基于演算子理论的含有未知不确定性机械臂的鲁棒非线性精确跟踪控制

设计了一种基于演算子理论的含有未知不确定性机械臂的鲁棒非线性精确跟踪控制系统.机械手臂的模型不确定性包含未知模型误差和外界扰动对系统性能的影响.考虑未知的不确定模型在设计精确跟踪控制器产生限制情况下,设计了一种基于演算子理论的反馈控制结构来消除不确定模型的影响.基于得到的控制结构,提出了新的精确跟踪条件用来改进机械臂的跟踪性能.最后通过仿真结果验证了设计系统的有效性.

关于非线性鞍点问题的一个新的非线性不精确Uzawa算法

本文针对非线性鞍点问题,借助于一个非线性映射,构造了一个新的非线性不精确Uzawa算法,该算法避免了传统Uzawa方法所必需的求逆运算.并通过精细分析得到了该算法在能量范数意义下收敛的充分条件,最后给出的数值实验验证了该方法的有效性.

一个非线性色散-耗散方程的显式精确解

本文通过直接代数方法与假设方法的一种结合求出了一个用于描述由冷离子和热电子组成的等离子体弱非线性离子声波演化的非线性色散－耗散方程的几类显式精确行波解．这里的结果包含已有文献的结果作为特例．

磁悬浮轴承弹性转子非线性系统的建模与控制

在考虑陀螺效应、转轴弹性与非线性电磁力的条件下,建立了磁悬浮轴承弹性转子系统动力学非线性控制模型;并采用精确非线性反馈方法,实现了对磁悬浮轴承弹性转子系统的有效控制。针对磁悬浮非线性模型与线性化后的模型、刚性磁悬浮与弹性磁悬浮模型所需控制参数进行了比较;仿真结果表明,考虑轴承弹性的非线性磁悬浮模型所需控制量与线性化模型及刚性磁悬浮模型所需控制量有较大的差异。电磁力的非线性及轴承的弹性对磁悬浮系统影响较大,不能忽略;该结果对工程实际具有一定的指导意义。

基于演算子理论的IPMC人工肌肉精确位置控制

IPMC(Ionic Polymer Metal Composite)人工肌肉是一种离子交换聚合金属材料,由于具有在低电压作用下可以产生较大弯曲的特性,已经被作为分布式传感器和执行器广泛应用于各种仿生机器人构建中。为了在各种仿生机器人中应用IPMC人工肌肉,期望的位置或偏移量必须能够精确地控制。针对这个问题,通过应用鲁棒右互质分解方法,本文设计一种基于演算子理论的IPMC人工肌肉精确位置控制系统,该系统不仅保证了鲁棒稳定性,而且能够实现精确的位置跟踪。最后,通过仿真和实验结果,系统的有效性进一步得到验证。

An Adaptive Spectral Conjugate Gradient Method with Restart Strategy

As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.

A polynomial Expansion Method and New General Solitary Wave Solutions to KS Equation

Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.

A New Generalization of Extended Tanh—Function Method for Solving Nonlinear Evolution Equations

Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.

Non-Lie Symmetry Groups of （2＋1）-Dimensional Nonlinear Systems

A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.

Computer Algebra and Solutions to the Karamoto-Sivashinsky Equation

The method of Riccati equation is extended for constructing travelling wave solutions of nonlinear partial differential equations. It is applied to solve the Karamoto-Sivashinsky equation and then its more new explicit solutions have been obtained. From the results given in this paper, one can see the computer algebra plays an important role in this procedure.

Comment on “Computer Algebra and Solutions to the Karamoto-Sivashinsky Equation” [Commun. Theor. Phys. （Beijing, China） 43 （2005） 39]

In a recent article [Commun. Theor. Phys. (Beijing, China) 43 (2005) 39], Xie et al. improved the extended tanh function method by introducing a generalized Riccati equation and its new solutions. Then they choose the Karamoto-Sivashinsky (KS) equation to illustrate their approach and obtain many exact solutions of the KS equation.So they claim that, by using their method, one not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear evolution equations. In this comment, we will show that the claim is incorrect.

Generating Lie Point Symmetry Groups of (2-10-Dimensional Broer-Kaup Equationvia a Simple Direct Method

Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.

Exact Solutions for a Higher-Order Nonlinear Schrodinger Equation in Atmospheric Dynamics

By giving prior assumptions on the form of the solutions, we succeed to find several exact solutions for a higher-order nonlinear Schroetinger equation derived from one important model in the study of atmospheric and ocean dynamical systems. Our analytical solutions include bright and dark solitary waves, and periodical solutions, which can be used to explain atmospheric phenomena.

Possible Linear Superpositions for Special Solutions of the Fifth-Order KdV-Type Equations

Using Lou and Ni's deformation and mapping idea in nonlinear equations to a set of fifth order KdV type equations, it is found that some types of solitary wave solutions and periodic solutions with special velocities can be linearly superposed to new exact solutions.

Study of （2＋1）-Dimensional Higher-Order Broer-Kaup System

Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.

Exact Solutions of Nonlinear Dynamics Equation in a New Double—Chain Model of DNA

The exact solutions of the general nonlinear dynamic system in a new double-chain model of DNA are studied by using both the Conte's Painlevé truncation expansion and the Pickering's truncation expansion. The symmetric kink-kink shape excitations can be found in both the Conte's truncation expansion and the Pickering's truncation expansion. Three types of new localized excitations, the asymmetric kink-kink excitations, the soliton-kink excitation, and the kink-soliton excitations, are found by using the Pickering's nonstandard truncation expansion.

Conditional Symmetries and Solutions to a Class of Nonlinear Diffusion-Convection Equations

The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.

New Exact Solutions of Two Nonlinear Physical Models

Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered.

Conditional Symmetry Groups of Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

The generalized conditional symmetry and sign-invariant approaches are developed to study the nonlinear diffusion equations with x-dependent convection and source terms. We obtain conditions under which the equations admit the second-order generalized conditional symmetries and the first-order sign-invariants on the solutions. Several types of different generalized conditional symmetries and first-order sign-invariants for the equations with diffusion of power law are obtained. Exact solutions to the resulting equations are constructed.

Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations

Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.