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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]

This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma _1 \subset \Gamma _2 \subset \mathbb {R}^n$ , with $\Gamma _1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $\Gamma _1$ that holds relative to $\Gamma _2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $\Gamma _1$ , then $\Gamma _1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal. [ABSTRACT FROM AUTHOR]

This paper proposes a new optimal control synthesis algorithm for multirobot systems under global temporal logic tasks. Existing planning approaches under global temporal goals rely on graph search techniques applied to a product automaton constructed among the robots. In this paper, we propose a new sampling-based algorithm that builds incrementally trees that approximate the state space and transitions of the synchronous product automaton. By approximating the product automaton by a tree rather than representing it explicitly, we require much fewer memory resources to store it and motion plans can be found by tracing sequences of parent nodes without the need for sophisticated graph search methods. This significantly increases the scalability of our algorithm compared to existing optimal control synthesis methods. We also show that the proposed algorithm is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our approach can synthesize optimal plans from product automata with billions of states, which is not possible using standard optimal control synthesis algorithms or model checkers. [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]

Purpose This paper aims to study the heat transfer phenomenon occurring between heated walls and impinging fuel, showing the strict relationship between cooling effect after impingement and enhancing of wallfilm formation. The study focuses on a fundamental task in terms of pollutant emissions in internal combustion engines, aiming at giving a major contribution to the optimization of energy conversion systems in terms of environmental impact.Design/methodology/approach The paper is based on experimental campaigns relevant at taking measurements of an impinging spray over a heated wall in a confined vessel. The results, in both qualitative and quantitative terms (measurements of liquid and vapour radial penetration and thickness), are numerically reproduced by a computational model based on a Reynolds Averaged Navier Stokes approach, properly validated through customized sub-models.Findings The paper provides quantitative results about the agreement between radial penetration and vapour thickness between measurements and simulation, achieved by taking into account the cooling effect determined by the fuel impingement. This validation of the numerical model allows the author to give more considerations about the link between wall temperature and wallfilm formation.Originality/value This paper presents an original approach for the simulation of wall heat transfer, by imposing a boundary condition at the wall that may consider the heat conduction and temperature cooling given by fuel impingement in both lateral and normal directions. The classical Dirichlet boundary condition, characterized by imposing a fixed temperature value, is, instead, replaced by an approach based on calculating the unsteady process that couples the heat fluxes between the fluid and the solid material and within the solid itself. [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]

This paper deals with the consensus tracking problem for a multiagent system with nonholonomic chained-form dynamics. A new distributed observer is first proposed for each follower to estimate the leader state and the leader input in a prescribed finite-time under both undirected and directed communication graphs. Then based on the observer and by adding a power integrator, a novel nonlinear protocol is designed such that the estimated leader state is tracked in a prescribed finite-time. Different from some existing finite-time consensus tracking approaches, an explicit bound without dependence on initial states is derived for the settling time. Therefore, in an unknown environment where initial conditions are unavailable, the proposed strategy is able to meet specific system requirements, e.g., a military target is tracked by a group of field robots in a prescribed time. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

This paper presents continuous-time multiagent systems for distributed minimax optimization subject to bounded constraints. All agents in the system are divided into two groups for minimization and maximization. The multiagent system features competitive intergroup interactions and cooperative intragroup interactions, both of which are based on the output information of agents. First, a proportional-integral (PI) intragroup interaction rule is utilized for consensus within each group in the system. With this interaction rule, the system is proved to be convergent to an optimal solution to the problem, under a certain requirement on the intergroup interactions. Second, another discontinuous intragroup interaction rule is introduced. It is proved that the system with such an interaction is still convergent to an optimal solution if the proportional gain exceeds a derived lower bound, without the previous requirement on the intergroup interactions. As a special case, the systems are further applied for distributed optimization. Finally, simulation results are presented to substantiate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global exponential stability of a $2\times 2$ linear hyperbolic system with a sampled-data boundary feedback control designed by means of the backstepping method for a nominal continuous input. We show that there exists a sufficiently small intersampling time (that encompasses both periodic and aperiodic sampling) for which the global exponential stability of the closed-loop system is guaranteed. In addition, we provide easily tractable sufficient stability conditions that can be used to find an upper bound of the maximum intersampling time. The results rely on the combination of the Lyapunov method and looped-functionals. The effectiveness of the proposed results is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios. [ABSTRACT FROM AUTHOR]

Equilibrium-independent dissipativity (EID) is a recently introduced system property that requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic supply rates for a common class of nonlinear control-affine systems. We provide an algebraic characterization of EID for such systems in the spirit of the Hill–Moylan lemma, where the usual stability condition is replaced by an incremental stability condition. Based on this characterization, we state results concerning internal stability, feedback stability, and absolute stability of EID systems. Finally, we study EID for discrete-time systems, providing the relevant definitions and an analogous Hill–Moylan-type characterization. Results for both continuous-time and discrete-time systems are illustrated through examples on physical systems and convex optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. First, by using the disintegration property of the conditional expectation, sufficient/necessary conditions are given for the internal stability of the concerned systems. Second, in order to separate the unknown exogenous disturbance from the state variables, the properties of convex functions are applied to prove the stochastic version of bounded real lemma (BRL). Third, the state feedback $H_\infty$ control problem is studied, and an $H_\infty$ control is designed based on the BRL. Finally, two numerical examples and one real-world regulation control example of synthetic genetic circuit are presented to show the effectiveness of our developed theory. [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]

This paper considers the stability analysis of nonlinear Lurie type systems where the nonlinearity is both (locally) sector and slope restricted. Convex conditions for verifying stability, computing outer estimates of reachable sets, and upper bounds on the induced $\mathcal {L}_2$ gain in a local or global domain are proposed. The conditions use a Lyapunov function that is quadratic on both the states and the nonlinearity and has an integral term on the nonlinearity. Numerical examples outline the benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

The goal of this paper is to explore the relationship between the network graph of a state-space representation of an observed process and the causal relations among the components of that process. We will show that the existence of a linear time-invariant state-space representation, with its network graph being the star graph, is equivalent to (conditional) Granger noncausal relations among the components of the output process. Granger noncausality is a statistical concept, which applies to arbitrary processes and does not depend on the representation of the process. That is, we relate intrinsic properties of a process with the network graph of its state-space representations. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of computing the distance between a given singular descriptor system $ (E,A)$ , and a nearest descriptor system that has impulsive initial conditions. The link between existence of impulsive initial conditions and zeros at infinity for the associated matrix pencil $sE - A$ is well-known. Much of the literature focusses on the case when only one of $E$ and $A$ is perturbed. We give a closed form expression of the distance to a nearest descriptor system having impulsive solutions via rank-1 perturbations when both $E$ and $A$ are perturbed. Next, for the case of perturbations without rank restrictions, we propose and evaluate the bounds for the distance. In the context of structured perturbations, we formulate and obtain an explicit expression for the distance, when $E$ and $A$ are Hermitian and are perturbed by Hermitian matrices. For a suitable class of systems, we also show that upper and lower bounds are within a factor of $\sqrt{2}$. We finally construct examples and compare the bounds obtained from our results with those from the literature as well as with computed values of the distance obtained via three numerical optimization techniques such as the structured low rank approximation, the Broyden–Fletcher–Goldfarb–Shanno algorithm, and direct optimization tools like globalsearch. [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]

This paper presents a systematic framework to analyze the global pinning-controllability of general complex networks with or without time-delay based on the properties of M-matrices and directed spanning trees. Some stability criteria are established to guarantee that a network can be globally asymptotically pinned to a homogenous state. By partitioning the interaction diagraph into a minimum number of components, a selective pinning scheme for a complex network with arbitrary topology is proposed to determine the number and the locations of the pinned nodes. In particular, this paper deeply investigates the roles of network nodes in the pinning control, including what kind of nodes should be pinned and what kind of nodes may be left unpinned. Numerical simulations are given to verify the theoretical analysis. [ABSTRACT FROM PUBLISHER]

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]