T-S模糊系统的脉冲稳定性

针对模糊控制系统提出了一种新的稳定性设计方法.该方法在传统T-S模型的局部子系统中引入脉冲控制项,构造了具有脉冲影响的模糊控制系统.然后,通过去模糊化技术,把具有脉冲影响的模糊系统转化为脉冲微分系统.这样,借助脉冲微分方程的比较原理和线性矩阵不等式技术,给出了模糊系统的脉冲稳定的充分条件.从而建立了模糊系统的简单脉冲控制策略.     

带有不确定参数的一类混沌金融系统的广义投影同步

针对带有不确定参数的一类混沌金融系统,提出了实现驱动系统和响应系统广义投影同步的自适应控制策略,并基于Lyapunov稳定性理论给出和验证了广义投影同步稳定性判据.数值仿真验证了控制策略和理论分析的有效性.     

一类具有非线性脉冲的捕食与被捕食系统的定性分析

实际的害虫控制策略由于受到资源有限、种群密度的影响,具有饱和效应或非线性特征.因此,该文对一类具有非线性脉冲控制策略的捕食与被捕食模型进行了全局定性分析.利用脉冲微分方程中的Floquet理论和比较方法,得到模型的天敌根除周期解全局渐近稳定的充分条件,通过分支理论,得到非平凡周期解存在性的条件,数值模拟验证了具有非线性脉冲的模型具有非常复杂的动态行为.     

基于脉冲扰动作用下一个捕食者-两个食饵模型的动力学性质

基于害虫的生物控制策略,分别利用Floquet乘子理论及脉冲比较定理,研究了一类具有脉冲效应的一个捕食者-两个食饵模型并进行了分析,得到害虫根除周期解的渐近稳定与系统持续生存条件.     

一类非线性时滞混沌系统的自适应脉冲同步

针对一类非线性时滞混沌系统,提出了一种新的自适应脉冲同步方案.首先基于Lyapunov稳定性理论、自适应控制理论及脉冲控制理论设计了自适应控制器、脉冲控制器及参数自适应律,然后利用推广的Barbalat引理,理论证明响应系统与驱动系统全局渐近同步,并给出了相应的充分条件.方案利用参数逼近Lipschitz常数,从而取消了Lipschitz常数已知的假设.两个数值仿真例子表明本方法的有效性.     

一类离散系统基于偏差分离的输出反馈控制

针对一类不确定离散系统,提出一种基于偏差分离的输出反馈双控制策略,首先设计动态输出反馈控制器镇定其标称系统(即不确定性为零的情形);然后通过构造降维观测器,在线获取不确定性信息,并采用线性的补偿器实时补偿系统的不确定性.该控制策略采用线性控制,在工程中可以方便地实现,具有好的工程意义.理论分析证明了闭环指数渐近稳定的充分条件.仿真结果表明该双控制策略的有效性.     

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.     

具时滞和脉冲的捕食者-食饵模型的动力学性质

基于害虫的生物控制和化学控制策略,考虑到化学杀虫剂对天敌的影响,利用脉冲微分方程建立了在不同的固定时刻分别喷洒杀虫剂和释放天敌的具有时滞的第III功能反应的捕食者-食饵脉冲动力系统.证明了当脉冲周期小于某个临界值时,系统存在一个渐进稳定的害虫灭绝周期解,否则系统持续生存.并用Matlab软件对害虫灭绝周期解及害虫周期爆发现象进行了数值模拟.     

一类有平方根功能反应、食饵避难及互相干扰的脉冲食物链系统研究（英文）

本文构建一类具有平方根功能反应,食饵避难与捕食者相互干扰的脉冲食物链系统;证明系统的一致有界性;利用小振幅扰动技术,弗洛凯理论和比较定理,研究食饵和顶端捕食者灭绝周期解的存在性和全局渐进稳定性;通过构造李雅普诺夫函数,得到系统持久的充分条件;然后通过数值模拟验证了理论结果,进一步揭示了系统复杂的动力学性质;最后分析所得结果的生物意义,并就相关控制策略提出了一些可行的意见与建议.     

一类不确定模糊脉冲切换系统的H∞控制

研究了一类参数不确定的模糊脉冲切换系统在任意切换下的H_∞控制问题.利用Lyapunov稳定性理论与线性矩阵不等式方法,给出了连续的脉冲切换系统满足H_∞性能的充分条件,并把这个条件转化为一个线性矩阵不等式,便于实现.     

基于脉冲控制的害虫管理数学模型研究

研究一类害虫管理SI传染病模型,考虑脉冲投放病虫和人工捕杀相结合,得到系统的灭绝周期解,给出此周期解的全局吸引性,并获得了系统一致持续生存的条件.给出了害虫管理综合防治策略.     

Pulse and constant control schemes for epidemic models with seasonality

Control schemes for infectious disease models with time-varying contact rate are analyzed. First, time-constant control schemes are introduced and studied. Specifically, a constant treatment scheme for the infected is applied to a SIR model with time-varying contact rate, which is modelled by a switching parameter. Two variations of this model are considered: one with waning immunity and one with progressive immunity. Easily verifiable conditions on the basic reproduction number of the infectious disease are established which ensure disease eradication under these constant control strategies. Pulse control schemes for epidemic models with time-varying contact rates are also studied in detail. Both pulse vaccination and pulse treatment models are applied to a SIR model with time-varying contact rate. Further, a vaccine failure model as well as a model with a reduced infective class are considered with pulse control schemes. Again, easily verifiable conditions on the basic reproduction number are developed which guarantee disease eradication. Some simulations are given to illustrate the threshold theorems developed.     

Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination

Since the investigation of impulsive delay differential equations is beginning, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a new SEIRS epidemic disease model with two profitless delays and vertical transmission, and analyze the dynamics behaviors of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ‘infection-free’ periodic solution, further, show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using a new modeling method, we obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delays, pulse vaccination and vertical transmission can bring different effects on the dynamics behaviors of the model by numerical analysis. Our results also show the delays are “profitless”. In this paper, the main feature is to introduce two discrete time delays, vertical transmission and impulse into SEIRS epidemic model and to give pulse vaccination strategies.     

New modelling approach concerning integrated disease control and cost-effectivity

Two new models for controlling diseases, incorporating the best features of different control measures, are proposed and analyzed. These models would draw from poultry, livestock and government expertise to quickly, cooperatively and cost-effectively stop disease outbreaks. The combination strategy of pulse vaccination and treatment (or isolation) is implemented in both models if the number of infectives reaches the risk level (RL). Firstly, for one time impulsive effect we compare three different control strategies for both models in terms of cost. The theoretical and numerical results show that there is an optimal vaccination and treatment proportion such that integrated pulse vaccination and treatment (or isolation) reaches its minimum in terms of cost. Moreover, this minimum cost of integrated strategy is less than any cost of single pulse vaccination or single treatment. Secondly, a more realistic case for the second model is investigated based on periodic impulsive control strategies. The existence and stability of periodic solution with the maximum value of the infectives no larger than RL is obtained. Further, the period T of the periodic solution is calculated, which can be used to estimate how long the infectious population will take to return back to its pre-control level (RL) once integrated control tactics cease. This implies that we can control the disease if we implement the integrated disease control tactics every period T. For periodic control strategy, if we aim to control the disease such that the maximum number of infectives is relatively small, our results show that the periodic pulse vaccination is optimal in terms of cost.     

Control of a dendritic neuron driven by a phase-independent stimulation

A dendritic neuron model exhibits bistability under continuous weak stimulation – the oscillatory synchronized regime and the quiet regime coexist. Complex nonlinear dynamics is observed when the neuron undergoes not only phase-dependent continuous weak stimulation, but also when it is driven by an external phase-independent stimulation. In the latter case basin boundaries between the synchronized and the quiet regime become complex and fractal. Simple strategies based on control pulses are not sufficient in these circumstances, because it becomes difficult to predict the dynamics of the neuron after the application of the control pulse. Therefore, a new neural control method is proposed. Initially, a weak phase control strategy is applied until fractal basin boundaries evolve into a deterministic manifold. Consequently, a single control pulse is immediately applied and the neuron evolves into the calm state.     

Various Feedforward Schemes and a Passivity Based Backstepping Feedback Control of an Elastic Robot

Lightweight constructions in industry plants lead to elastic deflections causing vibrations and a loss in tracking precision. In order to keep the tracking error for these elastic multibody systems low, the proposed control strategies are combinations of feedforward and feedback schemes. In this work various implemented strategies for computing a feedforward control are proposed and compared, which can be calculated with some simplifications from the mathematical model of the elastic multibody system. Some of these are considering the elastic deflections. The stabilization of the error dynamics is achieved by a simple PD-joint control or passivity based backstepping. In this algorithm the system is split into subsystems and for these subsystems simple control concepts can be applied. The feedback control law of the total system is obtained by means of backstepping theory, considering the internal energy flows in the system. Experimental results are presented to verify the control strategies. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The semistrong limit of multipulse interaction in a thermally driven optical system

We consider the semistrong limit of pulse interaction in a thermally driven, parametrically forced, nonlinear Schrödinger (TDNLS) system modeling pulse interaction in an optical cavity. The TDNLS couples a parabolic equation to a hyperbolic system, and in the semistrong scaling we construct pulse solutions which experience both short-range, tail-tail interactions and long-range thermal coupling. We extend the renormalization group (RG) methods used to derive semistrong interaction laws in reaction-diffusion systems to the hyperbolic-parabolic setting of the TDNLS system. A key step is to capture the singularly perturbed structure of the semigroup through the control of the commutator of the resolvent and a re-scaling operator. The RG approach reduces the pulse dynamics to a closed system of ordinary differential equations for the pulse locations.     

Transmission dynamics of a switched multi-city model with transport-related infections

Multi-city epidemic models with unrestricted travel, transport-related infection, general nonlinear incidence rate, and seasonality are analyzed. First, a multi-city SIR model is investigated. Seasonality is considered by assuming that the model’s parameters are time-varying and switching. Under this construction, the parameters can be smoothly-varying (for example, due to seasonal changes) or abruptly-varying (for example, due to school holiday breaks). The functional form of the incidence rate is assumed to take a general form that can change in time (for example, due to changes in population behaviour). The effects of transport-related infection and time-varying parameters are studied and some threshold conditions are established which guarantee that the disease-free solution is globally attractive. A screening process and pulse control strategies are applied to the multi-city SIR model in order to investigate and compare the benefits of each strategy. In the pulse control scheme, vaccine failure is considered and the inter-pulse period is not required to equal the seasonal period of the model parameters. Finally, some simulations are given as well as conclusions and future directions.     

大功率风电并网变流器系统中非线性脉冲扰动的同步控制研究

研究了一类大功率风力发电并网中具有非线性脉冲扰动的同步控制问题.利用Kirchhoff定律建立了一类风力发电系统电网侧变流器的数学模型.设计了适当的反馈同步控制器,借助Lyapunov稳定性理论,验证了该同步控制器的有效性.给出了一类最优算法来抑制并入电网电流中的非线性脉冲扰动,使得风力发电机所产生的电流和电网的电流同步.最后通过Matlab中的Simulink进行了仿真设计研究,验证了该理论结果的有效性.     

Speed feedback control of chaotic system

Based on the Lyapunov stabilization theory and matrix measure, this paper addresses the strategies of speed feedback control of chaotic system to the unsteadily equilibrium points, illustrated by a unified chaotic system and Rössler chaotic system. It is proved that the infimum of speed feedback control coefficient is less than that of displacement feedback control coefficient.