查看更多>>摘要：Denote by T(s ,t) the set of trees, whose vertex set can be partitioned into two independent sets of sizes s and t respectively. Given a tree T with stationary distribution pi and a vertex v is an element of T , the access time HT (tau , v ) is the expected length of optimal stopping rules from pi to v . In this paper, we get a sharp upper bound for max(v is an element of T) HT (pi, v ) and a sharp lower bound for min(v is an element of T)H(T)(pi ,v) among T(s ,t), respectively. The corresponding extremal graphs are also obtained. As a byproduct, it is proved that the path Pn maximizes max(v is an element of T) H-T ((pi) over bar, v ) and the star K-1,K-n-1 minimizes minvET HT ((pi) over bar, v ) among all trees on n vertices. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper discusses the issue of observer-based sliding mode control for fuzzy stochastic semi-Markov switching systems (S-MSSs) under cyber attacks. The underlying control signal is vulnerable to the deception attacks, in which the opponents inject fake data into the signal in a probabilistic way. Inspired by the unmeasurable states, an integral sliding surface dependent on a fuzzy observer is designed. Then, in consideration of the deception attacks, the conditions are established to achieve the stochastic stability for fuzzy sliding mode dynamics. Moreover, the proposed observer-based sliding mode control law guarantees the reachability of the sliding region. In the end, the simulation study on a single-link robot arm model is given to demonstrate the availability of the given results. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the source term of energy distribution in double distribution function approach is analysed in detail and a new discrete model is proposed to eliminate the error terms in previous models. The newly proposed model contains two coupling terms, i.e. a velocity-source coupling term and a temperature-force coupling term. The velocity-source coupling term is related to the transport of source which affects the accuracy of simulations of convection, chemical reaction and so on. The temperature-force coupling term is related to the inner product of force and temperature gradient which affects the accuracy of simulations of boundary layer and the edge of plumes in convection. We extended two new heuristic treatments to handle the adiabatic and isothermal boundary conditions. Their efficiency and accuracy are analyzed theoretically and proved by some numerical validations. Finally, we simulated natural convection flows with compression work and viscous dissipation over a wide range of Eckert number using the present model and obtained a scaling law between average Nusselt number and Eckert number. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the finite-time l(2)- l(infinity) filtering problem is investigated for discrete-time switched piecewise-affine systems against deception attacks, where switching signals are subject to the persistent dwell-time strategy. Considering the effect of deception attacks, a set of random variables obeying the Bernoulli distribution is used to describe the probability of false data injection between the plant and the filter. Based on the partition of state space with different operating regions, the objective of this paper is to design a mode-dependent and region-dependent filter such that the filtering error system is finite-time bounded and satisfies an l(2)- l(infinity) performance. By resorting to Lyapunov stability theory and finite-time analysis theory, some sufficient conditions are proposed to obtain such a desired filter. Finally, the availability of the proposed approach is demonstrated by two simulation examples. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This work studies the robust coordination control for a strong coupled and under-actuated unmanned autonomous helicopter (UAH) slung-load system subject to external disturbances. Firstly, disturbance observers are designed to obtain the disturbance estimations, and a dynamic coupling matrix is introduced to describe the coupling relationships between the UAH system and the slung-load system. Secondly, based on the proposed coupling matrix, a disturbance observer-based coordination control scheme is designed for the position system of the UAH and the slung-load one by using hierarchical sliding mode control. Thirdly, an improved controller is designed for the attitude system of the UAH by combining the backstepping control, disturbance observer, and dynamic surface control, in which the detrimental coupling is suppressed while the beneficial one is retained to improve control performance. Especially, the stability for the overall closed-loop system is guaranteed based on Lyapunov stability theory. Finally, some simulations are presented to show the effectiveness and advantage of the proposed control scheme. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the quasi-synchronization problem of heterogeneous fractional-order coupled neural networks (HFCNNs) is studied. In addition, we also take the spatial diffusion effect into consideration, and design an adaptive controller to attenuate the interference of heterogeneous terms. On the one hand, for quasi-synchronization, we propose a nonlinear distributed control law based on local information exchange between neighboring nodes, so that the synchronization error converges to a regulable bounded domain with a certain decay rate. On the other hand, leader-following quasi-synchronization, the reference trajectory is designed in advance and the corresponding distributed controller is developed to make the synchronization errors still tending to the bounded set. Finally, the simulation results show that the theoretical results are correct. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper is concerned with unconditional stability and optimal convergence of mass conservative type method for simulating wormhole propagation in porous media. Specifically, mass conservative characteristic finite element method (FEM) is used for the solute transport equation, the mixed FEM is used for velocity-pressure equation and Galerkin FEM for porosity equation. By error splitting technique, we prove the error of the solution between full discrete system and time discrete system is time-independent, while the numerical solution is bounded without certain time step restriction. Moreover, the optimal L-2 error estimates further hold in a general case by elliptic quasi-projection, where the unconditional r + 1 order accuracy of the concentration and porosity can be obtained with no loss of accuracy for r order approximation velocity-pressure equation. Numerical experiments are presented to verify the theoretical analysis and the effectiveness of the proposed method. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：There were many researches in source localization problem such as relative localization with GPS(Global Positioning System) and target tracking with wireless sensor network. When there is no noise or a little noise, there have been studies about an analytic solution. However, when the noise is not negligible, only the existence of local l(2) minimizing solution and the existence and uniqueness of l(1) minimization are known in particular conditions. This paper demonstrates the exact location of the source, which is the solution of l(1) minimization for squared distance errors with three measurements. It also shows that the number of sources is less than 3, and the nonunique cases with two or three solutions are classified in detail and presented along with some examples. We considered four critical points and their related singular points in the measurement circles. A few numerical implementations for the exact locations of the source are provided and compared with the approximated level set using many measurement grid points. (c) 2022 Published by Elsevier Inc.
查看更多>>摘要：In this article, we first discuss the 3-total rainbow index of unicyclic graphs. Moreover, we show a sharp upper bound for the 3-total-rainbow index of general graphs. Finally, we determine the 3-total-rainbow index of all small cubic graphs of order 8 or less. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this article, a compact difference method is proposed for fractional viscoelastic beam vibration in stress-displacement form. The solvability, the unconditional stability and the convergence rates of second-order in time and fourth-order in space are rigorously proved for the fractional stress v and the displacement u, respectively, under a mild assumption on the loading f. Numerical experiments are given to verify the theoretic findings. One of the main contributions of this article is to evaluate the positive lower- and upper-bound of the eigenvalues of the Toeplitz matrix Lambda generated from the weighted Grunwald difference operator for fractional integral operators, and thus prove that the matrix Lambda is positive definite and can induce a norm in a vector space. This finding improves significantly the existing semi-positive definiteness theory of the matrix Lambda for fractional differential operators and facilitates the proof of the stability and convergence for the stress v. (C) 2022 Elsevier Inc. All rights reserved.
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