Lie symmetry algebra of one-dimensional nonconservative dynamical systems

Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.

Nonlinear dynamical symmetries of Smorodinsky-Winternitz and and Fokas-Lagerstorm systems

General solutions of the Smorodinsky-Winternitz system and the Fokas-Lagerstorm system, which are superintegrable in two-dimensional Euclidean space, are obtained using the algebraic method （structure function）. Their dynamical symmetries, which are governed by deformed angular momentum algebras, are revealed.

Exponential Stability of Interval Time-Varying Dynamical System with Multidelay

This paper studies the exponential stability of interval time-varying dynamical system with multidelay. By the matrix measure and delay differential inequality, some sufficient conditions for exponential stability of interval time-varying dynamical system with multidelay are established. These conditions are an improvement and extension of the results achieved in earlier papers. Finally, a numerical example is given to demonstrate our result.

Investigation of the Quaternion Dynamical System

The quaternion Mandelbrot set is one of the most important sets in mathematics. In this paper we first give some properties of the quaternion algebra. Then, we introduce the quternion dynamical system. We are concerned with analytical and numerical investigation of the quaternion dynamical system.

A Simple Jerky Dynamics,Genesio System

The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we show that an algebraically simple system, the Genesio system can be recast into a jerky dynamics and its jerk equation can be derived from one-dimensional Newtonian equation. We also investigate the global dynamical properties of the corresponding jerk system.

Banach Algebra Dynamical Systems

Abstract This paper generalizes the C＊-dynamical system to the Banach algebra dynam- ical system （A, G, α） and define the crossed product A αG of a given Banach algebra dynamical system （A, G,α）. Then the representation of A α G is described when A ad- mits a bounded left approximate identity. In a natural way, the authors define the reduced crossed product A αG and discuss the question when A α G coincides with A αG.

Hybrid extended Fourier series for optimal control of nonlinear algebraic dynamical systems

The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.

Safety Verification of Semi-Algebraic Dynamical Systems via Inductive Invariant

To verify the safety of nonlinear dynamical systems based on inductive invariants, key issues include defining the most complete inductive condition and discovering an inductive invariant that satisfies the specified inductive condition. In this paper, to lay a solid foundation for future research into the safety verification of semi- algebraic dynamical systems, we first establish a formal framework for evaluating the quality of continuous inductive conditions. In addition, we propose a new complete and computable inductive condition for verifying the safety of semi-algebraic dynamical systems. Compared with the existing complete and computable inductive condition, this new inductive condition can be easily adapted to achieve a set of sufficient inductive conditions with different level of conservativeness and computational complexity, which provides us with a means to trade off between the verification power and complexity. These inductive conditions can be solved by quantifier elimination and SMT solvers.

ON THE SOLVABILITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMICAL SYSTEMS

The main purpose of the present paper is to examine the existence and local uniqueness of solutions of the implicit equations arising in the application of a weakly algebraically stable general linear methods to dissipative dynamical systems, and to extend the existing relevant results of Runge-Kutta methods by Humphries and Stuart(1994). [ABSTRACT FROM AUTHOR]

Modeling and Stability Analysis of a Communication Network System

In this work, the modeling and stability problem for a communication network system is addressed. The communication network system consists of a transmitter which sends messages to a receiver. The proposed model considers two possibilities. The first one, that messages are successfully received, while in the second one, during the sending process the transmitter breaks down and as a result the message does not reach the receiver. Timed Petrinets is the mathematical and graphical modeling technique utilized. Lyapunov stability theory provides the required tools needed to aboard the stability problem. Employing Lyapunov methods, a sufficient condition for stabilization is obtained. It is shown that it is possible to restrict the communication network system state space in such a way that boundedness is guaranteed. However, this restriction results to be vague. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.

基于PMU量测的电力系统k阶隐式离散动态状态估计

随着电力系统的快速发展,对系统状态的实时准确估计提出了更高要求。近年来,动态状态估计技术已成为监测电力系统实时运行状态的重要手段。提出了一种基于相量测量单元(phasor measurement unit,PMU)的电力系统动态状态估计(dynamic state estimation,DSE)方法,采用隐式离散化技术处理电力系统的非线性微分代数方程(nonlinear differential algebraic equations,NDAE)模型。建立了包含发电机动态、电网代数方程和潮流方程在内的电力系统NDAE模型,并结合PMU测量信息,对NDAE模型进行了线性化处理;基于隐式离散的方法提出了用于电力系统DSE的求解模型,实现对系统未知的动态和代数状态的有效地估计。基于WECC-9节点电力测试系统进行仿真实验,仿真结果表明,提出的基于PMU的动态状态估计方法,通过隐式离散化技术和NDAE模型的线性化处理,实现了对电力系统状态的准确估计,在实时监测电力系统状态方面具有显著的有效性和可靠性。

计及动态负荷的电力系统静止无功补偿器(SVC)与发电机励磁控制

基于微分代数控制系统的反馈线性化方法,进一步研究了具有非线性负荷的电力系统中静止无功补偿器(Static var compensator,SVC)和发电机三阶模型的励磁控制,表明具有非线性负荷和SVC装置的NDAS(3)仍可以通过状态反馈精确线性化,从而得到具有代数方程的Brunovsky标准型。提出了具有非线性负荷的电力系统SVC与发电机励磁控制的完全精确线性化设计。该控制方法可以同时满足发电机功角稳定和SVC节点处电压。仿真结果表明该方法具有很好的效果和优越性。

基于空间算子代数理论计算多体系统动力学建模

为了提高计算多体系统动力学正、反向动力学建模效率,应用空间算子代数理论,在通用计算机符号演算软件Mathematica6.0的环境下,对计算多体系统正、反向动力学进行设计与实现。广义质量是联系旋量力和旋量加速度的的重要参量,据此可形成正、反向动力学高效递推算法,用空间算子代数理论求出广义质量、正、反向动力学具有形式简洁、物理意义明确、编程效率高和直观等特征。运用VB.NET编程软件实现与Mathematica6.0软件无缝集成,对计算多体系统动力学仿真及正、反向动力学进行参数化分析与计算,给出编程实施过程及建模IDEFO方法。根据分析结果,对PUMA560机器人典型多体系统进行正、反向动力学建模,并与结果进行对比,通过算例验证结果的正确性和有效性。

信息流控制研究进展

信息流控制能够保证数据与隐私端到端安全,一直是信息安全领域研究的重点和难点.为介绍信息流控制相关的研究现状和进展,首先,从基于格、安全类型系统、安全进程代数和自动机这4个方面介绍了信息流控制的基本理论与模型;其次,从计算机层次结构由下而上出发,综述了基于硬件、操作系统、虚拟机、高级语言、低级语言、数据库和网络的信息流控制实现方法,并对比了各类研究的特点;然后,结合当今时代前沿技术,分析了信息流控制在云计算、移动互联、大数据和物联网等新技术下的应用;最后,总结了当前信息流控制相关研究中存在的问题,并针对今后该领域的研究趋势进行了展望,对下一步研究工作有一定的参考价值.

基于微分代数模型的AC/DC系统非线性控制器设计

针对电力系统实际负荷以及直流系统本身的非线性特性,在微分代数模型的基础上,将M导数、M括号以及MIMO微分代数系统反馈线性化技术运用到交直流并联系统非线性控制器设计中。在系统的M关系度小于系统阶数及其满足一定的条件时,可得到微分代数系统模型的Bronovsky标准形式,并对交直流混合(AC/DC)系统中发电机励磁控制和直流系统整流侧定电流控制律进行了深入研究。针对一个含有AC/DC的单机无穷大系统(SMIBs)进行实例仿真,研究结果表明所设计的非线性控制器与传统的PID控制器相比具有较好的阻尼特性,能进一步提高系统的动态稳定性。该控制器的设计方法可以很方便地应用于多机交直流并联系统的稳定性控制。

建立航空发动机状态空间模型的修正方法

以阶跃输入响应进行模型的检验, 提出了状态空间模型的修正方法: 基于动态响应较好的状态空间模型, 进行其矩阵B, D, F, G的修正, 获得基于稳态修正的模型, 解决了航空发动机状态空间模型检验与修正的问题。仿真表明, 使用该方法修正的状态空间模型具有与原非线性数学模型完全一致的稳态响应和基本一致的动态过程响应。这种方法为航空发动机多变量数字电子控制器的设计奠定了强有力的基础。

双时间尺度电力系统动态模型降阶研究(二)——降阶与分析

电力系统是一个多时间尺度的大规模非线性系统 ,其稳定性分析非常复杂。在实际的电力系统稳定分析中 ,具有快变特征的电磁变量的动态通常被略去 ,通过系统降阶使稳定性分析得以简化。然而 ,一个十分重要的问题是在什么条件下系统的降阶不会引起质的错误。同时 ,降阶后的系统代数方程的特征也需要进行充分的研究 ,以便对降阶后的系统模型进行分析。文中以基于物理电路的计及快慢动态的电力系统奇异摄动模型为基础 ,研究了系统降阶的条件 ,得到了当系统负荷模型为感应电动机和并联线性阻抗时系统降阶对系统稳定分析不会引起质的错误的重要结论。另外 ,文中还证明了在上述负荷模型下 。

极大代数方法在轧钢厂DEDS中的应用

本文用极大代数方法对某轧钢厂建立了离散事件动态系统（ＤＥＤＳ）模型，在周期分析与配置理论的基础上解决了最优调度与控制问题．

基于空间算子代数理论多体系统动力学雅可比矩阵设计与实现

应用空间算子代数理论,在通用计算机符号演算软件Mathematic5.2的环境下,对多体系统动力学雅可比矩阵进行设计与实现,主要用于速度和静力的高效递推算法,用空间算子代数理论求出雅可比矩阵简洁形式,具有编程效率高、直观等特征。运用VB.NET编程软件实现与Mathematic5.2软件无缝集成,对多体系统动力学仿真及雅可比进行参数化分析与计算,给出了实施过程。根据分析结果,对Stanford机器人进行了雅可比设计,并与结果进行了对比,通过算例验证了结果的正确性和有效性。

基于对策论的群机器人追捕-逃跑问题研究

将群机器人追捕-逃跑问题看成具有两个局中人的离散动态对策问题,考虑了距离影响、走步影响、有效包围3个因素,构造出威胁评估函数,通过计算各种可能的策略下追捕者对逃跑者的威胁值得到追捕者的支付矩阵,求解该矩阵即可得到每次走步时对抗双方的最优走步策略.以此作为双方策略选择的数学模型,并在此基础上提出了实时策略选择算法.仿真试验结果验证了该模型和算法的可行性.