Finally, the numerical experiments are provided to confirm the validity of the theoretical analysis. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper investigates the problem of resilient decentralized control for nonlinear inter-connected systems with unknown control directions under denial-of-service (DoS) attacks. For each subsystem, a novel switched sampled-data observer and an adaptive control architecture are respectively proposed to deal with the unavailable correction term in the existing results. Then a resilient decentralized adaptive controller is developed by employing the backstepping technique to reduce the negative influences of the system uncertainties and DoS attacks. By using average dwell time (ADT) and piecewise Lyapunov stability theories, one can ensure that the closed-loop system is semiglobally uniformly ultimately bounded (SUUB), while the output reference signal of each subsystem is tracked bounded. Furthermore, this scheme has a better utilization of computing and communication resources. Finally, the proposed scheme is verified by a power network system simulation. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Determining water surface profiles of steady open channel flows in a one-dimensional bounded domain is one of the well-trodden topics in conventional hydraulic engineering. However, it involves Dirichlet problems of scalar first-order quasilinear ordinary differential equations, which are of mathematical interest. We show that the notion of viscosity solution is useful in thoroughly describing the characteristics of possibly non-smooth and discontinuous solutions to such problems, achieving the conservation of momentum and the entropy condition. Those viscosity solutions are the generalized solutions in the space of bounded measurable functions. Generalized solutions to some Dirichlet problems are not always unique, and a necessary condition for the non-uniqueness is derived. A concrete example illustrates the non-uniqueness of discontinuous viscosity solutions in a channel of a particular cross-sectional shape. (C) 2021 The Authors. Published by Elsevier Inc.
查看更多>>摘要：This article is devoted to exploring the synchronization problem of coupled memristive neural networks (CMNN) under event-triggered control (ETC) for the first time. Firstly, combining the concept of Filippov solution with the theory of differential inclusion, the interval parameter system is introduced. Then, static event-triggered control (SETC) condition and dynamic event-triggered control (DETC) condition are given respectively based on a newly designed controller. Thirdly, some novel sufficient conditions are given to synchronize CMNN under ETC scheme by applying Lyapunov function and inequality techniques. Moreover, the positive lower bound of the trigger interval is calculated explicitly, which reveals that Zeno-behavior could be removed. Lastly, the validity of the provided ETC mechanism is further confirmed by an example. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The element-free Galerkin method is proposed for the dynamic Signorini contact problems with friction in elastic materials. The Dirichlet boundary conditions and the constrained conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method indicate that the convergence order depends on the spatial step, the time step, the largest degree of a complete Pascal's monomial basis in the moving least-squares approximation and the penalty factor. Numerical examples verify our theoretical results. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper focuses on the observer-based controller design issue for a class of discrete-time networked nonlinear systems. Due to the stochastic effects, the switching between subsystems occurs. The persistent dwell-time switching mechanism, which is more general than dwell-time switching and average dwell-time switching mechanisms, can well describe these switching cases with both fast and slow switchings. Furthermore, there is packet dropout during data transmission, which is described by Bernoulli white sequence, and a corresponding mechanism is used to compensate for the impact of packet dropout. Then based on the Lyapunov function approach, some sufficient conditions for mean-square exponentially stable and an expected H-infinity performance are derived. Finally, an illustrative example that demonstrates the superiority and feasibility of the proposed method is given. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper proposes an algorithm based on the Shultz iterative method and divided differences to find the roots of nonlinear equations. Using the new method, we present a rapid and powerful algorithm to compute an approximate inverse of an invertible tensor. Analysis of the convergence error shows that the convergence order of the method is a linear combination of the Fibonacci sequence and also is rapid and powerful in finding and keeping sparsity of the obtained approximate inverse of the sparse tensors. The algorithm is extended for computing the Moore-Penrose inverse of a tensor. As an application, we use the iterates obtained by the algorithm as a preconditioner for the tensorized Krylov subspace method, e.g., LSQR based tensor form to solve the multilinear system A star(N) X = B. Several examples are also provided to show the efficiency of the proposed method. Finally, some concluding remarks are given. (C) 2021 Elsevier Inc. All rights reserved.
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