The Relation between the Stabilization Problem for Discrete Event Systems Modeled with Timed Petri Nets via Lyapunov Methods and Max-Plus Algebra

A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. 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.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

Lyapunov-Based Output Containment Control of Heterogeneous Multi-Agent Systems With Markovian Switching Topologies and Distributed Delays

This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.

The Variational Lyapunov Method and Stability for Impulsive Delay Differential Systems

By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improved. An example is worked out to illustrate the advantages of the theorems.

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

Forecasting available parking space with largest Lyapunov exponents method

The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.

基于李雅普诺夫直接法的MMC控制策略研究

为改善PI控制下模块化多电平变换器(modular multilevel converter,MMC)的控制效果,提出了基于李雅普诺夫直接法的MMC控制策略。首先,建立MMC整流器的数学模型。其次,构造出MMC系统的李雅普诺夫能量函数。然后,在MMC数学模型和能量函数的基础上设计了控制系统。由奈奎斯特稳定判据分析了直流电压稳定性的影响因素,并在经典频域下通过伯德图对比分析了李雅普诺夫控制策略和PI控制策略的控制性能。最后,在负载阶跃、交流侧电压幅值阶跃和交流侧三相电压不平衡工况下对两种控制策略进行了仿真和半实物在环仿真研究。结果表明,李雅普诺夫控制策略较PI控制策略有着更好的控制效果,李雅普诺夫控制策略更适用于MMC此类非线性强耦合系统。

基于切换系统的独立微电网稳定控制设计

独立微电网是一个复杂的非线性系统,为解决典型光储柴独立微电网在能源约束下存在控制单元切换的问题,提出将非线性切换系统理论应用到主从控制下的主控单元切换问题上。首先,当主从控制下的储能系统和柴油发电机分别作为主控单元时,将它们视为两个子系统,建立非线性切换系统模型。然后,应用多Lyapunov函数法分析切换系统的稳定性,同时利用backstepping方法分别设计子系统的非线性控制器,保留系统的非线性特征。最后,采用美国国家能源实验室开发的仿真软件中的硬充电策略作为切换策略,保证切换过程中系统的稳定性。通过MATLAB仿真证明了所设计方法的有效性。

长相关随机模型FBM对光伏发电短期预测

针对光伏发电功率具有较强的波动性、间歇性输出,光伏功率预测精度较低,且难于给出具体预测时间长度等问题,提出了一种长相关随机模型分数阶布朗运动(fractional Brownian motion,FBM),用于光伏功率预测。首先,采用重标极差法计算长相关(long-range dependence,LRD)参数-Hurst指数,Hurst指数用于判断光伏功率数据是否满足长相关性,并通过最大李雅普诺夫指数(Lyapunov)计算出模型最大可预测时间尺度;其次,采用随机微分法建立FBM光伏功率预测模型,同时估计FBM预测模型参数值;最后,选取澳大利亚沙漠知识太阳能中心(Desert Knowledge Australia Solar Center,DKASC)、美国国家可再生能源实验室(National Renewable Energy Laboratory,NREL)以及北京国能日新科技有限公司的光伏功率数据集,从不同的地理环境、不同的气候特征、不同的规模大小电站进行验证。仿真结果表明,该模型较传统的Kalman、LSTM模型具有更高的预测精度,可为光伏并网的稳定和安全运行提供更好的理论支持,对电网调度部门具有较高的参考价值。

单相并网储能双向变流器线性时间周期模型的稳定性分析

针对传统线性时不变模型无法描述储能双向变流器多频次谐波间交互耦合现象的问题,提出了一种单相并网储能双向变流器的线性时间周期模型,并进行稳定性分析。基于线性时间周期理论对单相并网储能双向变流器进行建模,得到非线性时间周期模型;围绕周期轨道将该模型线性化,得到储能双向变流器的线性时间周期时域模型;通过傅里叶展开推出了储能双向变流器的线性时间周期频域模型;利用李雅普诺夫第一方法分析比例积分控制器在不同参数下的储能双向变流器小信号模型的稳定性及稳定边界。MATLAB/Simulink仿真实验结果表明:建立的单相并网储能双向变流器的线性时间周期模型具有准确性和稳定性,稳定性边界正确。

Analysis of the Boundary Stability of a Diffusion-Reaction System on a Nanolayer

In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.

Stewart平台神经网络非奇异终端滑模控制

针对Stewart平台的六自由度(six degrees of freedom,6-DOF)轨迹跟踪问题,提出一种基于神经网络的非奇异终端滑模控制方法并应用于Stewart平台的位置姿态控制中。通过分析Stewart平台的位置反解和速度反解,建立运动学方程,利用牛顿-欧拉方程建立动力学方程,并结合加速度反解得到了平台的状态空间表达式;基于非奇异滑模面函数,设计非奇异终端滑模控制律。考虑到径向基函数(radial Basis function,RBF)神经网络的逼近特性,采用RBF神经网络对模型未知部分进行自适应逼近,并利用Lyapunov第二法设计了自适应律;通过仿真证明控制器设计的有效性。仿真结果表明,相比于比例积分微分(proportional integral derivative,PID)控制器,提出的RBF神经网络非奇异终端滑模控制器具有更好的轨迹跟踪精度和动态特性。

基于结构Lyapunov矩阵的静态输出反馈镇定

线性时不变系统的静态输出反馈控制可行性等价于两个耦合的线性矩阵不等式解的存在性问题,这导致了一个非线性最优化问题,是无法直接求解的.针对线性时不变系统(LTI),深入研究这两个矩阵不等式的关系,通过构造一个结构Lyapunov矩阵,给出了一个问题有解的充分条件,并在此基础上提出一个静态输出反馈镇定算法.利用线性矩阵不等式(LMI)方法,可直接求解出相应的输出反馈增益.数值实例证明了该方法的有效性.

具有死区非线性输入的柔性臂自适应边界控制

研究了具有死区非线性和输入信号量化的柔性机械臂系统的边界控制问题。考虑柔性臂系统分布参数的特点,采用偏微分方程和边界条件描述柔性机械臂系统的动力学模型,并采用随机量化器对输入信号进行量化。对于输入受限的柔性机械臂系统,设计了一种自适应边界控制器,使柔性机械臂系统到达期望角度的同时抑制柔性机械臂系统的振动。该控制方案既能保证系统的稳定性,又能在输入信号量化和死区非线性的前提下满足控制要求。同时,利用Lyapunov方法证明了柔性机械臂系统的最终一致有界性。最后,通过数值仿真验证了所提出方法的有效性。

基于Lyapunov函数方法的海洋资源勘探拖缆水平振动的控制

为了提高海洋资源勘探拖缆系统的数据采集效率,提出了海洋资源勘探拖缆系统的水平主动振动控制的Lyapunov函数方法.利用线性变系数双曲方程描述拖缆系统,利用常微分方程描述深度控制器(水鸟)的动力学方程.选取海洋资源勘探拖缆和水鸟的总能量为Lyapunov函数,基于Lyapunov方法设计了控制规律,包括水鸟处拖缆的速度、斜率.该控制规律具有指数稳定性,有效解决了海洋资源勘探拖缆水平位移难以测量的问题.运用数值仿真,验证了所提出的控制策略的有效性.

滑移铰空间机器人基于分级Lyapunov方法的避障碍非完整运动规划

基于分级Lyapunov方法,讨论了载体姿态与位置均不受控制的滑移铰空间机器人末端运动轨迹的避 障碍运动学规划问题.首先以系统动量矩守恒关系及运动.Jacobi关系为基础,建立了控制设计所需的系统状态 方程及控制输出方程.此后,在Lyapunov函数的选取上采取分两级采取的方式,即初级Lyapunov函数确保 滑移铰空间机器人的末端抓手从初始位置运动到指定的终点位置,次级Lyapunov函数则确保末端抓手避开工作 空间中的障碍区域;两级合成则使空间机器人的末端抓手既实现了指定的位置移动又避开了障碍区域.系统数值 仿真,证明了方法的有效性.

n比特随机量子系统实时状态估计及其反馈控制

研究了n比特随机量子系统实时状态估计及其反馈控制的问题.对于连续弱测量(Continuous weak measurement, CWM)过程存在高斯噪声的情况,基于在线交替方向乘子法(Online alternating direction multiplier method,OADM)推导出一种适用于n比特随机量子系统的实时量子状态估计算法,即QSE-OADM (Quantum state estimation based on OADM).运用李雅普诺夫方法设计控制律,实现基于实时量子状态估计的反馈控制,并证明所提控制律的收敛性.以2比特随机量子系统为例进行数值仿真实验,通过与基于QST-OADM (Quantum state tomography based on OADM)算法和OPG-ADMM (Online proximal gradient-based alternating direction method of multipliers)算法的量子反馈控制方案的性能对比,验证了所提控制方案的优越性.

广义系统渐近稳定分析与镇定的Lyapunov方法

利用Lyapunov方法研究了广义系统的渐近稳定性分析及控制问题,首先提出一种新形式的Lyapunov方程,用来研究广义系统渐近稳定性与镇定问题,同时给出了利用Lyapunov方程判定具有脉冲形式下广义系统渐近稳定的充分必要条件。利用相应的Riccati方程完成镇定广义系统的状态反馈控制器的设计。本文所有结论对广义系统有无脉冲行为均适用。最后利用数值例子说明主要结果。

树形多体Hamilton系统的Lyapunov指数计算方法

研究了树形多体Hamilton系统Lyapunov指数的数值方法 .利用多体Hamilton系统的正则方程和辛算法 ,给出了多体Hamilton系统Lyapunov指数的计算方法 ,该算法具有较好的计算精度和通用性 .利用该算法可对系统的运动稳定性进行分析 .最后用算例说明了该算法的有效性 .

导弹高度控制变结构设计中Lyapunov方法应用

基于Lyapunov方法的变结构系统中运动分为正常运动及滑模运动。正常运动不具有对参数摄动及外界干扰的鲁棒性,故期望其运动稳定且快速地趋近滑模面,而这主要受Lyapunov矩阵Q及变结构控制参数k的影响;滑模运动具有鲁棒性,而滑模面的大小及滑动性能受制于Q。为了达到期望的性能指标,需要选择适当的Q和k。通过理论推导,分析了Q和k对运动性能的影响,得出了参数间的具体耦合作用,建立了相应的优化模型。通过某巡航导弹高度控制仿真,证明了按照理论分析所采取的优化能满足各项设计指标,且抖振得到较好削弱;通过弹体参数扰动仿真分析证明了变结构控制的鲁棒性优势。