分段线性微分包含系统的最优控制设计

针对分段线性微分包含系统,根据Hamilton-Jacobi-Bellman(H-J-B)不等式将最优控制设计问题转化成最优控制性能上界的优化问题及性能下界的求取问题.其中性能上界的优化是一组以反馈增益为寻优参数的双线性矩阵不等式(bilinear matrix inequalities,BMI)问题,而性能下界是一组基于线性矩阵不等式(linear matrixinequalities,LMI)的半正定规划问题.结合遗传算法和内点法设计了一种混合算法对BMI问题进行求解.算例表明方法的有效性.     

Robust estimation of parameters in nonlinear ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to model dynamic processes in many scientific fields. Parameter estimation is usually a challenging problem, especially in nonlinear ODE models. The most popular method, nonlinear least square estimation, is shown to be strongly sensitive to outliers. In this paper, robust estimation of parameters using M-estimators is proposed, and their asymptotic properties are obtained under some regular conditions. The authors also provide a method to adjust Huber parameter automatically according to the observations. Moreover, a method is presented to estimate the initial values of parameters and state variables. The efficiency and robustness are well balanced in Huber estimators, which is demonstrated via numerical simulations and chlorides data analysis.     

Delay differential equations under nonlinear impulsive control and applications to neural network models

In this paper,a class of delay differential equations with nonlinear impulsive control is discussed.Based on the nonsmooth analysis,criteria of stability are obtained for delay differential equations with nonlinear impulses control under certain conditions.These criteria can be applied to some neural network models.At the end of the paper,two examples are provided to illustrate the feasibility and effectiveness of the proposed results.     

Controlled mean-field backward stochastic differential equations with jumps involving the value function

This paper discusses mean-field backward stochastic differential equations (mean-field BSDEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.     

On differential structures of polynomial spaces in control theory

A valuable number of works has been published about Hurwitz and Schur polynomials in order to known better their properties.For example it is known that the sets of Hurwitz and Schur polynomials are open and no convex sets.Besides,the set of monic Schur polynomials is contractible.Now we study this set using ideas from differential topology,and we prove that the space of Schur complex polynomials with positive leading coefficient,and the space of Hurwitz complex polynomials which leading coefficient having positive real part,have structure of trivial vector bundle,and each space of (Schur complex and real,Hurwitz complex) polynomials has a differential structure diffeomorphic to some known spaces.     

Asymptotic and stable proper ties of general stochastic functional differential equations

The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.     

质量矩控制技术的机理分析及方程简化研究

针对质量矩控制技术的动力学问题,提出了质量矩控制导弹的动力学模型,通过对导弹各参数的理论和数值计算分析,对影响导弹快速响应的主要因素在不同的条件下进行研究,分析了质量矩控制方法迅速改变弹体姿态的能力;在自旋速度满足一定的条件下通过对模型参数的摄动分析,得到质量矩控制导弹的简化动力学模型,仿真分析表明该模型是非线性控制系统分析、设计的基础。     

Almost sure and moment exponential stability of predictor-corrector methods for stochastic differential equations

This paper deals with almost sure and moment exponential stability of a class of predictor-corrector methods applied to the stochastic differential equations of Ito-type.Stability criteria for this type of methods are derived.The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions.A numerical experiment further testifies these theoretical results.     

挠性结构振动控制中压电致动器/敏感器的优化配置

针对挠性结构的主动振动控制问题,给出了粘贴有若干压电片的挠性梁的数学模型。基于结构模态的可控可观性,提出一种压电致动器/敏感器同位位置的优化方法。该方法利用模态在可控可观性子空间上的正交投影来反映可控可观性的测度,并根据各阶模态在系统输出中的相对重要程度加权模态可控可观测性测度,由此得到致动器/敏感器的优化配置指标。通过数学仿证明了该优化方法的有效性。     

基于BMI的一类非线性系统的最优控制设计

将一类非线性系统进行分段线性处理,根据Hamilton Jacobi Bellman(H J B)不等式将最优控制设计问题转化成一组以反馈增益为寻优参数的、以最优控制性能上界为优化目标的一组双线性矩阵不等式(bilinearma trixinequalities,BMI)问题。BMI问题是NP难问题,对此将遗传算法和内点法结合设计了一种混合算法。数值实例结果表明对控制律的设计及其求解算法的有效性。     

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈[a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…     

一类非线性广义系统最优控制及应用

利用Zubov方法和最优控制理论研究了非线性广义系统的最优控制问题.首先将非线性广义系统正则化为非线性正常系统,对其施加状态反馈控制,继而构造含有调节参数向量的性能指标,并由偏微分方程解得该性能指标;最后应用最优化理论求得最优调节参数向量,得到非线性广义系统最优控制律.将有关结论应用于Logistic 增长的SIS模型,给出消除该传染病的条件.     

The generating set of the differential invariant algebra and Maurer-Cartan equations of a (2+1)-dimensional burgers equation

The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a (2+1)-dimensional Burgers equation, based on the theory of equivariant moving frames of infinite-dimensional Lie pseudo-groups.     

Optimal control of an M/G/1 retrial queue with vacations

In this note, we consider an M/G/1 retrial queue with server vacations, when retrial times, service times and vacation times are arbitrary distributed. The distribution of the number of customers in the system in stationary regime is obtained in terms of generating function. Next, we give heavy traffic approximation of such distribution. We show that the system size can be decomposed into two random variables, one of which corresponds to the system size of the ordinary M/G/1 FIFO queue without vacation. Such a stochastic decomposition property is useful for the computation of performance measures of interest. Finally, we solve simple problems of optimal control of vacation and retrial policies.     

基于方向久期与凸度免疫的资产负债优化模型

通过方向久期和方向凸度的免疫条件来控制资产配给中的利率风险,建立了银行资产负债组合优化模型.本文通过资产或负债价格对利率一阶导数受不同时段利率变动的影响而形成方向久期的思路,提出其二阶导数也受不同时段利率变动影响形成方向凸度的概念.通过资产或负债的凸度受不同时段利率变动的影响关系给出方向凸度的表达式,反映了即期利率及其变动对贴现现金流的影响,改变了现有研究忽略利率变化对凸度的影响的状况.通过方向久期和方向凸度的双重免疫建立优化模型,解决了无论利率在不同时段的变化量是否相同均可进行风险免疫问题.     

再制造逆向物流结构整合优化

在理论与实践中，将废旧品再制造成新品的经济与环保价值已得到广泛的重视。制造商对废旧品的收集有三种模式：（1）制造商直接从消费者手中收集；（2）制造商激励零售商收集；（3）制造商以合同形式委托第三方收集。再制造逆向物流系统是制造商为主的分散决策系统，本文以分散决策理论为基础，分别对上述三种模式建立数学模型，结果发现靠近消费者的零售商进行废旧品收集，对供应链成员最有利。最后指出了未来的研究方向。     

On the Solutions of the Matrix Equations in Optimal Stochastic Control

1.INTRoDUCTIoNoFTHEPRoBLEMConsiderthetime-invariantlinearIt6stochasticsystemwherexER,uCRm,FER,BERm,a=const.(i=1,2,'',k)arenaturalnumbers;W(t)=[W(t),W2(t),Wk(t)](tSo)isak-dimensionalstandardWienerprocesswithindependentcomponentsdefinedonthecompleteprobabilityspace(fl,FP),(A,B)iscontrollable.SupposethatRERmm,QERmxmaregivenpositivedefiniteweightingmatrices,Ereferstothemathematicalexpectation.ConsidertheoptimalstochasticcontrolDroblemItiswell-knownthatifthereisapositive…     

Optimal Grading Policies in the Online Acquisition of Used Products

Although online reverse commerce(recommerce)is convenient and efficient,it is not without caveats.It limits recommerce firms’flexibility to offer personalized prices and may cause mismatched grading between the firms and sellers of used products.This study examines a recommerce firm’s decision on grading criteria and prices.We find that the firm’s optimal policy exhibits two distinctly different patterns depending on the trade value of the product.We demonstrate that sellers’overestimate and underestimate errors have qualitatively different effects on firm profitability,and the effects crucially rely on the type of optimal policy.These findings can apprise firms on how to preset sorting criteria and prices as well as reduce grading errors.     

3型FIR滤波器优化设计研究

详细研究了3型FIR线性相位滤波器的幅频响应与正弦基函数神经网络算法之间的关系,提出并证明了该模型算法的收敛性定理,给出了3型FIR带通滤波器、海尔伯特变换器和微分器的优化设计实例。研究结果表明提出的算法避免了求高价逆矩阵的困难,有效解决了3型FIR高价数字滤波器优化设计的瓶颈问题。计算机仿真结果表明了正弦基函数神经网络算法在3型FIR高价数字滤波器优化设计领域中的有效性。     

北方农牧交错带土地利用结构的最优规划

运用线性规划、层次分析和模糊数学的隶属函数对北方农牧交错带土地利用结构的不同经济效益、投入水平和水土流失为目标的函数进行分权计算与综合评价,最后再运用模糊数学的隶属函数,得出几种评价中最可行的方案.优化方案为土地利用由2005年的农、林和草面积比例54:10:36调整为30:13:57.表8,参7.