Nonlinear Derivative and Integral Sliding Control for Tracked Vehicle Steering with Hydrostatic Drive

In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes.Therefore,it is significant to enhance the steering stability of tracked vehicle with hydrostatic drive to meet the need of future battlefield.In this paper,a sliding mode control algorithm is proposed and applied to achieve desired yaw rates.The speed controller and the yaw rate controller are designed through the kinematics and dynamics analysis.In addition,the nonlinear derivative and integral sliding mode control algorithm is designed,which is supposed to efficiently reduce the integration saturation and the disturbances from the unsmooth road surfaces through a conditional integrator approach.Moreover,it improves the response speed of the system and reduces the chattering by the derivative controller.The hydrostatic tracked vehicle module is modeled with a multi-body dynamic software RecurDyn and the steering control strategy module is modeled by MATLAB/Simulink.The co-simulation results of the whole model show that the control strategy can improve the vehicle steering response speed and also ensure a smooth control output with small chattering and strong robustness.

Nonexistence of Global Solutions for a Semilinear Double-Wave Equation with Nonlinearity of Derivative Type

In this paper,we study the blow-up of solutions to a semilinear double-wave equation with nonlinearity of derivative type.By using the iteration method and the differential inequality techniques,we can get the estimates of the lifespan and the blow-up of solutions in the subcritical case under some assumptions.

N-Soliton Solutions of General Nonlinear Schrdinger Equation with Derivative

The bilinear equation of the genera/nonlinear Schrodinger equation with derivative （GDNLSE） and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative （DNLSE） and its multisoliton solutions are given by reduction.

Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrdinger Equation

With the aid of a class of nonlinear ordinary differential equation （ODE） and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation （GDNLSE） have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given.

Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type

In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

Direct Perturbation Method for Derivative Nonlinear Schrdinger Equation

We extend Lou＇s direct perturbation method for solving the nonlinear Schrodinger equation to the case of the derivative nonlinear Schrodinger equation （DNLSE）. By applying this method, different types of perturbation solutions are obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.

NEW ORGANIC NONLINEAR OPTICAL MATERIALS OF CINNAMYLIDENE-ACETOPHENONE DERIVATIVES

we have synthesised a series of new optically nonlinear organic materials of cinnamylidene-acetophenone derivatives which have large nonl inear optical susceptibilities and short cut-off wavelengths.

NONLINEAR OPTICAL PROPERTY OF para-DISUBSTITUTED BENZYLIDENE-ANILINE DERIVATIVES

Forty para-disubstituted benzylidene-aniline derivatives were synthesized,and their second harmonic generation(SHG)efficiency was measured by the Kurtz powder technique.The effect of the electronic property and the position of the substituents on powder SHG efficiency was studied.

The Interaction and Degeneracy of Mixed Solutions for Derivative Nonlinear Schrodinger Equation

The mixed solutions of the derivative nonlinear Schrödinger equation from the trivial seed (zero solution) are derived by using the determinant representation. By adjusting the interaction and degeneracy of mixed solutions, it is possible to obtain different types of solutions: phase solutions, breather solutions, phase-breather solutions and rogue waves.

Peregrine Rogue Waves Generated by the Interaction and Degeneration of Soliton-Like Solutions: Derivative Nonlinear Schrödinger Equation

We study the Peregrine rogue waves within the framework of Derivative Nonlinear Schrödinger equation, which is used to describe the propagation of Alfven waves in plasma physics and sub-picosecond or femtosecond pulses in nonlinear optics. The interaction and degeneration of two soliton-like solutions and its relations for the breather solution have been analyzed. The Peregrine rogue waves have been considered from the two kinds of formation processes: it can be generated through the limitation of the infinitely large period of the breather solutions, and it can be interpreted as the soliton-like solutions with different polarities. As a special example, a special Peregrine rogue wave is generated by a breather solution and phase solution, which is given by the trivial seed (zero solution).

Nonlinear Jordan Higher Derivations of Triangular Algebras

In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

N-Fold Darboux Transformation for a Nonlinear Evolution Equation

In this paper, we present a N-fold Darboux transformation (DT) for a nonlinear evolution equation. Comparing with other types of DTs, we give the relationship between new solutions and the trivial solution. The DT presented in this paper is more direct and universal to obtain explicit solutions.

Exact solitary wave solutions of a nonlinear Schrdinger equation model with saturable-like nonlinearities governing modulated waves in a discrete electrical lattice

In this paper, we introduce and propose exact and explicit analytical solutions to a novel model of the nonlinear Schr¨odinger(NLS) equation. This model is derived as the equation governing the dynamics of modulated cutoff waves in a discrete nonlinear electrical lattice. It is characterized by the addition of two terms that involve time derivatives to the classical equation. Through those terms, our model is also tantamount to a generalized NLS equation with saturable;which suggests that the discrete electrical transmission lines can potentially be used to experimentally investigate wave propagation in media that are modeled by such type of nonlinearity. We demonstrate that the new terms can enlarge considerably the forms of the solutions as compared to similar NLS-type equations. Sine–Gordon expansion-method is used to derive numerous kink, antikink, dark, and bright soliton solutions.

DERIVATION AND INTEGRAL SLIDING MODE VARIABLE STRUCTURE CONTROL OF HYDRAULIC VELOCITY TRACKING SYSTEM

The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a derivation and integral sliding mode variable structurecontrol scheme (DI-SVSC) is proposed. An integral controller is introduced to avoid the assumptionthat the derivative of desired signal must be known in conventional sliding mode variable structurecontrol, a nonlinear derivation controller is used to weaken the chattering of system. The designmethod of switching function in integral sliding mode control, nonlinear derivation coefficient andcontrollers of DI-SVSC is presented respectively. Simulation shows that the control approach is ofnice robustness and improves velocity tracking accuracy considerably.

具有非线性斜导数边界条件的二阶完全非线性椭圆方程的障碍问题

在自然结构条件下证明了具有非线性斜导数边界条件的二阶完全非线性随圆方程障碍问题Ｗ＾２，∞解的存在性，唯一性和正则性。抗议了Ｓ。Ｌｅｎｈａｒ，Ｐ。Ｌ。Ｌｉｏｎｓ和陈亚浙等人关于Ｄｉｒｉｃｈｌｅｔ边界条件的工作。

Space Periodic Solutions and Rogue Wave Solution of the Derivative Nonlinear Schrodinger Equation

The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.

High-order numerical method for the derivative nonlinear Schrodinger equation

In this work,a fourth-order numerical scheme in space and two second-order numerical schemes in both time and space are proposed for the derivative nonlinear Schrodinger equation.We verify the mass conservation for the two-level implicit scheme.The influence on the soliton solution by adding a small random perturbation to the initial condition is discussed.The numerical experiments are given to test the accuracy order for different schemes,respectively.We also test the conservative property of mass and Hamiltonian for these schemes from the numerical point of view.

Dynamics analysis of higher-order soliton solutions for the coupled mixed derivative nonlinear Schrodinger equation

In this paper,the dynamics of the higher-order soliton solutions for the coupled mixed derivative nonlinear Schrodinger equation¨are investigated via generalized Darboux transformation.Given a pair of linearly independent solutions of the Lax pair,the oneto three-soliton solutions are obtained via algebraic iteration.Furthermore,two and three solitons are respectively displayed via numerical simulation.Moreover,the dynamics of solitons are illustrated with corresponding evolution plots,such as elastic collisions,inelastic collisions,and bound states.It is found that there are some novel phenomena of interactions among solitons,which may provide a theoretical basis for studying optical solitons in experiments.

KAM Tori for the Derivative Quintic Nonlinear Schrodinger Equation

This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-Wu[J.Math.Phys.、53,102702(2012)].