非均质Timoshenko梁在局部耦合反馈下的指数稳定性

研究了非均质Timoshenko梁在局部耦合反馈下的指数稳定性．首先利用有界Co—半群渐近稳定性判据，证明了闭环系统是渐近稳定的，然后用频域乘子方法证明了闭环系统也是指数稳定的．     

控制系统结构稳定性的一种定量分析方法

§1.引言及问题文[1]应用矩阵扰动分析方法研究了线性控制系统的结构稳定性,得到了闭环系统关于矩阵范数‖·‖2(?)‖·‖_F 和 ‖·‖_∞在标称参数点 P_0处的结构稳定裕度下界的一系列估计公式。受扰闭环系统保持无静差只是一个基本的要求,受扰闭环系统的其它动态品质指标的变化也是应考虑的。由于系统的谱的分布对其动态品质有很大的影响,为此需要研究使受扰闭环系统不仪保持无静差,且使其谱的分布在一个预先指定范围内变化的结构稳定问题。     

具有稳定自治动态的一般非线性系统的镇定问题

针对一般非线性系统,在它的自治动态是稳定的条件下,应用Lyapunov方法获得它可全局渐近稳定的充分条件,同时在系统函数是解析的情况下,基于输出反馈控制律,构造出了类Luenberger观测器,使得闭环系统的平衡点全局渐近稳定.     

一类具有闭环极点约束的不确定线性系统的保性能控制

主要研究了闭环系统的极点约束在一个给定圆盘中的保性能控制问题,基于线性矩阵不等式处理方法给出了状态反馈控制器存在的充要条件,并利用线性矩阵不等式的解给出了保性能控制器的设计方法,得到一个状态反馈控制器,使得对所有允许的不确定性闭环系统稳定,并且闭环性能指标值不超过某个确定的上界.最后以数值例子验证了结果的正确性.     

两端固定n根系列连接的Timoshenko梁在连接点加控制的镇定问题

文章研究两端固定n根系列连接的Timoshen]K0梁系统的镇定问题,假设该系统在连接点处剪切力和弯曲力矩是连续的,而横向位移和旋转角度是不连续的.在连接点处设置控制器,观测节点处的力,通过补偿器补偿后反馈回系统,构成闭环系统.通过对系统的矩阵化处理,对算子谱采用渐近分析的技巧,证明得到该闭环系统是渐近稳定的.并利用算子谱的分布等性质,在一定条件下得到了闭环系统的Riesz基性质,从而系统满足谱确定增长条件.     

基于边界输出反馈非线性波方程的自适应控制稳定性

研究了基于边界输出反馈非线性波方程的自适应控制稳定性问题.利用可测的终端速度,获得了高增益自适应控制器,使用加辽金方法获得闭环系统解的存在性与唯一性,同时,证明闭环系统是指数稳定的.     

Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定

研究具有边界控制的Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定问题.首先,给出开环系统在Salamon意义下的适定性;其次,运用半群方法和LaSalle不变原理,证明了闭环系统生成C_0-半群并且闭环系统是渐近稳定的;最后,设计了一个未知输入类型的状态观测器,其观测器状态渐近收敛于原系统的状态.     

具有动态边界的非均匀Euler-Bernoulli梁的边界反馈镇定

本讨论一端带有重物的Euler-Bernoulli梁的边界反馈镇定问题。在生物的质量忽略不计而只考虑重物的转动惯量的情况下，证明了同时在梁的自由端施加力和力矩反馈，闭环系统的能量可被指数镇定。进而对于系统只有力反馈或只有力矩反馈的情况，得到了闭环系统（指数）稳定的充分必要条件。     

一类随机非线性马尔可夫切换系统的输出反馈控制

研究了一类具有马尔可夫切换的随机非线性系统的输出反馈镇定问题.利用非线性增益观测器设计方法,结合反推技术,设计了输出反馈控制器,保证了闭环系统几乎处处有唯一解且闭环系统是几乎处处渐近稳定的.数值仿真验证了输出反馈控制器的有效性.     

多径路由网络化控制系统的路径调度与控制器协同设计北大核心CSCD

研究了带有多径通信路由的网络化控制系统的通信路径调度和控制器的协同设计问题.通过将不同通信路径切换及带来的时延变化建模为系统模态的切换,得到了所研究系统的切换系统模型.给出了使得闭环系统指数稳定的通信路径调度所需满足的条件,并提出了满足系统稳定和网络负载均衡的闭环通信路径调度方案和控制器设计方法.数值仿真算例验证了算法的优越性和有效性.     

Multistability in a system of two coupled oscillators with delayed feedback

In this paper, nonlocal dynamics of a system of two differential equations with a compactly supported nonlinearity and delay is studied. For some set of initial conditions asymptotics of solutions of considered system is constructed. By this asymptotics we build a special mapping. Dynamics of this mapping describes dynamics of initial system in general: it is proved that stable cycles of this mapping correspond to exponentially orbitally stable relaxation periodic solutions of initial system of delay differential equations. It is shown that amplitude, period of solutions of initial system, and number of coexisting stable solutions depend crucially on coupling parameter. Algorithm for constructing many coexisting stable solutions is described.     

Some minimal bimolecular mass-action systems with limit cycles

We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which is unstable for certain rate constants and then exhibits stable limit cycles, but no chaotic behaviour. For some rate constants in the Feinberg–Berner system, a stable equilibrium, an unstabe limit cycle, and a stable limit cycle coexist. All three networks are minimal in some sense.By way of homogenising these three examples, we construct bimolecular mass-conserving mass-action systems with four species that admit a stable limit cycle. The homogenised Feinberg–Berner system and the homogenised Wilhelm–Heinrich system admit the coexistence of a stable equilibrium, an unstable limit cycle, and a stable limit cycle.     

A stable-manifold-based method for chaos control and synchronization

A stable-manifold-based method is proposed for chaos control and synchronization. The novelty of this new and effective method lies in that, once the suitable stable manifold according to the desired dynamic properties is constructed, the goal of control is only to force the system state to lie on the selected stable manifold because once the stable manifold is reached, the chaotic system will be guided towards the desired target. The effectiveness of the approach and idea is tested by stabilizing the Newton–Leipnik chaotic system which possesses more than one strange attractor and by synchronizing the unified chaotic system which unifies both the Lorenz system and the Chen system.     

The stable set of the social conflict game with commitments: existence,uniqueness, and efficiency

We investigate the stable sets of social conflict games by employing the framework of the (abstract) system by Greenberg (Theory of social situations: an alternative game theoretic approach. Cambridge University Press, Cambridge, 1990). The social conflict game is a class of strategic games that includes the prisoners’ dilemma and the chicken game. We first show that the stable set generally fails to exist in a system that is directly derived from the social conflict game. In this system, the stable set exists if and only if the strong equilibrium exists in the underlying game. If the stable set exists, it coincides with the set of the strong equilibria that is equivalent to the core for the system. Then, we turn to a modified system where the players are allowed to make commitments. In the system with commitments, the stable set always exists, and it consists of efficient outcomes with a certain property. We also discuss the relationship between the core and the stable set for the system with commitments.     

Stability of periodically switched discrete-time linear singular systems

In this paper we present some necessary and sufficient conditions for the stability of periodically switched discrete-time linear index-1 singular system, (PSSS). In particular, it is proved that, if at least one subsystem of a PSSS is asymptotically stable, then there is a switching rule, so that the whole system is also uniformly exponentially stable. Furthermore, for a periodically switched control system with no stable subsystems, there exist a switching rule and feedback matrices, such that the obtained PSSS is uniformly exponentially stable.     

参激白噪声作用下蔡电路的脉冲控制

考察了参激白噪声和脉冲信号联合作用下蔡电路的渐近P阶矩稳定性问题,得到该随机脉冲系统的比较系统,从而可由该确定性比较系统的稳定性得到原随机脉冲系统的渐近P阶矩稳定性.并从理论上得到能使该随机脉冲系统渐近P阶矩稳定的参数取值范围,即在稳定区域内取值的参数组合能够用脉冲方法对该随机蔡电路实现混沌控制.最后用数值仿真验证了理论结果的正确性.     

On the dimension of the subspace of Liouvillian solutions of a Fuchsian system

The effect of small constantly acting random perturbations of white noise type on a dynamical system with locally stable fixed point is studied. The perturbed system is considered in the form of Itô stochastic differential equations, and it is assumed that the perturbation does not vanish at a fixed point. In this case, the trajectories of the stochastic system issuing from points near the stable fixed point exit from the neighborhood of equilibrium with probability 1. Classes of perturbations such that the equilibrium of a deterministic system is stable in probability on an asymptotically large time interval are described.     

Stability of superposed viscous-viscoelastic (Rivlin-Ericksen) fluids in the presence of suspended particles through a porous medium

The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying a Rivlin-Ericksen viscoelastic fluid containing suspended particles in a porous medium is considered. As in both Newtonian viscous-viscoelastic fluids the system is stable in the potentially stable case and unstable in the potentially unstable case, this holds for the present problem also. The effects of a variable horizontal magnetic field and a uniform rotation are also considered. The presence of magnetic field stabilizes a certain wave-number band, whereas the system is unstable for all wave-numbers in the absence of the magnetic field for the potentially unstable configuration. However, the system is stable in the potentially stable case and unstable in the potentially unstable case for highly viscous fluids in the presence of a uniform rotation.     

The set of stable switching sequences for discrete-time linear switched systems

In this paper we study the characterization of the asymptotical stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence. The obtained result reveals an underlying fundamental principle: a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them, provided that the switching is arbitrary. We also develop frequency and density indexes to identify those asymptotically stable switching sequences of the system.