关于高阶不确定非线性系统的鲁棒适应干扰衰减问题

研究一类高阶不确定非线性系统的鲁棒适应H∞干扰衰减问题。本质改进了加幂积分器技巧及backstepping算法,并设计出一个光滑鲁棒适应动态反馈控制律,使得闭环系统既具有内稳定性,又使系统达到干扰衰减．所得结果改进了相关文献中的结论．     

一定要分离参数吗？

分离参数是求解“求参数的取值范围”一类题目的常用技巧．本文精选三道典型题，以阐明该种解题技巧的适用性，供同学们参考．     

一类非严格双曲型守恒律整体连续解的存在性

该文利用初值扰动法，讨论了一类非严格双曲型守恒律Ｃａｕｃｈｙ问题整体连续解的存在性．这类方程包括了等熵气体动力学方程组．一个典型的变形方程组，弹性力学方程组，二次流守恒律和旋转退化方程等有意义的模型．     

“取倒数”在数列型不等式问题中的妙用

数列型不等式．综合了数列与不等式的内容，因而内涵丰富，故成为高考的热点和难点．对这类问题的处理常采取放缩、利用数列的单调性等技巧，而取一个数（式）的倒数在这类问题中却有着独特的作用，可谓“小技巧，办大事”．下面举例说明“取倒数”技巧的妙用．     

不确定非线性系统的鲁棒适应H_∞几乎干扰解耦问题

本文研究了带有不确定参数的非线性系统的鲁棒适应 H∞ 控制的几乎干扰解耦问题 .运用改进的加幂积分器技巧与递归设计方法 ,构造性地设计了一种光滑鲁棒动态反馈控制律 ,在保证闭环系统内稳定的基础上 ,使系统达到干扰衰减 .     

不确定非自治混沌陀螺仪在非线性输入下的有限时间稳定性

陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果.     

飞艇姿态跟踪系统的研究

研究了具有参数不确定和外部干扰的飞艇姿态跟踪控制问题．飞艇姿态运动的数学模型为一个多输入/多输出不确定非线性系统,根据该系统的特点,采用了一个基于不确定项上界的鲁棒输出跟踪控制器设计方法,应用输入/输出反馈线性化法和李雅普诺夫方法,设计了飞艇姿态鲁棒控制律,它可确保系统输出按指数规律跟踪期望输出．该控制器设计简单,易于实现．仿真结果表明:即使系统存在不确定性和外界干扰,仍可在闭环系统中实现精确的姿态控制．     

一个刚性守恒律方程组的全隐式差分方法

１．引言本文研究如下非线性刚性守恒律方程组的全隐式差分逼近． 方程（1．１）中的源项ｇ（ｕ,ｖ）定义为 ｇ（ｕ,ｖ）＝ｖ－（１－μ）ｆ（ｕ）,（１．２）其中ｆ是ｕ的一个给定函数,δ是一个小正参数,称为松弛时间,μ是参数．方程组（１．１）频繁出现于粘弹性力学中． 在零松弛时间限（δ→０）下,从（１．１）可得到如下方程组该方程组通常称为“平衡”模型,而方程组（１．１）称为“非平衡”模型． 文中将假设μ满足 ０＜ μ＜ １,（１．４）以便保证拟稳定性条件［１９,２０］和次特征条件［１１,２,３］： λ１≤λ＊…     

介紹新編初中算术課本(暫用本)

(一)1959年秋的初一学生,一般来說,还有学习算术的必要 1959年秋的初一学生,从他們在小学里所使用过的算术課本的内容來看,与普通教育当中应当掌握的算术知識和技巧相比較: 整数方面学的不全,例如,关于概念和性貭,学了整数的讀法和写法,沒有学整数的意义;学了交換律,没有学結合律和分配律,沒有学运算性貭;学了除法的意义和法則,沒有学“不能用零作除對”;关于計算技巧方面,口算和     

含参数不等式四类问题的辨析与求解

含参数的不等式历来是高考和竞赛命题的热点,也是中学数学的一个难点．大家都喜欢用分离参数法来解决这类问题,但如果不注意“有解”、“无解”、“恒成立”和“已知解集”这些条件的区别,是很容易犯错误的．下面给出三组命题,说明这四者之间的关系．用数形结合的思想,不难得出这些命题．     

Robust decentralized adaptive control for a class of uncertain neural networks with time-varying delays

This paper considers the robust control problem for a class of uncertain time-varying delayed neural networks, in which the activation function may be a discontinuous function. A robust decentralized adaptive sliding mode controller is proposed to guarantee the asymptotically stability of the system. The proposed controller, which does not dependent on the time delay, ensures the occurrence of the sliding manifold even when the system is undergoing parameter uncertainties and nonlinear input. Two numerical examples are given to show the effectiveness of the proposed controller.     

一类不确定非线性系统的适应输出反馈控制

针对一类存在有界干扰的线性参数化非线性系统，给出了一种新的适应输出反馈控制器．该控制器能保证闭环控制系统所有信号的全局有界性．该文将现有的非线性适应输出反馈控制方面的结果，从无扰动情形推广到了存在有界干扰的情形．仿真结果用来说明所设计控制器的有效性．     

Finite-time stabilization for hyper-chaotic Lorenz system families via adaptive control

This paper is concerned with finite-time stabilization of hyper-chaotic Lorenz system families. Based on the finite-time stability theory, a novel adaptive control technique is presented to achieve finite-time stabilization for hyper-chaotic system. The controller is simple and easy to be implemented, and can stabilize almost all well known high-dimensional chaotic systems. Simulation results for hyper-chaotic Lorenz system, Chua’s oscillator, Rössler system are provided to illustrate the effectiveness of the proposed scheme.     

Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques

In this paper, a robust adaptive control law for a class of uncertain nonlinear systems is proposed. The proposed controller guarantees asymptotic output tracking of systems in the strict-feedback form with unknown static parameters, and matched and unmatched dynamic uncertainties. This controller takes advantages of a robust stability property of the Lyapunov redesign method and a systematic design procedure of the backstepping technique. In fact, the backstepping technique is employed to enrich the Lyapunov redesign method to compensate for not only matched - but also unmatched-uncertainties. On the other hand, using the Lyapunov redesign method in each step of the conventional backstepping technique makes backstepping robust. The suggested controller is designed through repeatedly utilizing the Lyapunov redesign method in each step of the backstepping technique. Simulation results reveal the efficiency of the Lyapunov redesign-based backstepping controller.     

不确定关联时滞大系统的自适应分散镇定控制

针对时变的满足一定匹配条件的不确定关联时滞大系统,利用自适应界化技术,给出了设计分散镇定控制器的自适应的方法.其特点是在假设中系统不确定项是有界的,但界是未知的,且在关联项存在时变时滞的情况下证明了闭环自适应系统的渐近稳定性.最后举例说明了该方法的有效性.     

受扰不确定混沌系统的降阶修正函数投影同步

研究了具有不同阶数的受扰不确定混沌系统的降阶修正函数投影同步问题.基于Lyapunov稳定性理论和自适应控制方法,设计了统一的非线性状态反馈控制器和参数更新规则,使得混沌响应系统按照相应的函数尺度因子矩阵和混沌驱动系统的部分状态变量实现同步.方法考虑了实际系统中的模型不确定性和外界扰动,具有较强的实用性和鲁棒性.数值仿真证明了控制方法的有效性.     

Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach

In this paper, an adaptive sliding mode controller for a novel class of fractional-order chaotic systems with uncertainty and external disturbance is proposed to realize chaos control. The bounds of the uncertainty and external disturbance are assumed to be unknown. Appropriate adaptive laws are designed to tackle the uncertainty and external disturbance. In the adaptive sliding mode control (ASMC) strategy, fractional-order derivative is introduced to obtain a novel sliding surface. The adaptive sliding mode controller is shown to guarantee asymptotical stability of the considered fractional-order chaotic systems in the presence of uncertainty and external disturbance. Some numerical simulations demonstrate the effectiveness of the proposed ASMC scheme.     

Design of a coordinated adaptive backstepping tracking control for nonlinear uncertain active suspension system

This paper presents a novel adaptive backstepping tracking control for nonlinear uncertain active suspension system, which can achieve the coordinated control over the sprung-mass acceleration and suspension dynamic displacement for nonlinear uncertain active suspension system based on a developing model-reference system. First, according to adaptive backstepping control principle, this model-reference system is designed with purpose of providing the ideal reference trajectories for the sprung-mass displacement and vertical velocity, respectively. Then, the design of a coordinated adaptive backstepping tracking controller is conducted to make the control plant accurately track the prescribed performances of the model-reference system by virtue of the backstepping technique and Lyapunov stability theory, in which a virtual controller with online parameter regulation rules is designed and implemented to guarantee the stability of vehicle body. Finally, a numerical example is provided to verify the effectiveness of our designed adaptive backstepping tracking controller under various operating scenarios.     

一类不确定混沌系统的自适应同步

讨论了混沌系统的同步问题 .对一类不确定混沌系统 ,提出了一个新的自适应同步方法 ,可使响应系统在自适应控制器的控制下 ,实现与不确定混沌系统的同步 .最后给出了一个设计实例 .     

一类不确定非线性系统的适应H-infinity控制

主要讨论了一类具有不确定参数的非线性系统的通过适应输出反馈达到干扰衰减的问题．通过构造降维观测器,利用Backstepping方法设计输出反馈控制器,使闭环系统具有不确定参数的标准的增益问题可解,并使系统达到内稳定．