THE DIFFERENTIAL INTEGRAL EQUATIONS ONSMOOTH CLOSED ORIENTABLE MANIFOLDS

Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.

Adaptive proportional integral differential control based on radial basis function neural network identification of a two-degree-of-freedom closed-chain robot

A closed-chain robot has several advantages over an open-chain robot, such as high mechanical rigidity, high payload, high precision. Accurate trajectory control of a robot is essential in practical-use. This paper presents an adaptive proportional integral differential （PID） control algorithm based on radial basis function （RBF） neural network for trajectory tracking of a two-degree-of-freedom （2-DOF） closed-chain robot. In this scheme, an RBF neural network is used to approximate the unknown nonlinear dynamics of the robot, at the same time, the PID parameters can be adjusted online and the high precision can be obtained. Simulation results show that the control algorithm accurately tracks a 2-DOF closed-chain robot trajectories. The results also indicate that the system robustness and tracking performance are superior to the classic PID method.

An Introduction to Paraconsistent Integral Differential Calculus:With Application Examples

In this paper we show that it is possible to integrate functions with concepts and fundamentals of Paraconsistent Logic (PL). The PL is a non-classical Logic that tolerates the contradiction without trivializing its results. In several works the PL in his annotated form, called Paraconsistent logic annotated with annotation of two values (PAL2v), has presented good results in analysis of information signals. Geometric interpretations based on PAL2v-Lattice associate were obtained forms of Differential Calculus to a Paraconsistent Derivative of first and second-order functions. Now, in this paper we extend the calculations for a form of Paraconsistent Integral Calculus that can be viewed through the analysis in the PAL2v-Lattice. Despite improvements that can develop calculations in complex functions, it is verified that the use of Paraconsistent Mathematics in differential and Integral Calculus opens a promising path in researches developed for solving linear and nonlinear systems. Therefore the Paraconsistent Integral Differential Calculus can be an important tool in systems by modeling and solving problems related to Physical Sciences.

Fuzzy Self-adaptive Proportional Integration Differential Control for Attitude Stabilization of Quadrotor UAV

The technology of attitude control for quadrotor unmanned aerial vehicles(UAVs) is one of the most important UAVs' research areas.In order to achieve a satisfactory operation in quadrotor UAVs having proportional integration differential(PID) controllers,it is necessary to appropriately adjust the controller coefficients which are dependent on dynamic parameters of the quadrotor UAV and any changes in parameters and conditions could affect desired performance of the controller.In this paper,combining with PID control and fuzzy logic control,a kind of fuzzy self-adaptive PID control algorithm for attitude stabilization of the quadrotor UAV was put forward.Firstly,the nonlinear model of six degrees of freedom(6-DOF) for quadrotor UAV is established.Secondly,for obtaining the attitude of quadrotor,attitude data fusion using complementary filtering is applied to improving the measurement accuracy and dynamic performance.Finally,the attitude stabilization control simulation model of the quadrotor UAV is build,and the self-adaptive fuzzy parameter tuning rules for PID attitude controller are given,so as to realize the online self-tuning of the controller parameters.Simulation results show that comparing with the conventional PID controller,this attitude control algorithm of fuzzy self-adaptive PID has a better dynamic response performance.

SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅰ)FIRST-ORDER EQUATIONS

In this paper we give some results of integrability and several classes of integrable equations of first-order nonlinear ordinary differential equations. Many known results of integrability and integrable equations are special cases of them. They may be applied in physics and mechanics, and to derive soliton equations and find soliton solutions.

INTEGRABLE TYPES OF NONLINEAR ORDINARY DIFFERENTIAL EQUATION SETS OF HIGHER ORDERS

Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years Based on these papers and in virtue of Leibniz formula,and transformation set technique,this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders, moveover,its integrability is proven.The results obtained are the generalization of those in the references.

Proportion Integration Differentiation(PID)Control Strategy of Belt Sander Based on Fuzzy Algorithm

Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion integration differentiation(PID)was proposed by analyzing the signal transmission process and the dynamic characteristics of the grinding mechanism.The simulation results showed that compared with the classical PID control strategy,the system adjustment time was shortened by 98.7%,the overshoot was reduced by 5.1%,and the control error was 0.2%-0.5%when the system was stabilized.The optimized fuzzy control system had fast adjustment speeds,precise force control and stability.The experimental analysis of the surface morphology of the machined blade was carried out by the industrial robot abrasive grinding mechanism,and the correctness of the theoretical analysis and the effectiveness of the control strategy were verified.

THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUAFIONS ON S.P.SPACE

This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.

Improved quantum bacterial foraging algorithm for tuning parameters of fractional-order PID controller

The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.

Exponential Stability of Traveling Pulse Solutions of a Singularly Perturbed System of Integral Differential Equations Arising From Excitatory Neuronal Networks

We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly per-turbed systems of integral differential equations arising from neuronal networks.It has been proved that expo-nential stability of these orbits is equivalent to linear stability.Let (?) be the linear differential operator obtainedby linearizing the nonlinear system about its fast pulse,and let σ((?)) be the spectrum of (?).The linearizedstability criterion says that if max{Reλ:λ∈σ((?)),λ≠0}(?)-D,for some positive constant D,and λ=0 is asimple eigenvalue of (?)(ε),then the stability follows immediately (see [13] and [37]).Therefore,to establish theexponential stability of the fast pulse,it suffices to investigate the spectrum of the operator (?).It is relativelyeasy to find the continuous spectrum,but it is very difficult to find the isolated spectrum.The real part ofthe continuous spectrum has a uniformly negative upper bound,hence it causes no threat to the stability.Itremains to see if the isolated spectrum is safe.Eigenvalue functions (see [14] and [35,36]) have been a powerful tool to study the isolated spectrum of the as-sociated linear differential operators because the zeros of the eigenvalue functions coincide with the eigenvaluesof the operators.There have been some known methods to define eigenvalue functions for nonlinear systems ofreaction diffusion equations and for nonlinear dispersive wave equations.But for integral differential equations,we have to use different ideas to construct eigenvalue functions.We will use the method of variation of param-eters to construct the eigenvalue functions in the complex plane C.By analyzing the eigenvalue functions,wefind that there are no nonzero eigenvalues of (?) in {λ∈C:Reλ(?)-D} for the fast traveling pulse.Moreoverλ=0 is simple.This implies that the exponential stability of the fast orbits is true.

LOCAL PETROV-GALERKIN METHOD FOR A THIN PLATE

The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.

改进的神经网络PID在空调温度控制中的应用

为提高候机楼中央空调温度控制水平,针对候机楼中央空调系统具有时滞性、扰动因素较多等特点,提出了一种基于改进天牛须搜索(IBAS,improved beetle antennae search)算法的模糊径向基函数(RBF,radial basis function)神经网络(PID,proportion integration differentiation)控制方法,建立了空调区域温度控制模型,通过模糊RBF神经网络实现PID参数在线整定,解决系统非线性、时变的问题。同时由于神经网络参数存在难以选取问题,提出利用天牛须搜索(BAS,beetle antennae search)算法优化模糊RBF神经网络参数的方法,并引入莱维飞行机制和变步长策略对BAS算法进行改进,提高其跳出局部最优的能力和稳定性。仿真结果表明,采用IBAS算法优化的模糊RBF神经网络PID控制方法有效提高了系统的鲁棒性和自适应能力,对候机楼中央空调系统具有良好的控制效果。

PID Parameters for Tuning and Optimization of a Turbine EngineBased on the Simplex Search Method

A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control system for a turbine engine was developed. A performance index based on the integral of absolute error （IAE） was given as an objective function of optimization. In order to avoid the sensitivity that resulted from the initial values of the simplex search method, the traditional Ziegler-Nichols method was used to tune PID parameters to obtain the initial values at first, then the simplex search method was applied to optimize PID parameters for the turbine engine. Simulation results indicate that the simplex search method is a reasonable and effective method for PID controller parameters tuning and optimization.

Mechanism analysis of reaction S+(2D)+H2(X1Σg^+) → SH+(X3Σ-) + H(2S) based on the quantum state-to-state dynamics

We present a state-to-state dynamical calculation on the reaction S++ H2→ SH+ +H based on an accurate X2 A″ potential surface. Some reaction properties, such as reaction probability, integral cross sections, product distribution, etc.,are found to be those with characteristics of an indirect reaction. The oscillating structures appearing in reaction probability versus collision energy are considered to be the consequence of the deep potential well in the reaction. The comparison of the present total integral cross sections with the previous quasi-classical trajectory results shows that the quantum effect is more important at low collision energies. In addition, the quantum number inversion in the rotational distribution of the product is regarded as the result of the heavy–light–light mass combination, which is not effective for the vibrational excitation. For the collision energies considered, the product differential cross sections of the title reaction are mainly concentrated in the forward and backward regions, which suggests that there is a long-life intermediate complex in the reaction process.

Some notes on a conjecture of Zygmund

In this paper, some classes of differentiation basis are investigated and several positive answers to a conjecture of Zygmund on differentiation of integrals are presented.

THE UNIQUENESS AND EXISTENCE OF SOLUTION OF THE CHABACTERISTIC PROBLEM ON THE GENERALIZED KdV EQUATION

The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma￣[2], Ihe isolated wave in transmission line￣[3], and the isolated wave in the bound-ary surface of the divided layer fluid￣[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.

Inhomogeneous Cauchy-Riemann equation in Octonion space

The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION WITH A NONLOCAL BOUNDARY OPERATOR

In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.

STABILITY AND BOUNDEDNESS OF SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained.

Discrete Quantum Transitions, Duality: Emergence of Physical Structures and Occurrence of Observed Formations (Hidden Properties of Mathematical Physics Equations)

With the help of skew-symmetric differential forms, the hidden properties of the mathematical physics equations that describe discrete quantum transitions and emergence the physical structures are investigated. It is shown that the mathematical physics equations possess a unique property. They can describe discrete quantum transitions, emergence of physical structures and occurrence observed formations. However, such a property possesses only equations on which no additional conditions, namely, the conditions of integrability, are imposed. The intergrability conditions are realized from the equations themselves. Just under realization of integrability conditions double solutions to the mathematical physics equations, which describe discrete transitions and so on, are obtained. The peculiarity consists in the fact that the integrability conditions do not directly follow from the mathematical physics equations;they are realized under the description of evolutionary process. The hidden properties of differential equations were discovered when studying the integrability of differential equations of mathematical physics that depends on the consistence between the derivatives in differential equations along different directions and on the consistence of equations in the set of equations. The results of this work were obtained with the help of skew-symmetric differential forms that possess a nontraditional mathematical apparatus such as nonidentical relations, degenerate transformations and the transition from nonintegrable manifolds to integrable structures. Such results show that mathematical physics equations can describe quantum processes.