离散马尔科夫跳跃线性系统的非脆弱H∞滤波

针对一类离散有限模态马尔科夫跳跃线性系统(MJLs)的滤波问题,进行了具有乘性范数有界参数摄动的模态不依赖H∞非脆弱滤波器的设计研究.基于随机内部均方稳定(IMSS)理论,采用线性矩阵不等式(LMI)技术, 给出了模态不依赖H∞非脆弱滤波器存在的充分条件和设计方法; 利用线性矩阵不等式的仿射特性, 先将设计方法推广到跳变转移概率具有凸多面体不确定时的鲁棒模态不依赖H∞非脆弱滤波器设计, 然后进一步拓展到考虑系统参数具有凸多面体不确定时的鲁棒模态不依赖H∞非脆弱滤波器设计,最后通过算例数值仿真表明了所得结论的有效性.     

一类具有范数有界不确定性的非线性时滞系统的控制

本文研究了一类具有范数有界不确定性的非线性时滞系统的鲁棒稳定性及其控制问题,结合Lyapunov稳定性定理、线性矩阵不等式及自由权矩阵,给出了系统的状态反馈鲁棒二次稳定的充分条件以及控制器的设计,并建立了一个具有线性矩阵不等式约束的凸优化问题,得到不确定时滞系统的最优状态反馈控制律.仿真示例说明了该方法的可行性.     

锥-逼近多值函数和集值优化的近似解

最优性条件和对偶理论是集值向量优化研究领域的重点问题之一．本文的目的是建立一类广义凸集值优化的最优性条件和对偶定理,在锥-逼近多值函数概念的基础上,定义集值映射的一类新的广义不变凸性,称之为次不变凸集值映射,在这类广义凸性假设下,研究最优性条件和对偶定理．利用分析的方法,本文得到了集值优化问题关于弱近似极小元的一个最优性充分条件,以及Mond-Weir和Wolfe两种模型下的弱对偶定理、强对偶定理和逆对偶定理．本文所得结果丰富和深化了集值优化理论及其应用的研究内容．     

强锐角锥以及有效点集的路连通性

本文提出了强锐角锥的概念，并就无限维空间证明了一个凸锥为强锐角锥的必要充分条件。最后，作为强锐角锥概念的应用，研究了有效点集的路连通性。     

强锐角锥以及有效点焦的路连通性

本文提出了强锐角锥的概念，并就无限维空间证明了一个凸锥为强锐角锥的必要充分条件，最后，作为强锐角锥概念的应用，研究了有效点集的路连通性。     

气动弹性系统的模型确认与鲁棒颤振分析

研究了气动弹性系统的不确定性建模和鲁棒颤振分析问题.将结构的不确定性考虑为参数形式,非定常气动力的不确定性考虑为参数和未建模动态两种形式,建立了不确定系统的线性分式变换模型.分别使用基于Carathe-dory-Fejer插值定理和Nevanlinna-Pick插值定理的模型集检验方法进行了模型确认,在时间域和频率域中对模型集的有效性进行了验证,确定了不确定性的幅值.对于模型确认得到的不确定气动弹性系统,使用μ分析方法进行了鲁棒颤振分析.计算中,飞行速度是作为给定参数而不再是作为摄动变量,由此得到的鲁棒稳定性边界是匹配点解.仿真数值结果给出了鲁棒颤振速度,表明了方法的有效性.     

不确定变时滞模糊随机系统鲁棒稳定性

本文研究了不确定T-S模糊随机时滞系统的时滞相关鲁棒稳定性问题,这里的不确定性是范数有界的.通过构造新的Lyapunov泛函和矩阵不等式引理,利用具有时滞的非线性随机系统的Lypaunov稳定性理论和自由权矩阵方法,导出了使系统鲁棒均方指数稳定的时滞相关线性矩阵不等式(LMI)条件.该判据具有较低的保守性,适用时滞变化率大于1的情形.最后通过数值例子验证了所得结果的有效性.     

基于CVaR的相对鲁棒投资组合问题研究

鲁棒优化方法是处理不确定环境下决策问题的有效技术,已在众多领域得到广泛应用.为降低现有鲁棒投资组合选择模型的鲁棒性成本,避免结果过于保守,本文提出了具有优良特性的相对鲁棒CVaR风险度量,探讨了其计算等问题.由其所导出的鲁棒投资组合选择模型的转化、简约与求解等问题,为求解实际的金融投资决策问题奠定了基础.     

不确定结构振动的保成本鲁棒PID控制

研究了不确定结构振动的保成本鲁棒FID控制器设计问题。针对结构模态阻尼比及模态频率的不确定性，同时结合FID控制、保成本控制和H∞控制的优点，提出一种保成本鲁棒FID控制的设计方法，PID控制器的参数整定问题转化为线性矩阵不等式凸优化问题的求解。通过悬臂梁的仿真算例验证了该方法的可行性和有效性。     

具有饱和执行器多重滞后系统的鲁棒控制

利用LMIs方法,对一类具有非线性饱和执行器的不确定线性多重滞后系统的鲁棒镇定问题进行了研究,提出了新的鲁棒可镇定判据和相应的鲁棒无记忆状态反馈控制器设计方法.简洁的例子说明了结果的有效性.     

Stochastic linear programming with a distortion risk constraint

Coherent distortion risk measures are applied to capture the possible violation of a restriction in linear optimization problems whose parameters are uncertain. Each risk constraint induces an uncertainty set of coefficients, which is proved to be a weighted-mean trimmed region. Thus, given a sample of the coefficients, an uncertainty set is a convex polytope that can be exactly calculated. We construct an efficient geometrical algorithm to solve stochastic linear programs that have a single distortion risk constraint. The algorithm is available as an R-package. The algorithm’s asymptotic behavior is also investigated, when the sample is i.i.d. from a general probability distribution. Finally, we present some computational experience.     

Optimization‐based stability analysis of structures under unilateral constraints

This paper discusses an optimization‐based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing no‐compression cables; (ii) frictionless contacts; and (iii) elastic–plastic trusses with non‐negative hardening. It is shown that the stability of a given equilibrium point of these structures can be determined by solving a maximization problem of a convex function over a convex set. On the basis of the difference of convex functions optimization, we propose an algorithm to solve the stability determination problem, at each iteration of which a second‐order cone programming problem is to be solved. The problems presented are solved for various structures to determine the stability of given equilibrium points. Copyright © 2008 John Wiley & Sons, Ltd.     

多自由度振动系统响应集的支撑超平面法

对激励由凸集合建模的线性振动系统提出了响应集的概念，将数学上的微分包含问题简化为求解多自由度振动系统的响应集问题。在此基础上，利用凸集的性质提出了一种求解响应集的支撑超平面法，它是利用响应集的支撑超平面将问题转化为求解一类优化问题的解。对于三种典型的凸集载荷分别给出了各自的响应集，并比较和分析了它们的结果。     

Non‐convex dual forms based on exponential intervening variables,with application to weight minimization

We study the weight minimization problem in a dual setting. We propose new dual formulations for non‐linear multipoint approximations with diagonal approximate Hessian matrices, which derive from separable series expansions in terms of exponential intervening variables. These, generally, nonconvex approximations are formulated in terms of intervening variables with negative exponents, and are therefore applicable to the solution of the weight minimization problem in a sequential approximate optimization (SAO) framework. Problems in structural optimization are traditionally solved using SAO algorithms, like the method of moving asymptotes, which require the approximate subproblems to be strictly convex. Hence, during solution, the nonconvex problems are approximated using convex functions, and this process may in general be inefficient. We argue, based on Falk's definition of the dual, that it is possible to base the dual formulation on nonconvex approximations. To this end we reintroduce a nonconvex approach to the weight minimization problem originally due to Fleury, and we explore certain convex and nonconvex forms for subproblems derived from the exponential approximations by the application of various methods of mixed variables. We show in each case that the dual is well defined for the form concerned, which may consequently be of use to the future code developers. Copyright © 2009 John Wiley & Sons, Ltd.     

Data-driven construction of Convex Region Surrogate models

With the increasing trend of solving more complex and integrated optimization problems, there is a need for developing process models that are sufficiently accurate as well as computationally efficient. In this work, we develop an algorithm for the data-driven construction of a type of surrogate model that can be formulated as a set of mixed-integer linear constraints, yet still provide good approximations of nonlinearities and nonconvexities. In such a surrogate model, which we refer to as Convex Region Surrogate (CRS), the feasible region is given by the union of convex regions in the form of polytopes, and for each region, the corresponding cost function can be approximated by a linear function. The general problem is as follows: given a set of data points in the parameter space and a scalar cost value associated with each data point, find a CRS model that approximates the feasible region and cost function indicated by the given data points. We present a two-phase algorithm to solve this problem and demonstrate its effectiveness with an extensive computational study as well as a real-world case study.     

不确定离散模糊系统的最优保性能控制

对一类具有范数有界,时变参数不确定性的离散模糊时间系统和一个二次型性能指标,研究其最优保性能状态控制律的设计问题.通过采用线性矩阵不等式的方法,导出了存在保性能控制律的一个充要条件,进而,证明了该条件等价于一组线性矩阵不等式的可解性问题,并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示.在此基础上,通过建立并求解一个凸优化问题,给出了最优保性能控制律的设计方法.     

基于概率-凸集混合模型的汽车正面碰撞结构可靠性优化设计

本文基于概率和凸集模型研究汽车正面碰撞可靠性优化设计问题。根据汽车吸能结构厚度、材料参数等不确定参数类型,分别采用概率和多椭球凸模型进行描述,以汽车正面碰撞安全性可靠性指标为约束,考虑汽车吸能结构质量为优化目标,建立了一种基于混合模型的可靠性优化设计模型。采用拉丁方试验设计构造了目标函数和约束函数的Kriging近似模型,利用功能度量法求解可靠度指标值,通过基于移动因子序列优化与可靠性评定将嵌套优化解耦为单层次优化。实际算例表明算法具有较高的计算效率及精度,对实际设计工作有一定参考价值。     

Explicit model of dual programming and solving method for a class of separable convex programming problems

An objective function for a dual model of nonlinear programming problems is an implicit function with respect to Lagrangian multipliers. This study aims to address separable convex programming problems. An explicit expression with respect to Lagrangian multipliers is derived for the dual objective function. The exact solution of the dual model can be achieved because an explicit objective function is more exact than an approximated objective function. Then, a set of improved Lagrangian multipliers can be used to obtain the optimal solution of the original nonlinear programming model. A corresponding dual programming and explicit model (DP-EM) method is proposed and applied to the structural topology optimization of continuum structures. The solution efficiency of the DPEM is compared with the dual sequential quadratic programming (DSQP) method and method of moving asymptotes (MMA). The results show that the DP-EM method is more efficient than the DSQP and MMA.