查看更多>>摘要：The paper investigates the backstepping robust control problem for a class of nonlinear networked systems. The non-Lipschitz conditions of linear growth condition and Holder condition are considered in the time-varying disturbance and uncertainty. An important innovation is that the virtual controller is designed to be piecewise constant such that the usage of the command filter is avoided. In the process of designing the robust controller, a semi-synchronous event-triggered scheme is proposed to relieve the communication pressure in high-order systems. Thus, a switched controller without using average dwell time (ADT) is considered. The finite-time practical stability with the form of fast terminal sliding mode (TSM) is also obtained. Then, the Zeno behavior is excluded and a self-triggered scheme is further proposed to avoid the continuous monitoring of the event-triggered conditions. Compared with some existing command-filtered results, the design process is simplified and more suitable for networked systems. The effectiveness of the proposed theory is validated by the numerical simulation of a hypersonic vehicle. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The eccentricity matrix epsilon(G) of a graph G is derived from the corresponding distance matrix by keeping only the largest non-zero elements for each row and each column and leaving zeros for the remaining ones. The epsilon-eigenvalues of a graph G are those of its eccentricity matrix, in which the maximum modulus is called the epsilon-spectral radius. In this paper, we first establish the relationship between the majorization and epsilon-spectral radii of complete multipartite graphs. As applications, the extremal complete multipartite graphs having the minimum and maximum epsilon-spectral radii are determined. Furthermore, we study the multiplicities of epsilon-eigenvalues among complete multipartite graphs and identify all complete multipartite graphs with distinct epsilon-eigenvalues. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper proposes a finite difference method for a differential-algebraic system that couples an elliptic equation with a convection-diffusion-reaction equation with mixed derivatives. Herein the parabolic equation depends on the gradient of the solution of the elliptic equation. If the numerical approximation for this gradient presents lower accuracy then the numerical approximations for the solution of the parabolic equation can be deteriorated. In order to get a second order approximation for the solution of the parabolic equation, the challenges that we have to face are the construction of the right discretizations of the elliptic and parabolic equations that lead to a second order approximation for the gradient as well as the development of the numerical analysis of the proposed method. The differential system analysed can be used to describe the cell density and pressure dynamics in colonic crypts. Numerical simulations of cell dynamics in a crypt of the human colon during the formation of a micro-adenoma are presented. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We present an adaptive-observer-based event-triggered design for distributed three-dimensional output-feedback formation tracking of multiple uncertain underactuated underwater vehicles (UUVs) under a directed network. It is assumed that all nonlinear functions of the vehicle dynamics are unknown and the velocity information of vehicles is immeasurable for feedback. Compared with existing distributed tracking results for UUVs, the primary contribution of this study is the development of a state-transformation-based adaptive observer using a time-varying scaling signal to achieve the output-feedback three-dimensional formation tracking in the presence of unknown nonlinearities and the underactuation constraint. Based on the state transformation, local adaptive observers using neural network approximators and their adaptive laws are designed to estimate local unmeasured velocities of UUV followers. By designing distributed nonlinear error functions and auxiliary stabilizing signals, local output-feedback tracking laws with triggering conditions are recursively constructed to ensure preselected formation performance while solving the underactuation problem of the UUV dynamics. It is shown that the formation tracking errors remain within pre-designable time-varying bounds and finally converge to a neighborhood of the origin. Simulation results are presented to show the effectiveness of the suggested output-feedback formation tracking strategy. (C) 2022 Elsevier Inc. All rights reserved.
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