一种基于奇异摄动理论的鲁棒自适应非仿射非线性控制方法

文章针对一类具有参数不确定性和未知扰动项的非仿射非线性系统,提出了一种基于奇异摄动理论的鲁棒自适应控制方法.首先,通过控制输入构建了一个快变子系统,为原系统引入时标分离特性,使闭环系统可以在快变和慢变时间尺度上分解为两个降阶子系统:边界层子系统和降阶慢变子系统.在快时间尺度上,通过设计边界层子系统的结构使其在平衡点处指数稳定;在慢时间尺度上,针对含有参数不确定性和未知扰动项的降阶慢变子系统设计鲁棒自适应控制器.根据奇异摄动理论,闭环系统的跟踪性能可由降阶慢变子系统近似.文章提出的控制方法同时考虑了参数不确定性和未知扰动项的影响,在不忽略非仿射结构的前提下实现控制目标,不依赖于原系统的时标分离特性,且避免了反步法中的“复杂性爆炸”问题.两组与参考文献控制方法的对比仿真结果验证了文章控制方法的有效性.     

原子钟时间尺度的稳定性分析

本文在分析原子钟噪声模型的基础上,提出了时间尺度的综合钟思想,并证明了有关命题,试图为时间尺度的算法分析提供一种新的理论框架.根据这一原理,对经典的加权平均方法做了分析,清晰地揭示了这一至今仍被广泛应用的方法本身的某些固有缺陷.同时,根据原子钟噪声的动态模型,提出了一种新的时间尺度算法,并在计算机上做了模拟验证.     

一般时间尺度上时滞脉冲系统的双测度稳定性

讨论了一般时间尺度上时滞脉冲系统的双测度稳定性问题.我们引进了一个新的概念即一般时间尺度上时滞脉冲系统的(h_0,h)稳定性.利用Lyapunov函数法和分析法得到了一般时间尺度上时滞脉冲系统解的双测度稳定性判据.最后给出了一个例子以说明本文结论的有效性.     

飞轮储能系统放电过程中的非线性动力学现象分析

利用两时间尺度分析理论研究了飞轮储能系统放电过程中的复杂非线性动力学现象.首先通过归一化的参数变换,构建出具有两种时间尺度特征的飞轮储能系统无量纲动力学模型;继而引入快子系统瞬态平衡点的概念,研究快子系统以慢状态量为分岔参数的Hopf分岔现象,探索这种现象产生的物理机理,同时提供了相关的实验结果.文章解决了飞轮储能系统非线性动力学行为分析的难题,为进一步采取相应控制措施优化飞轮储能系统的运行提供理论依据.     

测量值异常下多时间尺度系统H_(∞)滤波北大核心CSCD

复杂的工业系统中经常存在快、慢动态耦合运行的多时间尺度现象,通过引入时间尺度参数,这类系统被建模为多时间尺度系统.由于实际系统运行过程中通常会有外部干扰或者噪声存在,为了准确获取系统的状态,判断系统运行状态以及设计控制算法,H_(∞)滤波器受到了广泛的研究关注.同时,系统在运行时可能产生传感器故障或者受到传感器攻击,引起了系统测量值的异常,导致滤波结果不精确无法满足滤波需求.因此,文章考虑测量值异常情形下的多时间尺度H_(∞)滤波问题,通过引入饱和函数约束测量值上界,同时设计依赖于时间尺度参数的滤波器,实现了系统的状态估计并且满足给定的H_(∞)性能,并且避免了设计过程中由于多时间尺度现象导致的“病态数值问题”.最后,通过仿真例子证明了文章所提方法的正确性和优越性.     

刚性化学Langevin方程的随机分裂模拟

对于反应动力学而言,尽管常微分方程已经成为了基本的研究工具,仍然无法精确描述离散分子的随机演变规律.化学Langevin方程的出现则打破了这个困境,使得研究者从随机角度进行动力学数值模拟成为可能.这种模拟可以为研究提供基本的动力学信息.建立了探测刚性并剖分系统为不同时间尺度子系统的自适应策略,并构建了基于算子分裂的多时间尺度反应体系的随机模拟方法.方法运用于两种基本的酶动力反应体系的模拟实验结果表明,随机分裂方法对于具有清晰时间差异的刚性系统能够实现高效且精确模拟,并且保持了反应体系的动力特性.     

一类非线性微分-代数系统的状态/输出反馈镇定

针对一类可能含有非Lipschitz连续性非线性项的非线性微分-代数系统的状态/输出反馈镇定问题进行研究.首先,利用反步法给出了一种状态反馈控制器的递归设计方法.其次,在非线性项和代数约束满足适当的假设条件下,基于输出反馈占优技术得到了一种输出反馈控制器的设计方法.虽然所给出的两种控制器仅依赖于微分系统的状态,但均能够保证闭环系统的状态是渐近稳定的.仿真结果验证了所提出的两种控制方法的有效性.     

含噪音高频数据动态整合估计波动率的方法

时间域和状态域方法是两种常见的非参数估计方法.前者主要使用的是最近的历史数据,而后者则主要依赖于过去的历史信息.本文在时间域上,通过对含噪音高频数据采用双时间尺度方法获得其波动率,进而获得经动态整合后的波动率.     

快速反应过程中的非线性扩散方程组

本文在多维空间中讨论具有实际应用背景的一类非线性反应扩散方程组,该方程组允许具有一定的退化性.这类问题在含有抗体和病毒两种反应物的非线性扩散系统的研究中具有重要的意义.本文用Bootstrap方法研究这类方程组弱解的存在性和唯一性;同时讨论了系统在反应速度非常快时弱解的收敛性,并得出了极限函数之间的关系.     

可线性化非线性回归预测模型的剖析与改进

本文通过对可线性化非线性回归预测模型的剖析 ,得出了两个重要结论 .在此基础上 ,推导出了含有回归系数变化的可线性化非线性回归预测模型的一种有效改进方法——泰勒级数法 .最后 ,给出了一个应用实例     

A stochastic model for interactions of hot gases with cloud droplets and raindrops

In this paper we analyze a stochastic model for interactions of hot gases with cloud droplets and raindrops. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic hot gases modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any hot gas dynamics model. We also carry out analysis on the stochastically ultimate boundedness, extinction and stability of the hot gases model.     

A stochastic model for internal HIV dynamics

In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and find out the mean and variance of this process. Numerical simulations conclude the paper.     

A stochastic model of AIDS and condom use

In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.     

Inner and outer loop optimization in semiconductor manufacturing supply chain management

Supply chain management (SCM) in semiconductor manufacturing differs from many other SCM applications in that it has to simultaneously consider both long and short time scale stochasticity and nonlinearity. We present a two-level hierarchical structure for SCM motivated by these considerations. A linear programming (LP)-based strategic planning module forms the outer loop which makes long timescale decisions on the starts of factories. A model predictive control (MPC) based tactical execution module forms the inner loop which generates short timescale decisions on the starts of factories by considering the stochasticity and nonlinearity on both supply and demand sides. Two representative case studies are examined under diverse realistic conditions with this integrated framework. It is demonstrated that given conditions of stochasticity, nonlinearity, and forecast error this hierarchical decision structure can be tuned to manage representative semiconductor manufacturing supply chains in a manner appealing to operations. This work was supported by grants from the Intel Research Council and the National Science Foundation (CMMI-0432429).     

Complex dynamics in a stochastic internal HIV model

In this paper, we analyze a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modeling. By analyzing the Lyapunov exponent, singular boundary and probability density, some new criteria ensuring stochastic stability, D-bifurcation and P-bifurcation for stochastic internal HIV model are obtained, respectively. Numerical simulation results are given to support the theoretical predictions.     

Stochastic sensitivity analysis of concentration measures

Central European Journal of Operations Research - The paper extends the traditional approach to measuring market concentration by embracing an element of stochasticity that should reflect the...     

Constrained optimization with stochastic feasibility regions applied to vehicle path planning

In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the sensors have measurement errors, the stochasticity of the data has to be incorporated into the models. In this paper, we consider using a genetic algorithm for the constrained optimization problem of finding the trajectory with minimum length between two locations, avoiding the obstacles on the way. To incorporate the variability of the sensor readings, we propose a modified genetic algorithm, addressing the stochasticity of the feasible regions. In this way, the probability that a possible solution in the search space, say x, is feasible can be derived from the random observations of obstacles and pathways, creating a real-time data learning algorithm. By building a confidence region from the observed data such that its border intersects with the solution point x, the level of the confidence region defines the probability that x is feasible. We propose using a smooth penalty function based on the Gaussian distribution, facilitating the borders of the feasible regions to be reached by the algorithm.     

WHEN TO CUT A STAND OF TREES?

This paper revisits the debate over the economic optimality of different timber harvest rules. The traditional Faustmann and Maximum Sustained Yield rotation determinations are confined to a deterministic world. Once stochasticity is introduced into the model formulation and the additional rental and management costs due to postponement of harvest are taken into account, we find that the optimal stopping time becomes random and varies in response to changes in the underlying price and growth processes. As a result, this stochastic optimal stopping time is bounded by the Faustmann cutting age from below if variabilities of the stochastic processes diminish to zero, but not necessarily by the MSY rotation from above.     

An improved particle swarm optimization algorithm combined with piecewise linear chaotic map

Particle swarm optimization (PSO) has gained increasing attention in tackling complex optimization problems. Its further superiority when hybridized with other search techniques is also shown. Chaos, with the properties of ergodicity and stochasticity, is definitely a good candidate, but currently only the well-known logistic map is prevalently used. In this paper, the performance and deficiencies of schemes coupling chaotic search into PSO are analyzed. Then, the piecewise linear chaotic map (PWLCM) is introduced to perform the chaotic search. An improved PSO algorithm combined with PWLCM (PWLCPSO) is proposed subsequently, and experimental results verify its great superiority.     

Modelling and optimization of reservoirs for long-term regulation with variable head using functional analysis

In this paper, functional analysis and minimum norm formulation are applied to maximize the total benefits from two hydro reservoirs. The hydroelectric power generation is treated as a nonlinear function; water head variation and stochasticity of the river flows are included. The resulting problem has a nonlinear objective function and linear constraints. The proposed method is computationally efficient, compared to previous techniques. Numerical results are presented for widely different water conditions for an actual system in operation.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors wish to thank B. C. Hydro for providing the reservoir data.