Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

A Cauchy integral formula for(p,q)-monogenic functions withα-weight

Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant

It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.

Feynman Path Integral Using Operator Integration in Banach Space

Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

Design of integral sliding mode guidance law based on disturbance observer

With the increasing precision of guidance,the impact of autopilot dynamic characteristics and target maneuvering abilities on precision guidance is becoming more and more significant.In order to reduce or even eliminate the autopilot dynamic operation and the target maneuvering influence,this paper suggests a guidance system model involving a novel integral sliding mode guidance law(ISMGL).The method utilizes the dynamic characteristics and the impact angle,combined with a sliding mode surface scheme that includes the desired line-ofsight angle,line-of-sight angular rate,and second-order differential of the angular line-of-sight.At the same time,the evaluation scenario considere the target maneuvering in the system as the external disturbance,and the non-homogeneous disturbance observer estimate the target maneuvering as a compensation of the guidance command.The proposed system’s stability is proven based on the Lyapunov stability criterion.The simulations reveale that ISMGL effectively intercepted large maneuvering targets and present a smaller miss-distance compared with traditional linear sliding mode guidance laws and trajectory shaping guidance laws.Furthermore,ISMGL has a more accurate impact angle and fast convergence speed.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.

Existence of Solutions of a Convolution Integral Equation

In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball Br belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.

Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

Computational intelligence interception guidance law using online off-policy integral reinforcement learning

Missile interception problem can be regarded as a two-person zero-sum differential games problem,which depends on the solution of Hamilton-Jacobi-Isaacs(HJI)equa-tion.It has been proved impossible to obtain a closed-form solu-tion due to the nonlinearity of HJI equation,and many iterative algorithms are proposed to solve the HJI equation.Simultane-ous policy updating algorithm(SPUA)is an effective algorithm for solving HJI equation,but it is an on-policy integral reinforce-ment learning(IRL).For online implementation of SPUA,the dis-turbance signals need to be adjustable,which is unrealistic.In this paper,an off-policy IRL algorithm based on SPUA is pro-posed without making use of any knowledge of the systems dynamics.Then,a neural-network based online adaptive critic implementation scheme of the off-policy IRL algorithm is pre-sented.Based on the online off-policy IRL method,a computa-tional intelligence interception guidance(CIIG)law is developed for intercepting high-maneuvering target.As a model-free method,intercepting targets can be achieved through measur-ing system data online.The effectiveness of the CIIG is verified through two missile and target engagement scenarios.

Application of Choquet Integral-Importance-Performance Analysis and TOPSIS Methods in Approaching the Preference Factors of Calligraphy and Seal Engraving Imagery

Classical Chinese characters,presented through calligraphy,seal engraving,or painting,can exhibit different aesthetics and essences of Chinese characters,making them the most important asset of the Chinese people.Calligraphy and seal engraving,as two closely related systems in traditional Chinese art,have developed through the ages.Due to changes in lifestyle and advancements in modern technology,their original functions of daily writing and verification have gradually diminished.Instead,they have increasingly played a significant role in commercial art.This study utilizes the Evaluation Grid Method(EGM)and the Analytic Hierarchy Process(AHP)to research the key preference factors in the application of calligraphy and seal engraving imagery.Different from the traditional 5-point equal interval semantic questionnaire,this study employs a non-equal interval semantic questionnaire with a golden ratio scale,distinguishing the importance ratio of adjacent semantic meanings and highlighting the weighted emphasis on visual aesthetics.Additionally,the study uses Importance-Performance Analysis(IPA)and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)to obtain the key preference sequence of calligraphy and seal engraving culture.Plus,the Choquet integral comprehensive evaluation is used as a reference for IPA comparison.It is hoped that this study can provide cultural imagery references and research methods,injecting further creativity into industrial design.

苦瓜皂苷L调控PI3K/AKT通路促进内皮祖细胞增殖能力和内皮功能的实验研究

目的:探讨苦瓜皂苷L对内皮祖细胞(EPC)增殖能力和内皮功能的作用及机制。方法:体外分离、培养、鉴定外周血EPC。使用不同浓度苦瓜皂苷L处理EPC 24 h后,应用细胞计数试剂盒(CCK-8)法检测各组细胞活力。使用AutoDock Tools 5.6软件,分别以磷脂酰肌醇3-激酶(PI3K)和蛋白激酶B(AKT)为受体,以药物分子苦瓜皂苷L为配体采用盲对接法进行分子对接。使用PI3K/AKT抑制剂LY294002和最佳使用浓度的苦瓜皂苷L单独或同时处理EPC 24 h后检测各组细胞活力和磷酸化PI3K(p-PI3K)、磷酸化AKT(p-AKT)及磷酸化内皮型一氧化氮合酶(p-eNOS)表达水平。结果:与对照组比较,苦瓜皂苷L呈剂量依赖性地促进EPC增殖,且40μmol/L的苦瓜皂苷L是最佳药物浓度。与对照组比较,LY294002可下调EPC细胞活力,苦瓜皂苷L可上调细胞活力。与苦瓜皂苷L组比较,共同使用苦瓜皂苷L和LY294002可降低细胞活力。分子对接结果显示,苦瓜皂苷L与PI3K和AKT均存在直接作用,形成稳定的锁钥结构。与对照组比较,LY294002可显著下调p-PI3K、p-AKT和p-eNOS蛋白水平;苦瓜皂苷L可上调p-PI3K、p-AKT和p-eNOS蛋白水平。与苦瓜皂苷L组比较,使用苦瓜皂苷L和LY294002可降低p-PI3K、p-AKT和p-eNOS蛋白水平。结论:苦瓜皂苷L通过PI3K/AKT信号通路靶向调节EPC的增殖能力,进而上调内皮型一氧化氮合酶(eNOS)活化水平以促进EPC内皮功能。

L型隔板弧形双钢板组合墙板抗爆性能试验与数值研究

弧形双钢板混凝土组合墙板结构具有和拱结构相同的传力机理,可以充分发挥混凝土优异的抗压性能,极大地提高了结构的承载力。该文开展了L型隔板弧形双钢板混凝土组合墙板(L-shaped-Curved Double Steel Concrete Composite Wallboard,L-CDSCW)在近场爆炸作用下的试验研究,通过混凝土的损伤分析和结构变形分析探究其抗爆性能。基于ANSYS/LS-DYNA软件进行了L-CDSCW试件爆炸响应的数值分析,参数化分析了不同关键参数对L-CDSCW试件抗爆性能的影响规律。结果表明:近场爆炸作用下,L-CDSCW试件未出现倒塌或崩塌现象,具有较强的抗爆性能;增加钢板厚度可以减小混凝土跨中凹陷深度和混凝土塑性破坏;增加TNT当量和降低爆距会显著增加底部钢板跨中最大挠度,同时也会增加混凝土跨中凹陷深度和混凝土损伤。研究结果可以为弧形双钢板混凝土组合板的应用提供一定的技术参考。

跗骨窦小切口与经外侧“L”形切口术对跟骨骨折患者的疗效

目的 比较跗骨窦小切口与经外侧“L”形切口术治疗跟骨骨折的疗效及对足功能恢复情况的影响。方法 研究对象选取2020年10月至2022年10月收治的跟骨骨折患者88例,按照手术方法分为对照组43例,研究组45例,对照组采用经外侧“L”形切口术,研究组采用跗骨窦小切口手术。检测比较2组手术情况及并发症发生情况、足功能、跟骨解剖结构、骨代谢、炎性因子、应激反应指标水平。结果 与对照组比较,研究组术后引流量、术中出血量较少,手术、住院及骨折愈合时间较短,并发症发生率较低(P<0.05)。与术前比较,术后3个月2组AOFAS评分、Bohler角、Gissane角、跟骨长度、跟骨高度、P1NP、骨特异性碱性磷酸酶(BALP)水平升高,且研究组高于对照组,抗酒石酸酸性磷酸酶(TRAP)、环磷酰胺(CTX)水平降低,且研究组低于对照组(P<0.05)。与术前比较,术后3 d 2组CRP、IL-6、MDA水平升高,但研究组低于对照组,SOD水平降低,但研究组高于对照组(P<0.05)。结论 跗骨窦小切口术治疗跟骨骨折效果理想,可减少手术创伤,减轻炎症及应激反应,且可促进术后足功能、骨代谢恢复,并发症少。

形状系数对20 L球内铝粉分散特性的影响研究

为研究不同形状系数(SF)的铝粉在20 L球型容器中的分散特征,通过建立描述气流携带粉尘形成两相分散系的非稳态数值模型,包括气体流动和粉尘颗粒运动轨迹方程,开展非稳态数值模拟,分析粉尘SF分别为0.2、0.4、0.6、0.8和1.0条件下的粉尘空间分布以及球室中心的湍流动能、速度随时间变化。结果表明:球室内气流携带粉尘分散可以分为进粉、扩散、稳定和沉降4个阶段,其分散均匀性和最大速度值随SF的增加而增强;SF越大,即颗粒形状越接近球形,铝粉尘的分散性越好;SF越小,粉尘容易堆积在壁面附近;标称浓度一定时,SF≤0.4,浓度峰值随SF的增加而增加;SF>0.4,浓度峰值随SF的增加而减小;铝粉-空气混合物的湍流动能最大值随SF值的增加而降低;铝粉颗粒的速度峰值随SF值的增加而升高。