混合系统的稳定性分析

研究了混合系统的稳定性问题.首先,对于混合系统给出了一种一般的模型,该模型能够描述混合状态的跳变现象.然后,定义了一种辅助函数作为系统能量的一种度量.基于该模型和辅助函数,得到了混合系统稳定性判定的一些新结果.这些结果给出了在离散状态改变时,在由于连续状态的跳变而引起的系统能量增加的情况下,混合系统仍保持稳定的充分条件.最后,给出了一种能量函数的寻找方案,并利用一个仿真实例验证了该方案的有效性.     

STATCOM的系统仿真

本文基于MATLAB中的动态仿真工具SIMULINK,建立了静止无功发生器的仿真模型.以含有静止无功发生器的单机无穷大系统为例,结合多目标控制方法,用S-Function仿真分析了静止无功发生器在系统暂态故障过程中的调节作用.仿真结果验证了本文所设计的多目标控制器的正确性以及本无功发生装置仿真模型的有效性.     

STATCOM的系统仿真

本文基于MATLAB中的动态仿真工具SIMULINK,建立了静止无功发生器的仿真模型。以含有静止无功发生器的单机无穷大系统为例,结合多目标控制方法,用S-Function仿真分析了静止无功发生器在系统暂态故障过程中的调节作用。仿真结果验证了本文所设计的多目标控制器的正确性以及本无功发生装置仿真模型的有效性。     

多目标控制方法的STATCOM系统仿真

为了研究采用多目标控制的静止无功发生器对电力系统的调节作用,建立了基于MATLAB的静止无功发生器的仿真模型。以含有静止无功发生器的单机无穷大系统为例,结合多目标控制方法,用S—Function仿真分析了静止无功发生器在系统暂态故障过程中的调节作用。仿真结果验证了所设计的多目标控制器的正确性以及该无功发生装置仿真模型的有效性。     

基于多李雅普诺夫函数的一般非线性系统渐近镇定

针对离散时间非线性系统, 提出一种基于多李雅普诺夫(Lyapunov)函数的控制器设计方法. 该方法不仅能够保证闭环系统稳定性, 还能够扩大闭环吸引域(Domain of attraction, DOA). 首先, 给出基于多Lyapunov函数下系统渐近稳定的充分条件. 结果表明, 由多个Lyapunov函数的负定不变集构成的并集是一个稳定的控制集合, 其从控制空间到状态空间的投影是闭环DOA的估计. 随后, 使用区间分析算法求解集合的内近似估计, 基于此算法可以求解多Lyapunov函数的负定不变集的近似值和闭环DOA的估计值, 并给出相应控制器的设计方法. 最后, 通过仿真算例验证了本文方法的有效性.     

随机时滞神经网络的全局指数稳定性

首先对一般随机系统的渐近特性进行了讨论.然后结合神经网络的特点,应用李雅普诺夫第二方法对一类随机时滞神经网络系统的全局指数稳定性进行了分析,给出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,并给出实例进行仿真实验.     

简单电力系统静态稳定性分析及研究

文章以一个单机-无穷大系统为例,分析了影响电力系统静态稳定性的因素,介绍了静态稳定性的分析方法,提出了提高电力系统静态稳定性的措施。通过采取改善电力系统基本元件的特性和参数及采用附加装置等措施,提高了电力系统的静态稳定性。     

带输出误差约束的单机电力系统自适应控制

针对带有静止无功补偿器(SVC)的单机无穷大电力系统,提出了一种自适应动态面与积分滑模控制相结合的控制方案,有效地克服了参数不确定性和外部扰动的影响,确保了系统跟踪误差能够在有限时间内收敛到稳定状态,提高了系统的收敛速度和跟踪精度。通过引入误差转换函数,使得功角的跟踪误差性能指标保持在预定的范围内。采用最小参数学习法在线估计径向基函数神经网络(RBFNN)理想权值向量的范数,避免了神经网络因估计自身权值向量维数增加而引起的“维数灾难”问题,极大减轻了控制器的计算负担。控制算法通过StarSim电力电子实时仿真实验平台进行实验验证,实验结果表明了所提控制方案的有效性。     

基于DSP控制的静止无功发生器控制器的研究

静止无功发生器(SVG)是柔性交流输电系统中的一种重要的控制器.由于以传统的单片机作为控制器的SVG受硬件资源与速度的限制,无法实现对电网的实时动态无功补偿,因此本文提出了一种基于DSP控制新型静止无功发生器的方案,并进行了深入的分析和研究.     

带有时变时滞和同步切换的忆阻神经网络的全局指数稳定性

本文建立并研究了一类具有时变时滞和不同切换机制的忆阻神经网络.利用李雅普诺夫稳定性理论,得到了该神经网络平衡点一致稳定性的充分条件,该充分条件直接有效地反映了时变时滞对稳定性的影响.数值模拟结果验证了理论结果的有效性.     

Stability analysis of constrained MPC with CLF applied to discrete-time nonlinear system

The problem of counting the number of spanning trees is an old topic in graph theory with important applications to reliable network design. Usually, it is desirable to put forward a formula of the number of spanning trees for various graphs, which is not only interesting in its own right but also in practice. Since some large graphs can be composed of some existing smaller graphs by using the product of graphs, the number of spanning trees of such large graph is also closely related to that of the corresponding smaller ones. In this article, we establish a formula for the number of spanning trees in the lexicographic product of two graphs, in which one graph is an arbitrary graph G and the other is a complete multipartite graph. The results extend some of the previous work, which is closely related to the number of vertices and Lapalacian eigenvalues of smaller graphs only.     

Stability analysis of constrained MPC applied to discrete-time nonlinear with CLF system

The model predictive control （MPC） strategy with a control Lyapunov function （CLF） as terminal cost is commonly used for its guaranteed stability. In most of the cases, CLF is locally designed, and the region of attraction is limited, especially when under control constraints. In this article, the stability and the region of attraction of constrained MPC that is applied to the discrete-time nonlinear system are explicitly analyzed. The region of feasibility is proposed to substitute the region of attraction, which greatly reduces the calculation burden of terminal constraints inequalities and guarantees the stability of the MPC algorithm. Also, the timevariant terminal weighted factor is proposed to improve the dynamic performance of the close-loop system. Explicit experiments verify the effectiveness and feasibility of the relative conclusions, which provide practically feasible ways to stabilize the unstable and/or fast-dynamic systems.     

Estimating the domain of attraction for non-polynomial systems via LMI optimizations

This paper proposes a strategy for estimating the domain of attraction (DA) for non-polynomial systems via Lyapunov functions (LFs). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst-case remainders in truncated Taylor expansions. Moreover, a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen LF, and another condition is provided for establishing whether such an estimate has been found. The proposed strategy can readily be exploited with variable LFs in order to search for optimal estimates. Lastly, it is worth remarking that no other method is available to estimate the DA for non-polynomial systems via LMIs.     

Estimating the domain of attraction via union of continuous families of Lyapunov estimates

This paper proposes a new approach to estimate the domain of attraction of equilibrium points of polynomial systems. The idea consists of estimating the domain of attraction via the union of a continuous family of Lyapunov estimates rather than via one Lyapunov estimate only as done in existing methods. This family is obtained through a convex LMI optimization by deriving a stability condition which takes simultaneously into account all considered Lyapunov functions. Moreover, inner approximations of the union of this family via a set with simple shape are also derived.     

Estimating the domain of attraction for uncertain polynomial systems

Estimating the Domain of Attraction (DA) of equilibrium points is a problem of fundamental importance in systems engineering. Several approaches have been proposed for the case of known polynomial systems allowing one to find the Largest Estimate of the DA (LEDA) for a given Lyapunov Function (LF). However, the problem of estimating the Robust DA (RDA), that is the DA guaranteed for all possible uncertainties in an uncertain system, it is still an unsolved problem. In this paper, LMI methods are proposed for estimating the RDA in the case of systems depending polynomially in the state and in the uncertainty which is supposed to belong to a polytope. Specifically, the issue of computing the Robust LEDA (RLEDA), that is the intersection of all LEDAs, is considered for common and parameter-dependent LFs, providing constant and parameter-dependent lower bounds. The computation of approximations with simple shape of the RLEDA in the case of parameter-dependent LFs is also discussed.     

离线鲁棒预测控制器综合方法的改进方案

对离线鲁棒预测控制器综合方法进行改进.离线鲁棒预测控制算法离线确定一个控制律序列,对应一组吸引域;在线根据当前状态位于哪个吸引域内部(或哪两个吸引域之间)选择相应的一个控制律(或相邻的两个控制律的线性插值).引入参数Lyapunov函数得到多包椭圆型吸引域和多包二次稳定的离线控制律,改进了控制器的可行性和最优性.改进的控制器保持了稳定性以及控制律关于系统状态的连续性.     

基于T-S模型的体操机器人系统模糊变结构控制

针对体操机器人（Acrobot）这类非线性系统,给出一种基于T—S模型的模糊变结构控制律设计．首先采用T—S模型建模,得到Acrobot的全局模糊模型;然后基于Lyapunov理论设计出保证Acrobot全局渐近稳定的模糊变结构平衡控制器．仿真结果表明,所设计的模糊变结构控制器与普通变结构控制器相比．可使Acrobot系统在垂直向上平衡点附近具有更大的吸引域和更强的鲁棒性．     

约束T-S模糊系统设计的模糊Lyapunov方法

通过引入模糊Lyapunov函数,研究一类执行器饱和的离散T-S模糊系统.对系统设计模糊抗积分饱和补偿器,得到系统稳定的充分条件,并扩大了系统的吸引域.这种方法避免了寻求一个满足系统所有模糊规则的公共正定矩阵P.最后,抗积分饱和补偿器增益通过迭代优化算法得到.