查看更多>>摘要：In this paper, we study the decentralized stabilization problem for large-scale high-order stochastic nonlinear systems with time-varying powers. By using the backstepping design technique, a new decentralized state-feedback controller is constructed to ensure the closed-loop system is globally asymptotically stable (GAS) in probability. Then we further redesign a new optimal controller to solve the decentralized inverse optimal stabilization (IOS) problem. Specifically, our redesigned stabilizing backstepping controller is not only globally asymptotically stable for the closed-loop system but also optimal for the meaningful cost function. Finally, a simulation example is given to illustrate the effectiveness of the designed controllers. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A B S T R A C T The problem of state estimation for nonlinear dynamic systems in the presence of randomly occurring injection attacks (ROIAs) is investigated. This paper requires no prior statistical information of the attacks, which relaxes the assumption of the existing result that the attack probability and the probability density function of attack signals need to be known. With the distribution of the attack probability and attack signals modeled as Beta distribution and Gaussian mixture distribution, a variational Bayesian based adaptive cubature Kalman filter is proposed to approximate the joint posterior distribution of the system state vector and unknown parameters. In addition, the update rules of the state and the statistical parameters of attacks are analytically derived by employing the fixed-point iteration approach. Finally, the effectiveness of the proposed filter is validated through numerical results.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We study and develop new first-order Godunov-type schemes for the weakly hyperbolic pressureless gas dynamics equations and augmented Burgers' equations. Each of these systems carries the information of propagation of waves with the same fluid velocity. The goal is achieved by first obtaining an Engquist-Osher (EO) type scheme for the pressureless system and then by enhancing the upwinding information present in the EO-type scheme to construct more accurate Godunov-type schemes. The resulting schemes present a lesser amount of numerical dissipation than existing Jordan decomposition-based Flux Difference Splitting (FDS) schemes recently proposed in [N. K. GARG, Numer. Algorithms, 83 (2020) 1091-1121] and are compact and robust. These schemes are tested on a number of numerical examples for one- and two-dimensional pressureless equations of gas dynamics and then to augmented Burgers' equations. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The paper is devoted to the comparison of one-dimensional blood flow models in application to the solution of model problems. In the viscid case, the non-Newtonian properties of blood are considered. Original one-dimensional models, based on the Carreau, Carreau-Yasuda, Cross, and Powell-Eyring rheological models, are constructed by the averaging of the Navier-Stokes equations.& nbsp;The approach to the analytical solution of problems in the inviscid case is proposed. The originality of the method is based on the small perturbation of the initial rest state, corresponding to zero velocity. It leads to the solution of the linear wave equations. The solutions of three problems - for the infinite, semi-infinite, and finite intervals are obtained. The examples are presented for the small parameter value & SIM;10 -2. Analytical solutions are used for the comparison of different one-dimensional models of blood flow, where the viscosity (Newtonian and non-Newtonian) is considered. The problems for the viscid models are solved numerically by the third-order WENO scheme. As the results of the comparison of models, the effects of the viscosity and velocity profile are analyzed.& nbsp;From a practical viewpoint, the solutions obtained by the perturbation method can be used for the testing of programs for numerical simulations and for the comparison of different blood flow models.& nbsp;(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We present a simple reactor-scale mathematical model of active biofilm dispersal that is controlled by a quorum sensing system. The model is cast as a system of three ordinary differential equations for the dependent variables biofilm thickness, quorum sensing sig-nal concentration in the reactor, and concentration of the growth limiting substrate in the reactor. The model is investigated with analytical and numerical techniques. We find that a single QS dispersal mechanism, depending on parameters, can lead to (i) continuous cell loss at a signal level at which the biofilm is entirely up-regulated, (ii) periodically repeating almost instantaneous cell loss with the biofilm switching between down-and up-regulated states, (iii) continuous cell loss at a signal level at which the biofilm is entirely down-regulated, or (iv) complete washout. We contrast this with a simple model of starvation induced dispersal, which is cast in the same modeling framework, but shows entirely dif-ferent dynamic behavior, in that it only permits washout or asymptotic convergence to a steady state at break-even concentration, depending on parameters.(c) 2021 Elsevier Inc. All rights reserved.
Mehboob, HiraMaqbool, KhadijaUllah, HameedSiddiqui, Abdul Majeed...
16页
查看更多>>摘要：This study presents the computational analysis of axisymmetric flow of Jeffrey fluid in a permeable micro channel with linear reabsorption. Mathematical formulation of complex problem has been carried out in cylindrical coordinates due to the axisymmetric flow. The nonlinear set of partial differential equations is solved by the recursive approach and hy-drodynamic aspects of axisymmetric flow of Jeffery fluid are explained in detail. Results are achieved for axial and radial velocity, hydrostatic pressure, stream function, leakage flux, and fractional reabsorption on the boundary. Numerical analysis has also been car-ried out to demonstrate the effects of emerging parameters due to linear reabsorption on the boundary of micro channel and relaxation time due to Jeffrey fluid parameters. The findings of the study suggest that axisymmetric flow decelerates by the growing values of relaxation time but the reabsorption rate gives the increasing effect on shear stress, vol-ume flow rate, and transverse velocity. This study is useful for bioengineers to design the medical tools required for the flow of bio fluids.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A novel implicit high-order compact difference scheme is established for the time-fractional Burgers' equation based on a newly developed nonlinear compact operator and the reduction order technique under the uniform mesh and graded mesh. Uniqueness, boundedness, convergence in the pointwise sense and stability in L-2-norm of the discrete solutions are proved by the Browder fixed point theorem and energy argument. Numerical examples with the smooth solution and nonsmooth solution are provided to confirm numerical theoretical results and demonstrate the efficiency of the high-order compact difference scheme.& nbsp;(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This work introduces a novel methodology for transforming a large set of connections into the corresponding set of equations as required by the flattening stage of the compilation process of object oriented models. The proposed methodology uses a compact representation of the connections in the form of a Set-Based Graph , in which different sets of vertices and different sets of edges are formed exploiting the presence of regular structures. Using this compact representation, a novel algorithm is proposed to find the connected components of the Set-Based Graph . This algorithm, under certain restrictions, has the remarkable property of achieving constant computational costs with respect to the number of vertices and edges contained in each set. That way, under the mentioned restrictions, the proposed methodology can transform a large set of connections into the corresponding set of equations within a time that is independent on the size of the arrays contained in the model.Besides describing the new algorithm and studying its computational cost, the work describes its implementation in a Modelica compiler and shows its application in different examples.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We investigate properties of differential and difference operators annihilating certain finite-dimensional spaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this technical note comes from considering subdivision schemes where annihilation operators play an important role. Indeed, subdivision schemes with the capability of preserving exponential functions can be used to obtain an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions, and annihilation operators are useful to automatically detect the frequencies of such functions. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Difference schemes are needed for approximating uncertain differential equations in applications. This paper mainly derives a new difference scheme called the Milstein scheme. It is theoretically shown that the Milstein scheme is superior to the previous Euler scheme. Then the Milstein scheme is applied to the method of moments so that the estimated uncertain differential equation fits the observations better. Moreover, the bias function is introduced to assess the precision of the estimation method. Finally, some numerical examples are given to verify the performance of both schemes and minimum cover estimation.(c) 2021 Elsevier Inc. All rights reserved.
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