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This paper proposes a low-cost, penalty parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function. The EG method employs the interior penalty discontinuous Galerkin (IPDG) formulation to weakly impose the continuity of the velocity function. However, despite its advantage of symmetry, the symmetric IPDG formulation requires a lot of computational effort to choose an optimal penalty parameter and compute different trace terms. To reduce such effort, we replace the derivatives of the velocity function with its weak derivatives computed by the geometric data of elements. Therefore, our modified EG (mEG) method is a penalty parameter-free numerical scheme that has reduced computational complexity and conserves the optimal convergence orders. Moreover, we achieve pressure robustness for the mEG method by employing a velocity reconstruction operator on the load vector on the right-hand side of the discrete system. The theoretical results are confirmed through numerical experiments with two- and three-dimensional examples. [ABSTRACT FROM AUTHOR]

This paper enriches a pre-existing decision algorithm, which in turn augmented a fragment of Tarski's elementary algebra with one-argument real functions endowed with a continuous first derivative. In its present (still quantifier-free) version, our decidable language embodies the addition of functions and multiplication of functions by scalars; the issue we address is the one of satisfiability. As regards real numbers, individual variables and constructs designating the basic arithmetic operations are available, along with comparison relators. As regards functions, we have variables of another sort, out of which compound terms are formed by means of constructs designating addition and differentiation. An array of predicates designates various relationships between functions, as well as function properties, that may hold over intervals of the real line; those are: function comparisons, strict and non-strict monotonicity / convexity / concavity, comparisons between the derivative of a function and a real-valued term. Our decision method consists in preprocessing the given formula into an equi-satisfiable quantifier-free formula of the elementary algebra of real numbers, whose satisfiability can then be checked by means of Tarski's decision method. No direct reference to functions will appear in the target formula, each function variable having been superseded by a collection of stub real variables; hence, in order to prove that the proposed translation is satisfiability-preserving, we must figure out a flexible-enough family of interpolating C 1 functions that can accommodate a model for the source formula whenever the target formula turns out to be satisfiable. With respect to the results announced in earlier papers of the same stream, a significant effort went into designing the family of interpolating functions so that it could meet the new constraints stemming from the presence of function addition (along with differentiation) among the constructs of our fragment of mathematical analysis. • A formal language RDF* concerned with differentiable real functions is proposed. • The class of differentiable functions treated is closed under addition. • The expressive power of RDF* is illustrated through a gallery of examples. • A satisfiability-preserving algorithm reducing RDF* formulas into an existential sentence of Tarskian algebra is presented. • The correctness of the reduction algorithm is reported. [ABSTRACT FROM AUTHOR]

• New segmentation deals with intensity inhomogeneity within biological images. • Use of continuous formulation of B-spline level set with RSF active contour model. • Use of Watershed algorithm with a relevant choice of object markers. • The efficiency is proved in terms of qualitative and quantitative evaluation. Image segmentation plays an important role in the analysis and understanding of the cellular process. However, this task becomes difficult when there is intensity inhomogeneity between regions, and it is more challenging in the presence of the noise and clustered cells. The goal of the paper is propose an image segmentation framework that tackles the above cited problems. A new method composed of two steps is proposed: First, segment the image using B-spline level set with Region-Scalable Fitting (RSF) active contour model, second apply the Watershed algorithm based on new object markers to refine the segmentation and separate clustered cells. The major contributions of the paper are: 1) Use of a continuous formulation of the level set in the B-spline basis, 2) Develop the energy function and its derivative by introducing the RSF model to deal with intensity inhomogeneity, 3) For the Watershed, propose a relevant choice of markers that considers the cell properties. Experimental results are performed on widely used synthetic images, in addition to simulated and real biological images, without and with additive noise. They attest the high quality of segmentation of the proposed method in terms of quantitative and qualitative evaluation. The proposed method is able to tackle many difficulties at the same time: overlapped intensities, noise, different cell sizes and clustered cells. It provides an efficient tool for image segmentation especially biological ones. [ABSTRACT FROM AUTHOR]

In this paper, a nearly optimal tracking control is proposed for n -links robotic manipulators subject to parameter uncertainties, time-profile failures, and input saturation constraints. Firstly, the practical terminal sliding-mode (PTSM) manifold with a linear additional term is proposed to combine the system states related to joint rotation, such that the controlled states quickly fall into a tiny neighborhood of the equilibrium once they reach the PTSM manifold. Secondly, a nearly optimal sliding-mode reaching law is designed by using the adaptive dynamic programming (ADP) technique. Benefiting from a non-quadratic positive defined mapping of the proposed performance index, which relates to the derivative of the sliding-mode function, reduced-order system dynamics can be constrained to a desired region. For the bounded actuator fault caused by various inducements such as the power supply fluctuation and the wear of parts, a radial basis function neural network (RBFNN) is introduced to compensate for this, and the input saturation constraints of the controlled plant are also compensated at the same time. Innovatively, the node weights of RBFNN are updated by the critic network of the ADP framework, such that the integrity of the proposed control strategy is improved. Simulations verify the main conclusions. • The hyperbolic tangent function nested with terminal attractor is employed to form a sliding surface, such that the faster convergence of tracking errors. • The adaptive updating of the critic weight is introduced into the RBFNN weight update mechanism, so that the fault information and overrun output of joint actuators can be synchronously compensated. [ABSTRACT FROM AUTHOR]

We derive a change of variable formula for C 1 functions U : R + × R m → R whose second order spatial derivatives may explode and not be integrable in the neighbourhood of a surface b : R + × R m − 1 → R that splits the state space into two sets C and D. The formula is tailored for applications in problems of optimal stopping where it is generally very hard to control the second order derivatives of the value function near the optimal stopping boundary. Differently to other existing papers on similar topics we only require that the surface b be monotonic in each variable and we formally obtain the same expression as the classical Itô's formula. [ABSTRACT FROM AUTHOR]

In this study, the fixed-time synchronization (FXTS) of delayed memristive neural networks (MNNs) with hybrid impulsive effects is explored. To investigate the FXTS mechanism, we first propose a novel theorem about the fixed-time stability (FTS) of impulsive dynamical systems, where the coefficients are extended to functions and the derivatives of Lyapunov function (LF) are allowed to be indefinite. After that, we obtain some new sufficient conditions for achieving FXTS of the system within a settling-time using three different controllers. At last, to verify the correctness and effectiveness of our results, a numerical simulation was conducted. Significantly, the impulse strength studied in this paper can take different values at different points, so it can be regarded as a time-varying function, unlike those in previous studies (the impulse strength takes the same value at different points). Hence, the mechanisms in this article are of more practical applicability. • Novel fixed-time stability theorem with indefinite derivative of Lyapunov function. • Impulse strength can take different values at different impulse points. • New fixed-time synchronization mechanisms via three different controllers. • Settling time is related to the selection of the impulse points and the impulse strength. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fixed-time synchronization for fuzzy inertial neural networks with time-varying coefficients and time delays. The fuzzy inertial neural networks are transformed into two forms of first-order differential systems, and then two kinds of different controllers of time-variable are designed. In these schemes, a series of novel criteria are proposed to ensure the fixed-time synchronization for the drive-response fuzzy inertial neural networks via state feedback control methods. Sufficient conditions of delay-dependent and delay-independent are obtained in terms of algebraic inequalities, not the matrix inequalities. Moreover, these new criteria allow the derivative of the Lyapunov function can be positive, but not negative definite as the earlier work. And the algebraic conditions become easy to be tested under the new criteria. Finally, two examples are added to illustrate effectiveness of the results we obtained. Meanwhile, a new image encryption algorithm is proposed based on the synchronization of drive-response networks, and the effectiveness of this algorithm is also demonstrated. [ABSTRACT FROM AUTHOR]

[Display omitted] • We propose a new approach named NDO-NODE to stabilize the training and improve generalization of NODE, which injects the inductive bias of a function library on derivative calculation. • We prove the generalization ability of the learned NDO: it can output derivatives for functions belonging to the library with small errors. • Experiments show that NDO-NODE can consistently improve both the interpolation and extrapolation accuracy on these tasks with one pre-trained NDO. Also, it can stablize the training for stiff ODEs. Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential equations, is popular in learning dynamics recently due to its robustness to irregular samples and its flexibility to high-dimensional input. However, the training of NODE is sensitive to the precision of the numerical solver, which makes the convergence of NODE unstable, especially for ill-conditioned dynamical systems. In this paper, to reduce the reliance on the numerical solver, we propose to enhance the supervised signal in the training of NODE. Specifically, we pre-train a neural differential operator (NDO) to output an estimation of the derivatives to serve as an additional supervised signal. The NDO is pre-trained on a class of basis functions and learns the mapping between the trajectory samples of these functions to their derivatives. To leverage both the trajectory signal and the estimated derivatives from NDO, we propose an algorithm called NDO-NODE, in which the loss function contains two terms: the fitness on the true trajectory samples and the fitness on the estimated derivatives that are outputted by the pre-trained NDO. Experiments on various kinds of dynamics show that our proposed NDO-NODE can consistently improve the forecasting accuracy with one pre-trained NDO. Especially for the stiff ODEs, we observe that NDO-NODE can capture the transitions in the dynamics more accurately compared with other regularization methods. [ABSTRACT FROM AUTHOR]

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any Hölder smooth function up to a given approximation error in Hölder norms in such a way that all weights of this neural network are bounded by 1. The latter feature is essential to control generalization errors in many statistical and machine learning applications. • Rates and complexity for smooth function approximation in Hölder norms by ReQU neural networks. • Explicit and uniform bounds for weights of the approximating neural network. • Exponential convergence rates for analytic functions. [ABSTRACT FROM AUTHOR]

In recent years, polydopamine (PDA) has attracted extensive attention of researchers due to its unique chemical structure and functional groups. However, a comprehensive review of PDA-based materials in electrocatalysis and photocatalysis is still lacking. The aim of this review is to summarize recent progress and development of PDA-assisted electrocatalytic and photocatalytic reactions. Owing to its unique advantages in surface modification, it has been a good platform for the construction of electrocatalytic and photocatalytic materials. With the development of biological sources, PDA has been increasingly applied in the field of materials science. However, it is still lacking of a comprehensive review which focuses on PDA surface modification strategies and its derivative function for electrocatalysis and photocatalysis applications. Here in this article the preparation and polymerization mechanism of PDA and its derivatives has been firstly reviewed. Then their physical and chemical properties have been introduced, including chemical reactivity, optical property, conductivity, and cohesiveness. Thirdly, the electrocatalytic and photocatalytic activities of PDA and its derivatives have been demonstrated. Finally, the advances of their electrocatalytic and photocatalytic applications have been summarized including hydrogen production, pollutant degradation, and CO 2 reduction. We believe this synthetic study can provide critical information for mussel-inspired chemistry, which will be of great interest for researchers from chemistry, materials, biology, medicine, and interdisciplinary. This paper can provide readers with a general framework of PDA and its derivatives in the field of photocatalysis and electrocatalysis including hydrogen production, pollutant degradation, and CO 2 reduction. [Display omitted] • Bioinspired polydopamine for electrocatalysis and photocatalysis are overviewed. • The mechanism of polydopamine derivatives assisted electrocatalytic hydrogen evolution reaction is classified and discussed. • The design and fabrication of polydopamine and photoresponsive semiconductor for photocatalytic reaction. • This review bodes well for the development of electrocatalysis and photocatalysis field founded on multifunctional polydopamine. • The advances of electrocatalytic and photocatalytic applications of polydopamine have been summarized. [ABSTRACT FROM AUTHOR]

• A mathematical model for inverters' connection transients in weak and strong grids. • An improvement of transients using a phase limiter algorithm. • A set of experiments which validates the proposal. • Analysis of virtual impedance and measurement filter dynamics. This paper derives a mathematical model suitable for analysis of connection behavior of the inverter-based grids and, using that model, it presents guidelines to control grid-forming inverters' rate of change in frequency as function of output power (virtual inertia), or in other words "measured power filters". Furthermore, in order to improve the transient response, an angle difference limiter control is proposed. An angle difference limiter is a control algorithm which is constantly checking the angle difference between the inverter and the grid in the connection point limiting power peaks during the transients. The performance of the angle difference limiter is analyzed in detail and validated with an experimental microgrid consisting of two three-phase inverters and a variable load. The paper analyzes the connection of inverters in weak and strong grids validating the performance of the proposed angle difference limiter. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

This paper contributes to a stress-constrained topology optimization approach for the design of shell-infill structures. Based on the density method, we utilize the two-step filtering and projection scheme and local volume constraint for generating the shell and non-uniform infills, respectively. The topology optimization formulation is defined as a Robust Minimum Compliance problem with Volume and Stress constraints (RMCVS), where the robust method is used to eliminate undesired topological characteristics. We globalize the static and transient stress constraints through the p-norm function, and tailor material interpolation and stress relaxation schemes for both cases, respectively, to avoid numerical difficulties. Sensitivity analysis is provided, and the derivatives of the objective function and constraints with respect to the design variable fields are derived. We then validate the suggested method through several 2D and 3D benchmarks. The results illustrate that the method is robust to generate various shell-infill structures while limiting the maximum static and transient stress. • Designing stress-constrained structures with dense shells and heterogeneous infills. • Both static and transient stress constraints are considered. • Computational cheap, since no need to tailor failure criteria for heterogeneous infills. • The robustness of the approach is validated through numerical examples. [ABSTRACT FROM AUTHOR]

Most research on control of nonlinear systems using backstepping concentrates on construction of feedback controllers to achieve stability and/or steady-state tracking performance. Little research considers systematic methods for tuning nonlinear feedback controllers to guarantee the transient performance. This paper investigates how parameters of a backstepping controller can be determined to achieve the predefined settling time and overshoot, which are basic criteria for the transient performance. First, some modifications are made for the backstepping design method by introducing more parameters so that there are more degrees of freedom for parameter tuning. Second, the pole-placement method is used for the linear part of the closed-loop system corresponding to a backstepping controller. Third, an objective function is defined by summing the square of errors between the corresponding coefficients of the desired and real characteristic polynomials. Fourth, constraints are introduced to guarantee the negative semi-definiteness of the time derivative of the Lyapunov function. Fifth, the controller parameters can be found by minimizing the objective function. Finally, simulation and experimental results show that, compared with the existing method, the proposed method is more effective and efficient for fine tuning backstepping controllers. [ABSTRACT FROM AUTHOR]

This paper presents the fuzzy power series method to solve the second-order differential equation under generalized Hukuhara differentiability with fuzzy and real coefficients. For this purpose, different types of fuzzy analytic functions by attention to generalized Hukuhara differentiability, ordinary and singular points are introduced. Since in the discussion of fuzzy power series, the concept of the fuzzy convergence radius is one of the most essential and fundamental concepts, the fuzzy convergence radius under the generalized division is defined. Fundamental theorems, such as fuzzy ratio tests, the convergence of the fuzzy geometric series, are expressed and proven. In addition, it has been shown that the fuzzy convergence radius of fuzzy power series does not change concerning derivatives under operators such as derivatives and integrals. It has been shown that the fuzzy analytic functions are still fuzzy analytic functions concerning derivatives under fuzzy operators, summation, multiplication, and generalized division. Then, the uniqueness of the solution of the second-order fuzzy differential equations with fuzzy and real coefficients in the form of a fuzzy power series by attention to the type of generalized differentiability is shown. Finally, there are examples to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

• A marching cubes-based isogeometric topology optimization method with parametric level set is proposed. • The proposed method can provide accurate material description of elements cut by structural boundaries. • A relaxed topology derivative is introduced to conduct sensitivity analysis. • The effectiveness of the proposed method is well illustrated by several 2D and 3D numerical examples. The level set method can provide superior benefits for topology optimization problems because of its smooth and distinct description of structural boundaries. However, in this method, the elements cut by structural boundaries are not descripted accurately. This paper proposes a marching cubes-based isogeometric topology optimization method with the parametric level set to address this issue. In the proposed method, the marching cubes algorithm is applied in the framework of isogeometric analysis to clearly distinguish the structural boundaries, enabling the creation of an accurate material description model during topology optimization. The relaxed topology derivative (RTD) is introduced to measure the sensitivity of the Lagrange function and alleviate the dependence on the initial design in the level set method. Several 2D and 3D numerical examples for minimizing mean compliance problems are tested to illustrate the effectiveness of the proposed method, including a multi-patch structure with a complicated design domain. [ABSTRACT FROM AUTHOR]

• An interval sequential linear programming for nonlinear robust optimization is proposed. • An approximate possibility sensitivity is proposed to efficiently obtain the partial derivatives of the constraints. • A novel iterative mechanism is established to improve the convergence rate. • Two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency. In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to transform the uncertain optimization into several possibility-sensitivity analyses and deterministic linear optimization problems that are sequentially solved. At each cycle, a possibility-sensitivity analysis method is proposed to obtain the approximate partial derivatives of the uncertain constraints at the current design point, based on which a deterministic linear optimization model is constructed and the design point is updated by solving the linear optimization. Moreover, an iterative mechanism is created to adaptively update the design space and improve the convergence rate. Finally, two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• Level-set method is applied for stress-based topology optimization of plate problems. • Solving optimization problems with arbitrarily complex geometries and boundaries. • A stabilized least-squares method is applied for solving level-set-based equations. • The shape derivatives, adjoint method, and p -norm aggregation function are used. In this paper, we present a stress-based topology optimization of plate structures by using a finite element level-set (LS) method. Since stress constraints are independent with LS-based design variables, the singularity phenomenon arising in topology optimization under stress constraints can be resolved without using any relaxation technique. The finite element method is used for solving LS-based equations of design variables and the state and adjoint equations of plate structures with arbitrary complex geometries and boundaries of the design domain. To obtain stable finite element solutions without any oscillation, both unsteady LS convection-diffusion equation and LS re-initialization convection-reaction equation are solved using a stabilized least-squares finite element method. [ABSTRACT FROM AUTHOR]

Abstract Based on an approach coupling geomatics (i.e. satellite imagery analysis) and fieldwork, this paper provides an in-depth analysis of the impacts of September 2017 hurricanes on the beaches of Saint-Barthélemy Island. First, it highlights the key role of low-frequency high-intensity events in driving high rates of changes on coastal systems. Importantly, all the studied beaches underwent shoreline retreat, detected along 47.73–100.00% of transects (mean shoreline movement ranging from −2.76 to −18.39 m). The stability line retreat was lower on highly-modified beaches because of the presence of longitudinal structures compared to natural beaches that mostly suffered severe vegetation destruction. Second, the methodology proposed here allowed attributing changes to specific anthropogenic drivers. Both natural (i.e. the hurricane's path and hurricane waves' direction) and anthropogenic (especially shoreline hardening and vegetation modification) drivers explain the high variability observed in the nature, intensity and spatial distribution of hurricanes' impacts on beaches. Based on the quantitative assessment of impacts, this paper advocates for the restoration of a 50 m-wide buffering area in front of human constructions, the exposure of which has considerably increased due to wave impact, which implies to establish new setback guidelines. So as to better assist decision-makers in disaster risk reduction on small islands, we therefore recommend the systematic inclusion, i.e. documentation and integration into GIS datasets, of human disturbances, as the latter highly influence shoreline and beach response. We propose a replicable methodology to address this challenge. Highlights • We propose a new replicable method that allows attributing changes to anthropogenic drivers. • Beach response was highly influenced by the degree of shoreline hardening. • Longitudinal coastal structures induced beach sediment loss. • Accretional features mainly occurred where the indigenous vegetation was preserved. • Quantifying cyclone-induced shoreline retreat allows defining setback guidelines. [ABSTRACT FROM AUTHOR]

Abstract In this paper we focus on two sources of enhancement in accuracy and computational demanding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered accuracy order in approximating the function or higher for the derivatives. In this paper we discuss on the scheme dealing with the infinitely differentiable Gaussian kernel function. Studies on the accuracy, convergency and computational efforts with various sets of data sites are provided. Moreover, to make large scale problems tractable the improved fast Gaussian transform is considered picking up the computational cost at an acceptable level preserving the accuracy of the computation. [ABSTRACT FROM AUTHOR]

We analyze the sequence obtained by consecutive applications of the Cantor–Bendixson derivative for a noncommutative scattered C ⁎ -algebra A , using the ideal I A t ( A ) generated by the minimal projections of A . With its help, we present some fundamental results concerning scattered C ⁎ -algebras, in a manner parallel to the commutative case of scattered compact or locally compact Hausdorff spaces and superatomic Boolean algebras. It also allows us to formulate problems which have motivated the “cardinal sequences” programme in the classical topology, in the noncommutative context. This leads to some new constructions of noncommutative scattered C ⁎ -algebras and new open problems. In particular, we construct a type I C ⁎ -algebra which is the inductive limit of stable ideals A α , along an uncountable limit ordinal λ , such that A α + 1 / A α is ⁎-isomorphic to the algebra of all compact operators on a separable Hilbert space and A α + 1 is σ -unital and stable for each α < λ , but A is not stable and where all ideals of A are of the form A α . In particular, A is a nonseparable C ⁎ -algebra with no ideal which is maximal among the stable ideals. This answers a question of M. Rørdam in the nonseparable case. All the above C ⁎ -algebras A α s and A satisfy the following version of the definition of an AF algebra: any finite subset can be approximated from a finite-dimensional subalgebra. Two more complex constructions based on the language developed in this paper are presented in separate papers [21,22] . [ABSTRACT FROM AUTHOR]

In this paper, we propose an innovative classification method which combines texture features of images filtered by Gaussian derivative models with extreme learning machine (ELM). In the texture image classification, feature extraction is a very crucial step. Thusly, we use linear filters consisting of two Gaussian derivative models, difference of Gaussian (DOG) and difference of offset Gaussian (DOOG), to detect texture information of images. Besides, ensemble extreme learning machine (E 2 LM) is proposed to reduce the randomness of original ELM and used as the classifier in this paper. We evaluate the performance of both the texture features and the classifier E 2 LM by using three datasets: Brodatz album, VisTex database and Berkeley image segmentation database. Experimental results indicate that Gaussian derivative models are superior to Gabor filters, and E 2 LM outperforms the support vector machine (SVM) and ELM in classification accuracy. [ABSTRACT FROM AUTHOR]

The solutions of Hamilton-Jacobi (HJ) equations may contain discontinuous derivatives, which brings numerical difficulties in capturing sharply these derivatives. This paper presents a third-order weighted compact nonlinear scheme (WCNS) and a third-order perturbed WCNS (WCNS-P) for solving HJ equations. A linear combination of hybrid cell-edge and cell-node values of the function is applied to approximate the spatial derivatives of the function. For the WCNS, the upwind-biased nonlinear weighted interpolation is used for the unknown cell-edge values, while for the WCNS-P perturbations with a free parameter is introduced to the upwind-biased linear interpolation. The free parameter can be optimized to reduce numerical errors in smooth regions. To enhance the numerical stability, a monotone polynomial interpolation method is designed to switch the WCNS-P to the WCNS. Several numerical experiments are performed to test the order of accuracy and the discontinuity-capturing ability of the two schemes. • Two types of weighted compact nonlinear schemes are constructed to solve Hamilton-Jacobi equations. • A switching condition of two schemes is designed to avoid numerical oscillations near discontinuities. • The two schemes can achieve third-order accuracy and have good resolution near corner singularities. • The two schemes have good performance in the noise reduction. [ABSTRACT FROM AUTHOR]

This paper addresses the stability analysis of neural networks with a time-varying delay, where the delay is periodically varying bounded function with constrained derivatives. In order to obtain less conservative stability criteria, two novel Lyapunov-Krasovskii functionals (LKFs) with delay-derivative-variation-dependent matrices are constructed. In one LKF, two delay-product terms are double utilized and more free matrices are incorporated. Additionally, a new type of the LKF with delay-derivative-variation-dependent matrices, namely, the neuronal-activation-function-based looped functional, is developed by accounting for the periodic nature of the delay function and the coupling information of the system state and the neural activation function. Then, several stability conditions of delayed neural networks are developed by combining some integral inequalities. Finally, the superiority and validity of developed stability conditions are validated on two benchmark examples. • A class of Lyapunov-Krasovskii functional (LKF) with delay-derivative-variation-dependent matrices (DDVDM) is developed. • A new type of looped LKF, named the neuronal-activation-function-based looped functional, is proposed. • A novel viewpoint that the developed LKF with DDVDMs improves the delay-product-type LKF can be provided. [ABSTRACT FROM AUTHOR]

In this paper, the problems on the existence and uniqueness, and the input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are considered. The existence and uniqueness for the global solution of such systems is studied by using the Lyapunov function, the theory of stochastic analysis, and the function of the impulsive density. In order to overcome the difficulty stemming from the simultaneous presence of the indefinite derivative for the Lyapunov function, the bounded external disturbances, and a nonnegative and bounded time-varying delay, one impulsive generalized Halanay inequality of integral version is established. The input-to-state stability, the integral input-to-state stability, the stochastic input-to-state stability and the e λ t (λ > 0) -weighted input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are investigated, respectively. One example is provided to illustrate the effectiveness of the theoretical results obtained. [ABSTRACT FROM AUTHOR]

When DC-side energy storage batteries participate in frequency regulation, inconsistent inertia requirements exist for frequency deterioration and recovery stages. In addition, the frequency regulation power can lead to the DC overvoltage of the DFIG. To address these issues, this paper proposes a voltage suppression strategy (VSS) during multi-stage frequency regulation with the DC-side energy storage batteries. In the frequency deterioration stage, a SOC segmented feedback inertia control (SSFIC) is developed to reduce the frequency change rate. In the frequency recovery stage, to mitigate transient maximum frequency deviation, a maximum frequency differential inertia control (MFDIC) is constructed by incorporating the transient maximum frequency deviation into inertia control coefficient. In the frequency regulation stage, to decrease the steady state frequency deviation and avoid the secondary frequency drop, an exponential inertia droop control (EIDC) is created by considering the droop coefficient as an exponential function of the frequency change rate. To suppress the DC voltage fluctuation, a DC voltage compensation control (DVCC) is presented to transform the active power of SSFIC, MFDIC and EIDC to the d-axis current compensation increment of GSC. Extensive simulation results have proved that the proposed strategy can successfully enhance the frequency regulation and voltage suppression ability. [ABSTRACT FROM AUTHOR]

This paper studies the problem of global output-feedback stabilization by adaptive method for a class of planar nonlinear systems with unmeasurable state dependent growth and unknown output function. It is worth emphasizing that not only the growth rate, but also the upper and lower bounds of the derivative of output function are not required to be known in the paper. To solve the problem, we propose a new adaptive output-feedback control scheme based on only one dynamic high-gain, by skillfully constructing the new Lyapunov function, and flexibly using the ideas of universal control and backstepping. It is shown that the state of the closed-loop system is bounded while global asymptotic stability can be achieved. Two examples including a practical example are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on decomposition strategies for large-scale optimization problems. The cooperative co-evolution approach improves the scalability of evolutionary algorithms by decomposing a single high dimensional problem into several lower dimension sub-problems and then optimizing each of them individually. However, the dominating factor for the performance of these algorithms, on large-scale function optimization problems, is the choice of the decomposition approach employed. This paper provides a theoretical analysis of the interaction between variables in such approaches. Three theorems and three lemma are introduced to investigate the relationship between decision variables, and we provide theoretical explanations on overlapping subcomponents. An automatic decomposition approach, based on the mixed second order partial derivatives of the analytic expression of the optimization problem, is presented. We investigate the advantages and disadvantages of the differential grouping (DG) automatic decomposition approach, and we propose one enhanced version of differential grouping to deal with problems which the original differential grouping method is unable to resolve. We compare the performance of three different grouping strategies and provide the results of empirical evaluations using 20 benchmark data sets. [ABSTRACT FROM AUTHOR]

In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic logic 2Int. The proof makes use of the faithful embedding of 2Int into intuitionistic logic with respect to validity and shows that conversions of dual proofs can be sidestepped. [ABSTRACT FROM AUTHOR]

This paper presents three innovative techniques to estimate external perturbation torques acting on an Earth-orbiting satellite. The proposed techniques overcome the problem of derivative reconstruction from noisy measurement in the estimation procedure of the environmental perturbation torques. For this purpose, in the first technique, known as nonlinear disturbances observer (NDO) technique, derivative term is eliminated in the estimation equations by employing auxiliary variable vector and by selecting appropriate design parameters. In the second proposed approach, the robust exact differentiation via second-order sliding mode theory, known as Levant differentiator, is employed to decrease derivative estimation error in the process of estimation. To improve the performance of the Levant differentiator, the final innovative approach, known as sub-band adaptive robust differentiator (SARD) technique, is proposed in which the derivative term in the estimation process is reconstructed by using Levant differentiator and sub-band adaptive filter theory. In the SARD technique, the original noisy measurement signal is divided into sub-band signals and then, the Levant differentiator is applied to each sub-band signals to construct exact differentiator from noisy measurement. The novel aspect of paper is employing second-order sliding mode theory in the sub-bands frequency to improve the performance of derivative reconstruction in the presence of measurement noise. In this regard, a nonlinear model of the earth-orbiting satellite is simulated using specific navigation disturbances and the results verified the feasibility of the proposed strategies. [ABSTRACT FROM AUTHOR]

Importance analysis deals with the investigation of influence of individual system components on system operation. This investigation can be qualitative or quantitative. The qualitative analysis focuses on finding scenarios in which a degradation/improvement of a specific component or a group of components results in a degradation/improvement of the whole system, while the quantitative one deals with numerical estimation of components importance. In this paper, we propose a new approach for importance analysis of Multi-State Systems (MSSs). The qualitative or quantitative importance analysis is based on the identification of critical states. The new approach can be used for calculation of all types of critical states. It is based on the application of direct partial logic derivatives. These derivatives are one of the methods of logical differential calculus. In this paper, the specifics of these derivatives for importance analysis of MSSs are considered in detail. [ABSTRACT FROM AUTHOR]

A multi-defender single-invader target defense game is a differential game where the invader intends to enter a target area protected by a group of defenders, while the defenders intend to capture the invader before it enters. This game has been extensively studied and a geometric solution exists. However, this solution has only been justified under special cases. The main contribution of this paper is to prove that the geometric solution satisfies the HJI equation under the general condition. Specifically, the target area is not required to take a peculiar shape, such as circles, lines, etc. In addition, the defenders are allowed to move freely in the two-dimensional plane, the capture range of the defenders is non-zero, and the number of defenders is not restricted. This generalized formulation imposes an important challenge on an essential step of the proof, computing the derivatives of the value function. This challenge is resolved in this paper therefore the proof can be accomplished. The significance of studying the geometric solution is that it provides a state feedback control law using an adequate amount of computation. The target defense game is inherently challenging to be solved with numerical methods, because it is highly nonlinear and suffers from the curse of dimensionality. The proof presented in this paper provides a solid theoretic foundation for the geometric solution, so the difficulties raised by the numerical methods can be circumvented. [ABSTRACT FROM AUTHOR]