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Abstract: In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework. [Copyright &y& Elsevier]

Time-varying problems frequently arise in the territories of science and engineering, and most of the time-varying problems can be described by dynamic matrix equations. As a powerful tool for solving dynamic matrix equations, the zeroing neural network (ZNN) develops fast in recent years. Convergence and robustness are two main performance indicators of the ZNN model. However, the development of the ZNN is focused on the improvement of its convergence in the past, and its robustness to noises is rarely considered. In order to achieve fast convergence and robustness of the ZNN model, a novel activation function (NAF) is presented in this paper. Based on the NAF, a noise-tolerant parameter-variable ZNN (NTPVZNN) model for solving dynamic Sylvester matrix equations (DSME) is realized, and its fixed-time convergence and robustness to noises are verified by rigorous mathematical analysis and numerical simulation results. Besides, two examples of electrical circuit currents computing and robotic manipulator trajectory tracking using the proposed NTPVZNN model in noisy environment further demonstrates its practical application ability. [ABSTRACT FROM AUTHOR]

An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]

Abstract It is well-known that the quality of random number generators can often be improved by combining several generators, e.g. by summing or subtracting their results. In this paper we investigate the ratio of two random number generators as an alternative approach: the smaller of two input random numbers is divided by the larger, resulting in a rational number from [ 0 , 1 ]. We investigate some basic theoretical properties of this approach and show that it yields a good approximation to the ideal uniform distribution. The focus of this paper, however, is on the empirical performance of the new transformation when applied to different generators. For a thorough statistical evaluation, we use the well-known test suite TestU01 (see L'Ecuyer and Simard, 2007). We apply the ratio transformation to moderately bad generators, i.e. those that failed up to 40% of the tests from the test battery Crush of TestU01. We show that more than half of them turn into empirically very good generators that pass all tests of Crush and BigCrush from TestU01 when the ratio transformation is applied. In particular, generators based on linear operations seem to benefit from the ratio, as this breaks up some of the unwanted regularities in the input sequences. Thus the additional effort to produce a second random number and to calculate the ratio allows to increase the quality of available random number generators, at least in a statistical sense. [ABSTRACT FROM AUTHOR]

Abstract The goal of this paper is to propose an optimal fault tolerant control (FTC) approach for multi-agent systems (MASs). It is assumed that the agents have identical affine dynamics. The underlying communication topology is assumed to be a directed graph. The concepts of both inverse optimality and partial stability are further employed for designing the control law fully developed in the paper. Firstly, the optimal FTC problem for linear MASs is formulated and then it is extended to MASs with affine nonlinear dynamics. To solve the Hamilton-Jacobi-Bellman (HJB) equation, an Off-policy Reinforcement Learning is used to learn the optimal control law for each agent. Finally, a couple of numerical examples are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the finite-time robust control problem of a class of nonlinear time-delay systems with general form, and proposes some new delay-independent and delay-dependent conditions on the issue. First, by developing an equivalent form, the paper studies finite-time stabilization problem, and presents some delay-dependent stabilization results by constructing suitable Lyapunov functionals. Then, based on the stabilization results, we study the finite-time robust control problem for the systems, and give a robust control design procedure. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the finite-time stabilization and robust stabilization for the systems. It is shown that, by using the method in the paper, the obtained results do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden. Moreover, different from existing finite-time results, the paper also presents delay-dependent sufficient conditions on the finite-time control problem for the systems. [ABSTRACT FROM AUTHOR]

• Fractional-order reaction-diffusion system. • Taylor approximation techniques. • Fourier spectral method in high dimension. • Mathematical analysis and numerical simulations of noninteger-order dynamics. In this paper, a competition model which describes the spatial interaction among three species in nonlinear fashion is considered. In the model, the standard time derivative is replaced with the Atangana-Baleanu fractional operator in the sense of Caputo. Linear stability analysis which serves as a guide in the choice of parameters when numerically simulating the full system is also examined. The existence and uniqueness of solutions are studied via a fixed point theorem. Different numerical approximation techniques are introduced. Numerical results presented in one and two dimensions revealed some spatiotemporal Turing patterns such as stripes and spots. [ABSTRACT FROM AUTHOR]

• Fractional-order reaction-diffusion system with Caputo-Fabrizio and Atangana-Baleanu Caputo operators. • Finite difference approximation in one and two dimensions. • Fourier spectral method of approximation. • Mathematical analysis and numerical simulations of time-fractional reaction-diffusion model Locally asymptotically stable. This paper considers mathematical analysis and numerical treatment for fractional reaction-diffusion system. In the model, the first-order time derivatives are modelled with the fractional cases of both the Atangana-Baleanu and Caputo-Fabrizio derivatives whose formulations are based on the notable Mittag-Leffler kernel. The main system is examined for stability to ensure the right choice of parameters when numerically simulating the full model. The novel Adam-Bashforth numerical scheme is employed for the approximation of these operators. Applicability and suitability of the techniques introduced in this work is justified via the evolution of the species in one and two dimensions. The results obtained show that modelling with fractional derivative can give rise to some Turing patterns. [ABSTRACT FROM AUTHOR]

Highlights • Mathematical model for low grade gliomas that fits well to medical data. • Net growth coefficient is split in proliferation and natural death rates. • Global stability of tumour free equilibrium under suitable assumptions is proved. • Sensitivity analysis reveals the impact of model parameters on the solution. Abstract Gliomas are the most frequent type of primary brain tumour. Low-grade gliomas (LGGs) in particular are infiltrative and incurable with a slow evolution that eventually causes death. In this paper, we propose a mathematical model for the growth of LGGs and its response to chemotherapy. We validate our model with medical data and show that the proposed model describes real patients' data quite well. A mathematical analysis of the model shows the existence of a unique non-negative solution. We further investigate the stability of steady-state solutions. In particular, we demonstrate the global stability of a tumour-free equilibrium in the case of sufficiently strong constant and asymptotically periodic treatment. A sensitivity analysis of the model indicates that the proliferation rate has the biggest impact on solutions of the model. We also numerically investigate the stability of the fitting procedure. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider the issues for increasing computation schemes performance while modelling non-isothermal convective diffusion using Caputo fractional derivative model. We propose to solve the considered problem using locally one-dimensional finite difference scheme. As the numerical computation of fractional derivative has the biggest influence on computational complexity, an additional approximation procedure of logarithmic complexity is proposed. The procedure represents finite difference form of the fractional derivative as two sets of partial Taylor series which are modified in the process of sequential computations during modelling. As the considered model is non-isothermal, two coupled processes of different speeds are considered. In this case the use of non-uniform time steps can be efficient to improve performance. The proposed approximation procedure is modified for the case of non-uniform time steps and the trial and error method is used to dynamically change time step length during modelling. Time interval in which such schemes are efficient is experimentally determined. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we aim to compute numerical approximations of the integral of a function by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called indicators which indicate where the variance takes relative large values. The stratification method is based on the optimal allocation strategy in order to decrease the variance from one iteration to another. Numerical experiments show and confirm the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we introduce a new extension to the extreme value type-1 (Gumbel) distribution, by constructing a slash type distribution. The result is a distribution with greater kurtosis than the Gumbel distribution. Properties of the distribution such as moments, moment generating function and kurtosis and asymmetry coefficients for the distribution are studied. Maximum likelihood estimation and moments estimators are applied and a simulation study is presented to illustrate parameter recovery. Results of applications to two real data sets, one from a wind velocity study and the other from snow accumulation indicate that the new model seems to perform better in the presence of atypical observations. Highlights • An extension of the Gumbel model is presented. • This extension allows to obtain a bigger range to the kurtosis coefficient. • Euler's constant and the zeta and polygamma functions are related. • The parameter estimation was approached using the method of moments and the MLE. • Simulations and two real data sets show the good performance of this new model. [ABSTRACT FROM AUTHOR]

Abstract The main intention of the present work is to develop a numerical scheme based on radial basis functions (RBFs) to solve fractional stochastic integro-differential equations. In this paper, the solution of fractional stochastic integro-differential equation is approximated by using strictly positive definite RBFs such as Gaussian and strictly conditionally positive definite RBFs such as thin plate spline. Then, the quadrature methods are used to approximate the integrals which are appeared in this scheme. When we use thin plate spline to approximate the solution of mentioned equation, we encounter logarithm-like singular integrals which cannot be computed by common quadrature formula. To overcome this difficulty, we introduce the non-uniform composite Gauss–Legendre integration rule and employ it to estimate the singular logarithm integral appeared in this case. This method transforms the solution of linear fractional stochastic integro-differential equations to the solution of linear system of algebraic equations which can be easily solved. We also discuss the error analysis of the proposed method and demonstrate that the rate of convergence of this approach is arbitrary high for infinitely smooth RBFs. Finally, the efficiency and accuracy of the proposed method are checked by some numerical examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a meshless numerical wave flume, based on the generalized finite difference method (GFDM), is adopted to accurately and efficiently simulate the interactions of water waves and current. The GFDM, a newly-developed meshless method, is truly free from mesh generation and numerical quadrature. The proposed meshless numerical wave flume is the combination of the GFDM, the second-order Runge–Kutta method, the semi-Lagrangian approach, the sponge layer and the ramping function. The problems of wave-current interactions in flumes with horizontal and inclined bottoms are accurately and stably investigated by the proposed meshless scheme, respectively. The changes of waveform can be obviously found, while the cases of coplanar, opposing and no currents are stably simulated. Besides, the distribution of steady current in the flume with inclined bottom, which is governed by an inverse Cauchy problem, is acquired by the GFDM in a stable manner. Numerical results of wave-current interactions are compared with other solutions to verify the accuracy of the proposed meshless scheme. Additionally, different parameters of the proposed meshless numerical scheme are examined to validate the consistency and stability of the proposed numerical wave flume for solutions of wave-current interactions. [ABSTRACT FROM AUTHOR]

Highlights • We proposed a class of improved stochastic theta methods, driven by the error corrected and exponential error corrected ODEs solvers, to solve a general class of linear and nonlinear stochastic differential equations. • Using the Itô–Taylor expansion under the Lipschitz conditions and linear growth bounds, we analyzed the mean–square convergence of the proposed scheme in the strong sense. • We investigated the numerical stability properties of a linear test equation with real parameters, based on the Descarte's rule of signs, and sufficient conditions for the mean–square stability of solutions are provided. • Numerical examples are reported to confirm the theoretical results, and to illustrate the efficiency of the proposed methods for solving one and two dimensionals stochastic differential equations. Abstract In this paper, we present a family of stochastic theta methods modified by ODEs solvers for stochastic differential equations. This class of methods constructed by adding error correction and exponential error correction terms to the traditional stochastic theta methods. Using the Itô–Taylor expansion, analyzed mean-square convergence under the Lipschitz conditions and linear growth bounds. Also, we concern mean-square stability analysis of our proposed methods. Numerical examples are presented to demonstrate the efficiency of these methods for the pathwise approximation solution of some stochastic differential equations. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with asynchronous stabilization for a class of discrete-time Markovian jump systems. The mode of designed controller is considered to be not perfectly synchronous with the activated mode of the Markovian jump system. In order to achieve the asymptotic stability with asynchronous controller, a conditional probability is introduced to describe the asynchronism of system and controller modes, which is dependent on the active system mode. Besides, due to the difficulty in acquiring all the mode transition probabilities in practice, the transition probabilities of the Markovian jump system and the controllers are supposed to be partially unknown. A necessary and sufficient condition is developed to guarantee the stochastic stability of the resultant closed-loop system and further extended to asynchronous stabilization with partially known transition probabilities. Finally, the effectiveness and advantages of the proposed methods are demonstrated by two illustrative examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a generalized trajectory tracking problem for a closed-loop control system is formulated in the optimal control context. A linear time varying plant is considered to track a closed-loop desired trajectory generated by a given mechanism. The theoretical results are obtained based on the Hamilton-Jacobi-Bellman theory in which some generalized semiquadratic value functions are employed as the Lagrangian. In addition, we employ a non-integer order integral of Riemann-Liouville type as the cost functional, so that the trajectory tracking process can be evaluated in an extended optimum manner wherein the fractionality plays the main role. By selecting a suitable fractional order of the integral, a satisfactory optimal control system can be deduced in which least concentration on selecting the weighting matrices is needed. To show the effectiveness of the results, some numerical examples illustrate the potentials. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the decentralized event-triggered H ∞ control for switched systems subject to network communication delay and exogenous disturbance. Depending on different physical properties, the system state is divided into multiple communication channels and decentralized sensors are employed to collect signals on these channels. Furthermore, decentralized event-triggering mechanisms (DETMs) with a switching structure are proposed to determine whether the sampled data needs to be transmitted. In particular, an improved data buffer is presented which can guarantee more timely utilization of the sampled data. Then, with the proposed DETMs and data buffer, a time-delay closed-loop switched system is developed. After that, sufficient conditions are presented to guarantee the H ∞ performance of the closed-loop switched system by utilizing the average dwell time and piecewise Lyapunov functional method. Since the event-triggered instants and the switching instants may stagger with each other, the influence of their coupling on the H ∞ performance analysis is systematically discussed. Subsequently, sufficient conditions for designing the event-triggered state feedback controller gains are provided. Finally, numerical simulations are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the stability analysis of systems with interval time-varying delay. A new augmented vector containing single and double integral terms is constructed and the corresponding Lyapunov functional with triple integral terms is introduced. In order to improve the estimating accuracy of the derivatives of the constructed Lyapunov functional, single integral inequalities and double integral inequalities via auxiliary functions are employed on the first step, then an extended relaxed integral inequality and reciprocally convex approach are further utilized to narrow the scaling room of the functional derivatives. As a result, some novel delay-dependent stability criteria with less conservatism are derived. Finally, numerical examples are provided to check the effectiveness of the theoretical results and the improvement of the proposed method over the existing works. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a robust self-triggered model predictive control (MPC) scheme is proposed for linear discrete-time systems subject to additive disturbances, state and control constraints. To reduce the amount of computation on controller sides, MPC optimization problems are only solved at certain sampling instants which are determined by a novel self-triggering mechanism. The main idea of the self-triggering mechanism is to choose inter-sampling times by guaranteeing a fast decrease in optimal costs. It implies a fast convergence of system states to a compact set where it is ultimately bounded and a reduction of computation times to stabilize the system. Once the state enters a terminal region, the system can be stabilized to a robust invariant set by a state feedback controller. Robust constraint satisfaction is ensured by utilizing the worst-case set-valued predictions of future states in such a way that recursive feasibility is guaranteed for all possible realisations of disturbances. In the case where a priority is given to reducing communication costs rather than improvement in control performance in a neighborhood of the origin, a feedback control law based on nominal state predictions is designed in the terminal region to avoid frequent feedback. Performances of the closed-loop system are demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract A class of networked nonlinear control systems with norm-bounded uncertainties is presented in this paper. The class is represented by Takagi–Sugeno (T-S) fuzzy models with packet processing. The network loop delay is considered either as known delay or random delay. For the former case, we develop conditions that guarantee the robust asymptotic stability and state-feedback stabilization with strict dissipativity and cast the results in linear matrix inequality (LMI) framework. Next employing a probabilistic-based delay partitioning method to deal with random delay, we establish novel LMI criteria for strict dissipative stability analysis and feedback synthesis. The efficacy of the ensuing techniques is demonstrated by numerical solution of typical examples and Mont Carlo simulation. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to existence and uniqueness of minimal mild super solutions to the obstacle problem governed by integro-partial differential equations. We first study the well-posedness and local Lipschitz regularity of Lp solutions (p ≥ 2) to reflected forward-backward stochastic differential equations (FBSDEs) with jump and lower barrier. Then we show that the solutions to reflected FBSDEs provide a probabilistic representation for the mild super solution via a nonlinear Feynman–Kac formula. Finally, we apply the results to study stochastic optimal control/stopping problems. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the problem of global finite-time stabilization via output feedback for a class of switched stochastic nonlinear systems whose powers are dependent of the switching signal. The drift and diffusion terms satisfy the lower-triangular homogeneous growth condition. Based on adding a power integrator technique and the homogeneous domination idea, output-feedback controllers of all subsystems are constructed to achieve finite-time stability in probability of the closed-loop system. Distinct from the existing results on switched stochastic nonlinear systems, the delicate change of coordinates are introduced for dominating nonlinearities. Moreover, by incorporating a multiplicative design parameter into the coordinate transformations, the obtained control method can be extended to switched stochastic nonlinear systems with nonlinearities satisfying the upper-triangular homogeneous growth condition. The validity of the proposed control methods is demonstrated through two examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper, an active fault tolerant control (AFTC) scheme is proposed for more electric aircraft (MEA) equipped with dissimilar redundant actuation system (DRAS). The effect of various fault/failure of hydraulic actuator (HA) on the system performance is analyzed in this work. In nominal condition, the state feedback control law is designed for primary control surfaces. In the presence of fault/failure of certain HA, control allocation (CA) scheme together with integral sliding mode controller (ISMC) is retrofitted with existing control law and engaged the secondary (redundant) actuators into the loop. A modified recursive least square (RLS) algorithm is proposed to identify the parametric faults in HA and to measure the effectiveness level of the actuator. In an event of failure of all HA's in the system, electro hydraulic actuators (EHA) are taken in loop to bring the system back to its nominal operation. In order to stabilize the closed-loop dynamics of HA and EHA, fractional order controllers are designed separately for each actuator. Simulations on the lateral directional model of aircraft demonstrated the effectiveness of the proposed scheme as compared to the existing methods in the literature. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the parameter estimation problems of multivariate equation-error autoregressive moving average systems. Firstly, a gradient-based iterative algorithm is presented as a comparison. In order to improve the computational efficiency and the parameter estimation accuracy, a decomposition-based gradient iterative algorithm is presented by using the decomposition technique. The key is to transform an original system into two subsystems and to estimate the parameters of each subsystem, respectively. Compared with the gradient-based iterative algorithm, the decomposition-based algorithm requires less computational efforts, and the simulation results indicate that this algorithm is effective. [ABSTRACT FROM AUTHOR]

Abstract The multi-taper spectrum (MTS) estimator enjoys a relatively low computational complexity and high estimation accuracy making it an attractive method for spectrum sensing in cognitive radio (CR) networks. However, it is difficult to guarantee both detection and false alarm probabilities when its design is based on fixed threshold, especially when the noise power fluctuates due to channel conditions. In this paper, a new adaptive threshold method to guarantee both detection and false alarm probabilities for MTS based spectrum sensing is proposed. By means of estimating noise power and signal power, the decision of adaptive threshold is able to adapt the noise fluctuation and achieve efficient trade-off between detection and false alarm probabilities. A closed form expression for the adaptive threshold is derived for both additive white Gaussian noise (AWGN) channel and multipath fading channel. Several metrics are employed to compare the performance of the proposed adaptive threshold method with that of the fixed threshold methods such as: error decision probability, detection probability, false alarm probability and throughput. The obtained results show that the proposed method achieves better spectrum efficiency and high throughput in comparison with the conventional fixed and adaptive threshold methods presented in the literature. [ABSTRACT FROM AUTHOR]

Abstract The power sharing of AC/DC micro-grids is researched in this paper. The proposed strategy mainly include two parts: the primary power event triggering control with secondary control and an adaptive quasi sliding mode voltage control in inner-loop. Firstly, a event triggering power sharing control (ETPSC) based on P − F droop curve is developed to regulate the voltage and frequency of AC and voltage of DC with the aim of the proportional power sharing between AC and DC micro-grids. The triggered threshold of ETPSC can be chosen to decide the transmitted power between AC and DC micro-grids. When the difference power between AC and DC micro-grids is less than the triggered threshold of power flow, there is no power sharing between AC and DC micro-grids, which can less the number of switching the power flow direction and the transmitted line power loss. The ETPSC has a great robust for the disturbances of load and improve the stability of the system. An adaptive quasi-sliding-mode control,which is implemented easily and flexibly with small computational burden and only based on input/output (I/O) measurement data but not the model any more, is used to control voltage in inner-loop. The effectiveness of the proposed control schemes is demonstrated by some numerical simulations and experimental results. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the lag projective synchronization of fractional-order delayed chaotic systems. The lag projective synchronization is achieved through the use of comparison principle of linear fractional equation at the presence of time delay. Some sufficient conditions are obtained via a suitable controller. The results show that the slave system can synchronize the past state of the driver up to a scaling factor. Finally, two different structural fractional order delayed chaotic systems are considered in order to examine the effectiveness of the lag projective synchronization. Feasibility of the proposed method is validated through numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we mainly concentrate on the control issue of a variable length drilling riser under condition of unknown disturbances and output constraint. The studied flexible drilling riser system with variable length, variable tension, variable speed and restricted boundary output is essentially a nonlinear distributed parameter system. For achieving the vibration suppression and ensuring the boundary output within the constrained range, an appropriate control scheme with output signal barrier is put forward by integrating boundary control method, barrier Lyapunov function with finite-dimensional backstepping technique, where disturbance observer is employed for coping with the boundary disturbance. Moreover, the Lyapunov's synthetic method is applied for the steadiness research of the studied flexible drilling riser system, and the simulations are presented to display the usefulness of proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel augmented complex-valued normalized subband adaptive filter (ACNSAF) algorithm is proposed for processing the noncircular complex-valued signals. Based on the augmented statistics, the proposed algorithm is derived by computing a constraint cost function. Due to contain all second-order statistical properties, the ACNSAF algorithm can process the circular and noncircular complex-valued signals simultaneously. Moreover, the stability and mean square steady-state analysis of the proposed algorithm is derived by using the energy conservation principle. Computer simulation experiments on complex-valued system identification, prediction and noise cancelling show that the proposed algorithm achieves the improved mean square deviation and prediction gain compared to the ACNLMS algorithm. And the simulation results are consistent with the analysis results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the problem of synchronization on interval type-2 (IT2) stochastic fuzzy complex dynamical networks (CDNs) with time-varying delay via fuzzy pinning control is fully studied. Firstly, a more general complex network model is considered, which involves the time-varying delay, IT2 fuzzy and stochastic effects. More specifically, IT2 fuzzy model, as a meaningful fuzzy scheme, is investigated for the first time in CDNs. Then, with the aid of Lyapunov stability theory and stochastic analysis technique, some new sufficient criteria are established to ensure synchronization of the addressed systems. Moreover, on basis of the parallel-distributed compensation (PDC) scheme, two effective fuzzy pinning control protocols are proposed to achieve the synchronization. Finally, a numerical example is performed to illustrate the effectiveness and superiority of the derived theoretical results. [ABSTRACT FROM AUTHOR]

Highligths • Construct a novel TRBG architecture. • Present chaotic system based true random bit generation using fixed-point arithmetic to realize on FPGA board. • FPGA implementation of the proposed TRBG scheme with a few number of logical operations. • Verifying randomness of generated bit by carrying out NIST tests. Abstract The aim of this paper is to present a true random bit generator (TRBG) based on a memristive chaotic circuit and its implementation on Field Programmable Gate Array (FPGA) board. The proposed TRBG architecture makes use of a memristive canonical Chua's oscillator and a logistic map as entropy sources, while the XOR function is used for post-processing. The optimal parameter set for the chaotic systems has been chosen by carrying out numerical simulations of the system and adopting the scale index parameter to determine the degree of non-periodicity of the obtained bit streams. The proposed TRBG system has been then modeled and co-simulated on the Xilinx System Generator (XSG) platform and implemented on the Xilinx Kintex-7 KC705 FPGA Evaluation Board, obtaining experimental results in agreement with the expectations. Finally, the system has been validated with statistical analysis by using the NIST 800.22 statistical test suite. [ABSTRACT FROM AUTHOR]

Highlights • A vp-MPM is proposed for weakly compressible problems. • A slope limiter is employed to suppress spurious pressure oscillations. • The vp formulation is incorporated into the ICFEMP to suppress pressure oscillation. • The vp-MPM has much less extra variables than a Hu-Washizu principle based method. Abstract The weakly compressible material point method (WCMPM) suffers from volumetric-locking and numerical oscillation in modeling fluid flow and fluid-structure interaction problems. In this paper, a v-p formulation of the material point method (vp -MPM) is proposed for weakly compressible problems based on a two-field variational principle. As only the velocity v and the pressure p are the independent variables, the v - p formulation has much less extra variables than those based on the Hu-Washizu multi-field variational principle which takes the velocity, strain and stress as independent variables. The pressure is assumed independently in the control volume of each gird node. Spurious pressure oscillation reduces but still occurs at the interface of discontinuity due to large pressure gradient difference across the interface. Therefore, a slope limiter is employed to suppress the oscillation and the general interpolation functions are used to eliminate the cell-crossing error. In order to extend the method to the fluid-structure interaction problems, the v-p formulation is incorporated into the improved coupled finite element material point method. Several numerical examples are presented to validate the vp -MPM. [ABSTRACT FROM AUTHOR]

Highlights • The discrete adjoint mixing-plane is formulated and implemented on a legacy CFD code. • Automatic differentiation is used along hand-differentiation of high-level routines. • Adjoint-based sensitivities show good agreement with finite-differences. • Coupling between rows is evidenced by the computed sensitivities. • Multi-row aero-thermal problems can be efficiently handled. Abstract The use of high-fidelity computational fluid dynamics (CFD) tools in turbomachinery design has seen a continuous increase as a result of computational power growth and numerical methods improvement. These tools are often used in optimization environments, where gradient-based optimization algorithms are the most common due to their efficiency. In cases where the optimization contains a large number of design variables, the adjoint approach for calculating the gradients is beneficial, as it provides a way of obtaining function sensitivities with a computational cost that is nearly independent of the number of design variables. The interaction between adjacent blade rows is of utmost importance for the performance of multistage turbomachines. The most commonly used method to address these effects (i.e. coupling in the simulation of multiple rows) is the mixing-plane treatment, that has become a standard industrial tool in the design environment. In this paper, the formulation and implementation of an adjoint solver for multistage turbomachinery applications are presented, namely the adjoint counterpart of the mixing-plane formulation used in the direct solver. The solver is developed using the discrete ADjoint approach, where the partial derivatives required for the assembly of the adjoint system of equations are obtained using automatic differentiation tools. The sensitivity of several performance metrics relative to neighbor blade/hub row geometry and boundary conditions are shown to highlight the physical coupling in multi-row turbomachines. The verification of the adjoint multistage solver against the finite-difference approach is performed successfully with relative differences below 1 %. [ABSTRACT FROM AUTHOR]

Highlights • Seventh order finite volume compact-WENO scheme is proposed for solving 1D and 2D hyperbolic conservation laws. • The parametrized maximum principle preserving and the parametrized positivity satisfying flux limiter flux limiter is coupled with the scheme. • The one dimensional HLLC flux function is used to compute the interface fluxes. • High-resolution properties with compact stencil. Abstract In this paper, we construct a new seventh-order finite volume compact weighted essentially non-oscillatory (WENO) scheme for solving one and two dimensional hyperbolic conservation laws. We extend the main idea of fifth-order finite volume compact-WENO scheme which comes from the original WENO schemes to construct the present seventh-order scheme, where fourth-order compact stencils will be combined with nonlinear weights to get seventh-order finite volume compact-WENO scheme. The parametrized maximum principle preserving flux limiter is coupled with the seventh-order compact-WENO scheme for solving scalar hyperbolic conservation laws and the parametrized positivity satisfying flux limiter is applied to the new scheme for solving compressible Euler equations to maintain positive density and pressure. The HLLC (Harten, Lax and van Leer) flux function is used to compute the interface fluxes in the finite volume formulation. A number of 1D and 2D numerical tests are performed to demonstrate the efficiency and high-resolution properties of the proposed high-order compact scheme. [ABSTRACT FROM AUTHOR]

Highlights • A new grid system is developed to detect the areas needing high-resolution mesh. • The grid system can locally refine the grid for surface water flow simulation. • The method could accelerate the model by about 3 times without accuracy loss. • The grid system is very suitable for integrating into the shallow water flow model. • The new grid system based model could be used for efficient and accurate prediction. Abstract Aiming at improving the computational efficiency without accuracy losses for surface water flow simulation, this paper presents a structured but non-uniform grid system incorporated into a Godunov-type finite volume scheme. The proposed grid system can detect the key topographic features in the computational domain where high-resolution mesh is in need for reliably solving the shallow water equations. The mesh refinement is automatically carried out in these areas while the mesh in the rest of the domain remains coarse. The criterion determining the refinement is suggested by a dimensionless number with a fixed value of 0.2 after sensitivity analysis. Three laboratory and field-scale test cases are employed to demonstrate the performance of the model for flow simulations on the new non-uniform grids. In all of the tests, the grid system is shown to successfully generate high-resolution mesh only in those areas with abruptly changing topographic features that dominate the flooding processes. To produce numerical solutions of similar accuracy, the non-uniform grid based model is able to accelerate by about two times comparing with the fine uniform grid based counterpart. [ABSTRACT FROM AUTHOR]

Highlights • A direct-forcing IB projection method is proposed for solving FSI problems. • It is a two-stage approach with a prediction-correction process. • A virtual force is introduced and distributed on the immersed solid bodies. • This method allows larger time step than traditional direct-forcing IB methods. • Accuracy of the velocity field is super-linear in space in 1, 2 and maximum norms. Abstract In this paper, we propose a simple and novel direct-forcing immersed boundary (IB) projection method in conjunction with a prediction-correction (PC) process for simulating the dynamics of fluid-solid interaction problems, in which each immersed solid object can be stationary or moving in the fluid with a prescribed velocity. The method is mainly based on the introduction of a virtual force which is distributed only on the immersed solid bodies and appended to the fluid momentum equations to accommodate the internal boundary conditions at the immersed solid boundaries. More specifically, we first predict the virtual force on the immersed solid domain by using the difference between the prescribed solid velocity and the computed velocity, which is obtained by applying the Choi–Moin projection scheme to the incompressible Navier–Stokes equations on the entire domain including the portion occupied by the solid bodies. The predicted virtual force is then added to the fluid momentum equations as an additional forcing term and we employ the same projection scheme again to correct the velocity field, pressure and virtual force. Although this method is a two-stage approach, the computational cost of the correction stage is rather cheap, since the associated discrete linear systems need to be solved in the correction stage are same with that in the prediction stage, except the right-hand side data terms. Such a PC procedure can be iterated to form a more general method, if necessary. The current two-stage direct-forcing IB projection method has the advantage over traditional one-stage direct-forcing IB projection methods, consisting of the prediction step only, by allowing much larger time step, since traditional methods generally request quite small time step for flow field relaxed and adjusted to the solid body movement even using implicit scheme. Numerical experiments of several benchmark problems are performed to illustrate the simplicity and efficient performance of the newly proposed method. Convergence tests show that the accuracy of the velocity field is super-linear in space in all the 1-norm, 2-norm, and maximum norm. We also find that our numerical results are in very good agreement with the previous works in the literature and one correction at each time step appears to be good enough for the proposed PC procedure. [ABSTRACT FROM AUTHOR]

Highlights • Generalization of the 2014 version of the ZIBC combining RANS/LES and the IB method. • Extended presentation of the Zonal Immersed Boundary Conditions approach. • First RANS/LES and IBC application to a full space launcher at high Reynolds number. • ZDES/IBC is highly validated for both the statistical field and the spectral content. Abstract One of the next foreseen challenges in CFD consists in the capability to simulate quantitatively the spectral content of the turbulent flow around realistic geometries. In this context, the present work focuses on a new methodology named ZIBC standing for Zonal Immersed Boundary Conditions enabling to account for complex configurations at high Reynolds numbers. The numerical strategy allowing the coupling between a turbulence modeling method (e.g. RANS, URANS, ZDES, LES or DNS) and IBC (Immersed Boundary Conditions) is detailed. In this paper, the modeling method retained is the Zonal Detached Eddy Simulation (ZDES) which has reached a high level of maturity on turbulent separated flow simulations. This methodology is applied to a full space launcher configuration to assess its capability to return the interactions between the technological details, modeled with IBC, and the simplified afterbody, modeled with a body-fitted (BF) approach consisting in classical no-slip boundary conditions, in the turbulent flow field surrounding the main stage of the space launcher afterbody. The proposed method is thoroughly assessed on a realistic geometry of the European Ariane 5 launcher and the ZIBC simulation is successfully compared with the available experiments. [ABSTRACT FROM AUTHOR]

The unbalanced magnetic pull results in the nonlinearity of the system for the permanent magnet synchronous motor rotor having mixed eccentricity. The mass unbalance and static eccentricity form multi-frequency excitation, which results in the coupling effect of forward and backward whirling motions on the steady-state of super harmonic resonance. The analysis is difficult due to the phases of complex amplitudes of two motions which is no longer time invariant compared with the main resonance. To solve this problem, an analysis method of complex amplitudes is presented in this paper. The rotor is considered a Jeffcott rotor, and multi-scale method is applied to this system. A mathematical analysis method of the complex amplitude phases is employed for their time variant characteristics. The results show that both phases are linear time variant and their variation rates are both equal in magnitude to the difference between twice the excitation frequency and natural frequency of the generating system. The characteristics lead to the frequency shift of the two motions by the difference value from the natural frequency of the generating system. The numerical analysis reveals that the phases are independent of the initial condition and hence the complex amplitudes. The analysis solves two problems: the analytical solution of the rotor system carrying phases information can be expressed, which is in good agreement with the numerical result, and the solution construction is analyzed easily, which indicates the contribution of every component of the analytical solution. The phase characteristics analysis is the prerequisite for the frequency characteristics which can be easily carried out, and the coupling mechanism of the two motions is explained. • A mathematical analysis method is presented to solve the problem of the time variant complex amplitude characteristics. • The mode coupling mechanisms of the forward and backward whirling motions, mass unbalance and static eccentricity are explained. • The frequency shift is discovered which is caused by linear time variant phase of the complex amplitude. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical computation of the matrix p th root of stochastic matrices. In particular a collection of theoretical results concerning the p th root of stochastic matrices is reported and some numerical methods are described. The aim of the paper is to highlight the properties of such methods when they are applied to numerically compute the p th root of a stochastic matrix when it is expected to be stochastic too. [ABSTRACT FROM AUTHOR]

Highlights: [•] The paper presents new results on global stability of second-order interval CGNNs. [•] It is the first paper to study global stability of general second-order interval CGNNs. [•] The new results can also be used to verify the stability of first-order interval CGNNs. [ABSTRACT FROM AUTHOR]

The oriented shift and inverse of double-emulsion globules containing two inner droplets with different sizes and locations in modest extensional flows are investigated numerically in this paper through a boundary element method. The asymmetric layout of daughter droplets leads to the asymmetric inner flow field and pressure field inside the globule, which causes its asymmetric rheological behaviors. The direction of shift is determined not only by the size ratio r R 2 /r L 2 and the location ratio d R /d L of two inner droplets, but also by some flow factors such as the capillary number Ca. There is a critical capillary number Ca c as a function of r R 2 /r L 2 and d R /d L , beyond which the globule will move to the right, otherwise, it will shift to the opposite direction. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we analyze an SIS epidemic model with partially protective vaccination of efficacy e ∈[0, 1]. The model exhibits backward bifurcation for certain parameter values. The primary aim of this paper is to investigate the possibility of eliminating the infections in static as well as exponentially growing populations with a public health strategy based solely on vaccination. The critical vaccination rate ψ * above which the endemic infection dies out and the conditions on model parameters that ensure its existence are obtained. It has been found that eliminating the infection requires an application of control measures other than vaccination to reduce the basic reproduction number to below the reinfection threshold and then vaccinate susceptible individuals with a rate slightly greater than ψ *. The implication is that, generally, even if all newborns get vaccinated immediately after birth, an effective control is not necessarily assured except if the basic reproduction number is reduced to below the reinfection threshold. We further include the fatality of the infection and investigate its impact on the dynamics. Some numerical simulations are given to illustrate the theoretical analysis. [Copyright &y& Elsevier]

Sliced Latin hypercube designs have found a wide range of applications. Such a design is a special Latin hypercube design that can be partitioned into slices which are still LHDs when the levels of each slices are collapsed properly. In this paper we propose a method for constructing sliced Latin hypercube designs with second-order orthogonality. The resulting designs are further augmented to be nearly orthogonal sliced Latin hypercube designs which have much more columns. Also, two methods of generating nearly orthogonal sliced Latin hypercube designs are proposed. The methods are convenient, efficient and capable of accommodating any number of slices. [ABSTRACT FROM AUTHOR]

Approximate Numerical Expressions (ANEs) are linguistic expressions involving numerical values and referring to imprecise ranges of values, illustrated by examples such as “ about 100 ”. In this paper, a general principle is proposed to interpret uncontextualised ANEs as intervals of denoted values. It is based on an empirically justified combination of characteristics of numerical values, both arithmetical and cognitive, and in particular, taking into account the cognitive salience of numbers. This general principle is instantiated in two computational models that can be extended so as to take into account the applicative context. An empirical study is conducted to assess the performances of the two models, comparing them to state-of-the-art methods, on real interpretations collected through an on-line questionnaire. Results validate the proposed characteristics used to build the models and show that they offer the best performances in estimating the median interval chosen as representative of the collected intervals. [ABSTRACT FROM AUTHOR]

Constrained control for stochastic linear systems is generally a difficult task due to the possible infeasibility of state constraints. In this paper, we focus on a finite control horizon and propose a design methodology where the constrained control problem is formulated as a chance-constrained optimization problem depending on some parameter. This parameter can be tuned so as to decide the appropriate trade-off between control cost minimization and state constraints satisfaction. An approximate solution is computed via a randomized algorithm. Precise guarantees about its feasibility for the original chance-constrained problem are provided. A numerical example shows the efficacy of the proposed methodology. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]

Abstract: In this paper, a new epidemic SIS model with nonlinear infectivity, as well as birth and death of nodes and edges, is investigated on heterogeneous networks. The global behavior of the model is studied mathematically. When the basic reproductive number is less than or equal to unity, it is verified that the disease dies out; otherwise, the model solutions lead to positive steady states. This paper provides a concise mathematical analysis to verify the global dynamics of the model. [Copyright &y& Elsevier]