控制系统ɭ1优化设计最优解的存在性和次优解*

本文初步研究了控制对象有z平面单位圆上零极点时?1优化设计问题解的存在性，指出在此种情况下?1优化问题的最优解不一定总是存在。提出了解存在性的判别定理。在最优解不存在时给出了次优解的求取方法。     

单纯形法设计l~1最优反馈控制器

本文进一步讨论了离散系统l~1优化设计问题,证明了l~1优化设计问题的最优解和一个标准线性规划问题的最优解相同,直接利用单纯形法就可得出l~1最优控制器。文中给出了算例,该算例表明了l~1最优控制器的非唯一性。     

弹丸姿态解算方法研究

研究弹丸轨道优化问题,为提高有效命中率,对解算方法都需要确定有效的初值,以往设定初值时存在一定的盲目性,往往解算出来的值与方程组的最优解存在较大误差,需要多次校对才能得到较准确的解,无疑加大了工作量.针对上述问题,采用方向余弦法,利用三轴磁阻传感器测量地磁场在弹体坐标系三轴上的分量,通过Matlab仿真分析了初值设定对解算结果的影响,提出了一种通过逐步缩小初值范围提高解算精度的方法,使姿态解算误差可控制在0.3°以内,计算量也有了较大的减少.     

CDMA有限精度序列解相关NP-hard问题的求解方法

该文首先分析了应用有限精度序列为解相关矩阵序列的解相关接收机,将有限精度解相关的多用户检测问题归约为线性约束整数优化问题,同时证明此问题为NP－hard问题。然后给出了用于寻找最优有限精度序列即求解此NP－hard问题的算法。结果说明,最优有限精度解相关器的性能甚至在大的信道占用时较无限精度解相关多用户检测器下降很小。     

结合AI方法解求SPOT影像外方位元素

针对ＳＰＯＴ影像外方位元素解求中存在的问题,在充分考虑了ＳＰＯＴ卫星特点的基础上,结合人工智能原理设计了分层全局最优的搜索控制算法,不仅保证了算法的严密性,而且简洁、实用。     

三维实体布局中改进局部最优解的冲突决策方法

利用博弈论中冲突决策的思想实现了三维实体布局从一个局部最优解向另一个更好的局部最优解跳跃的算法，部分克服了传统算法的主要瓶－局部最优陷井的问题。理论分析及实例计算表明，当布局问题陷入某－局部最优解时，该算法利用冲突决策策略能有效地春跳入另一个更好的局部最优点上。通过一系列这样的跳跃，最终使布局问题获得一个高质量的解。     

年龄相关的种群空间扩散系统的广义解与收获控制

研究了由积分偏微分方程描述的年龄相关的种群空间扩散系统的收获控制问题.首先利用不动点方法证明了对于有界死亡率μ的系统广义解的存在性,但这是预备的结果.进一步,运用上述结果、先验估计和紧性定理,证明了对于在r=A附近无界的μ的系统解的存在惟一性.其次,利用类似方法得到系统最优收获控制的存在性.最后,利用G^ateax微分和Lions的变分不等式理论,推得了控制为最优的必要条件;从而得到了由积分偏微分方程和变分不等式构成的最优性组.最优性组能够确定最优控制.还建立了表征最优控制的Euler_Lagrange组.这些结果可为种群系统控制问题的实际研究作为理论参考.     

基于改进扩展卡尔曼滤波的姿态解算算法研究

为了解决标准扩展卡尔曼滤波器(EKF)在多旋翼无人机姿态解算中精度较低的问题,提出了一种改进扩展卡尔曼滤波算法(BPNN-EKF),使得解算精度得到较大提升。针对EKF存在预测模型参数要求具有先验已知性,在工程实践中难以获得准确的参数,以及标准EKF对非线性系统采用线性化模型带来的误差等问题,利用神经网络的非线性映射能力和自适应能力对标准EKF的估计值进行补偿,减小模型以及滤波参数误差对最优估计值的影响,从而提高最优估计精度。仿真实验证明,BPNN-EKF对多旋翼无人机姿态解算精度的提升具有显著作用。     

背包问题最优解的结构

讨论背包问题的最优解,引入背包问题的阶的概念,并对背包问题的阶作出深入的讨论,在此基础上得到背包问题的最优解的一般形式。     

基于当前最优解的人工蜂群算法

为克服人工蜂群算法在求解函数优化问题时存在收敛精度低、收敛速度慢的缺点,提出一种改进的人工蜂群算法。为提高人工蜂群算法的局部搜索能力和避免早熟收敛,跟随蜂在当前最优解的周围进行局部搜索,并随着迭代次数的增加,逐渐缩小侦查蜂在当前最优解周围的局部搜索范围。通过6个标准测试函数完成仿真实验,结果表明,与基本人工蜂群算法相比,改进算法在寻优精度和收敛速度上均得到提高。     

Existence of Solution for Generalized Coupled Differential Riccati Equation

By means of the recursive method, the existence of solution is obtained for the generalized coupled differential Riccati equation. As an application, we apply the existence results to consider the optimal control of Markovian jump linear singular system, and obtain the desired explicit representation of the optimal controller for the optimal control problem with the finite horizon.     

SISO多率离散系统L1优化问题求解研究

采样系统ｌ＾１优化设计的关键在于多率离散系统Ｌ＾１翁化问题的解决，本文讨论了其基本问题的性质，证明了对于基于ＳＩＳＯ多率Ｌ＾１优化问题，总可以通过构造相应的单变量Ｌ＾１优化问题或多变量易求解Ｌ＾１优化问题，求得次优解。     

One-machine n-part-type optimal setup scheduling: analyticalcharacterization of switching surfaces

The authors consider optimal setup scheduling of a single reliable machine. Production flow of n different part types and the setup process are described by differential equations. Setup change rates are control variables. Necessary conditions on optimal setup changes are characterized analytically, and optimal setup change times are derived for a given setup change sequence. The linearization of optimal setup switching surfaces is derived, indicating the existence of attractors observed in numerical optimal solutions. The approach developed in this paper establishes a strong basis for studying multimachine production systems and for constructing tractable near-optimal numerical solution techniques     

改进粒子群算法优化微生物连续发酵过程

针对微生物连续发酵生产1,3-丙二醇动力学模型,以稳态时刻1,3-丙二醇的浓度最大化为目标函数,建立以注入甘油浓度和稀释速率为优化变量的优化模型。证明了该模型最优解的存在性。进一步,构造了改进的粒子群优化算法求解此优化模型。数值结果表明稳态时刻1,3-丙二醇的浓度比已有结果有显著提高。     

预测控制约束边界效应与解决方法研究

约束预测控制（Constrained model predictive control,CMPC）中,因约束的存在,优化过程中最优控制作用可能会在可行域的边界取值,也就是说会 有一个或多个变量饱和,即约束边界效应. 而过程控制中操纵变量饱和是我们不希望出现的. 对此,首先基于稳态模型,对期望值位于可行域内时最优解必在期望值处达到给出证明;同时证明了期望值在可行域外时最优解可转化为期望值到可行域的投影. 其次,针对变量在动态及稳态过程中饱和的情况提出了改善控制性能的措施——调整目标函数;终端约束的加入,为预测控制系统稳定性提供了保障. 通过对包含约束的连续搅拌釜式反应器（Continuous stirred tank reactor,CSTR）系统进行仿真实验,验证了所提方法的正确性,并说明了对目标函数进行适当调整,可有效改善系统的控制性能.     

Two-warehouse inventory model with ramp-type demand and partially backlogged shortages

In this article, we consider an inventory model for items that are stored in two-warehouses when demand is a general ramp-type function of time. Shortages are allowed and a constant fraction of shortages is backlogged. The existence and uniqueness of optimal solution is proved for both – the single-warehouse and the two-warehouse models. An algorithm is developed to facilitate the choice between the two-warehouse and the single-warehouse systems and hence to obtain the optimal replenishment policy. Numerical examples are presented. Sensitivity analysis with respect to the parameters of the model is performed.     

Supervisory control of partially observed discrete event systems with arbitrary control patterns

In this paper, we study supervisory control of partially observed discrete event systems with arbitrary control patterns. First, we present a necessary and sufficient condition for the existence of a supervisor for a given non-empty and closed language K. Next, we consider the case where the language K does not satisfy the condition. We prove that there always exists its infimal superlanguage for which there exists a supervisor when the set Gamma of control patterns is closed under intersection. This infimal superlanguage is the optimal solution larger than K. On the other hand, when Gamma is closed under union, there does not necessarily exist its supremal sublanguage for which there exists a supervisor. In other words, the optimal solution smaller than K does not exist in general. So, in this case, we present a suboptimal solution smaller than K.     

l1 optimal robust controller for SISO plant undercoprime factor perturbations

The problem of synthesis of l₁ optimal robust controller for SISO plant under coprime factor perturbations and bounded external disturbance is considered. A geometric interpretation of l₁ optimal robust controller, standard l₁ optimal controller, and two other optimal robust controllers is presented. The existence of l₁ optimal robust linear controller is proved and an algorithm for approximate solution of the problem is proposed. The algorithm is reduced to approximate solution of finite family of standard l₁ optimization problems     

Solution quality of random search methods for discrete stochastic optimization

In this paper, we propose a framework for selecting a high quality global optimal solution for discrete stochastic optimization problems with a predetermined confidence level using general random search methods. This procedure is based on performing the random search algorithm several replications to get estimate of the error gap between the estimated optimal value and the actual optimal value. A confidence set that contains the optimal solution is then constructed and methods of the indifference zone approach are used to select the optimal solution with high probability. The proposed procedure is applied on a simulated annealing algorithm for solving a particular discrete stochastic optimization problem involving queuing models. The numerical results indicate that the proposed technique indeed locate a high quality optimal solution.