极小-极大-加系统的周期时间的输出反馈独立配置

在数字电路中, 两个时间信号通过逻辑电路的与门相当于极大运算, 通过逻辑电路的或门相当于极小运算. 极小—极大—加系统可用于数字电路的时间分析. 对于一类非线性极小—极大—加系统(F, G, H), 运用极大—加代数和有向图方法得到了在输出反馈作用下的周期时间能独立配置的一个充分条件.     

广义连续系统极小极大控制反问题初探

将极小极大控制的反问题推广到广义系统.针对给定的性能指标,通过受限等价变换,得到判别广义连续系统控制器是极小极大控制器的充要条件及其等价的频率条件.最后针对广义系统H∞次优控制的反问题进行了讨论.     

非线性极大极小系统全局优化算法的分析

非线性极大极小系统的全局优化可用于柔性制造和智能交通的决策与控制.实现了非线性极大极小系统的全局优化算法的仿真,并进行了计算时间分析.数值实验表明了全局优化算法的可行性.算法的计算时间主要由系统的优化极大射影矩阵数目决定,而优化极大射影矩阵数目与系统解析式中单极大式的系数紧密相关,系数取值越分散,简约极大射影矩阵的效果越好,计算效率越高.     

关于分块极大极小矩阵性质的研究

利用矩阵分解、矩阵的Hadamard积和数学归纳法研究分块极大极小矩阵的性质.将极大和极小矩阵推广为分块极大和分块极小矩阵.在给出矩阵行列式、逆和特征多项式的同时,得到该类矩阵半正定的充要条件,还讨论了矩阵的无限可分性.     

极大极小投资组合选择模型和均衡价格系统

讨论了市场上不存在无风险资产条件下投资组合选择的极大极小模型,推导出市场上不存在无风险资产时极大极小模型的最优投资策略和有效前沿,得到了资本市场均衡时存在唯一的非负均衡价格系统的充分必要条件和各资产均衡价格的解析表达式.     

一般模糊极小极大神经网络的改进研究

针对一般模糊极小极大神经网络在处理重叠超盒和包含超盒时,出现新的类而标识为未知类,进而无法达到聚类预期效果的问题,提出了通过超盒的收缩过程来加入新类或删除一个已存在类的一般模糊极小极大神经网络,它继承了一般模糊极小极大神经网络的优点,并且避免了一般模糊极小极大神经网络在分类时的随意性,弥补了一般模糊极小极大神经网络无法达到聚类预期效果的目的,以及提高了模式分类的准确性和高效性.最后,通过实例验证了方法实用有效.     

随机删失下极大似然估计的局部渐近正态与渐近极小极大有效

研究观察数据被随机右删失时 ,参数分布族的局部渐近正态与渐近极小极大有效 .建立局部渐近正态成立的充分条件 ,给出渐近极小极大风险的下界以及达到该下界的充分必要条件 ,并证明随机删失下参数极大似然估计的渐近极小极大有效.     

一类一阶Hamilton系统的次调和解

运用临界点理论中的极小极大方法得到一类一阶Hamilton系统的次调和解的存在性定理.     

一类局部非二次Hamilton系统的次调和解的存在性

运用极小极大方法得到一类局部非二次的Hamilton系统的次调和解的存在性定理.     

LINEX损失函数下位置参数函数的极小极大估计

主要研究了在LINEX损失函数下位置参数函数的极小极大估计,为了给出它的极小极大估计存在的一个充分条件,将位置参数θ限定在一个有界区间上,并且当其函数h(θ)满足一定条件时,h(θ)的极小极大估计是存在的,并给出了证明.     

一类广义半无限规划问题的一阶最优性条件

本文利用一个精确增广Lagrange函数研究了一类广义半无限极小极大规划问题。在一定的条件下将其转化为标准的半无限极小极大规划问题。研究了这两类问题的最优解和最优值之间的关系,利用这种关系和标准半无限极小极大规划问题的一阶最优性条件给出了这类广义半无限极小极大规划问题的一个新的一阶最优性条件。     

Box-total dual integrality,box-integrality,and equimodular matrices

Mathematical Programming - Box-totally dual integral (box-TDI) polyhedra are polyhedra described by systems which yield strong min-max relations. We characterize them in several ways, involving the...     

Min-max control of systems approximated by simple models:L 1-Type cost functionals

A control problem for actual processes, modeled by simple dynamic linear systems, is studied. A min-max approach is taken, since the problem is reduced to the control of a model, whose output is affected by an input-dependent signal constrained in norm.Particular attention is given to the features of the penalty functional, since it is desired to synthesize the min-max control by means of a feedback on the states of the model; for example, a quadratic functional does not have this property. AnL ₁-type functional is then proposed, which is not differentiable; by means of duality techniques, however, the minimization can be carried out. The min-max is obtained both by iterative algorithms, both as a function of the actual value of the model state: this function is the solution of a set of partial differential equations.This work was supported by the CENS and the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni, Consiglio Nazionale delle Ricerche (CNR), Roma, Italy.     

Morse indices of critical manifolds generated by min-max methods with compact lie group actions and applications

We derive some upper and lower bounds for Morse indices of critical manifolds generated by min-max principles for functionals invariant under a general compact Lie group or a finite group action. The results generalize the similar results in the nonequivariant (no group action) case. In doing so, we also generalize the extension theorem of Dugundji type in the nonequivariant case to the equivariant (group action) case. As an application, we obtain a precise growth estimate for the whole sequence of critical values given by the min-max procedure for some superquadratic second-order differential equations. It is well-known that this growth estimate is crucial in showing the existence of multiple solutions of some superquadratic perturbed Hamiltonian systems and equations.     

DUALITY IN LINEAR CONTROL SYSTEMS

The present paper establishes various duality relations-equalities which exist in linear control systems. By means of these relations, we demonstrate various duality properties in the theory of linear control systems. In particular we discuss the duality of controllability and observability of linear systems, the concepts of controllability and observability in stochastic systems the duality of regulator and observer of time-invariant systems and the duality property of reduced dimension observers etc. The duality relation established here is used to solve the problem of min-max state estimation in systems with uncertainty.     

THE MORSE CRITICAL GROUPS OF THE MINMAX THEOREM

The author gives a new min-max theorem and studies the local homology propertiesof critical points that is got by min-max theorem.In particular,this result includes manymin-max theorem of link type,which can be applicable to nonlinear analysis.     

Synthesis of min-max strategies

We present the min-max control for a class of nonlinear uncertain dynamical systems. In particular, we discuss the problems of tracking and adaptive adjustment of the control effort.Dedicated to G. Leitmann     

Approximating a two-machine flow shop scheduling under discrete scenario uncertainty

This paper deals with the two machine permutation flow shop problem with uncertain data, whose deterministic counterpart is known to be polynomially solvable. In this paper, it is assumed that job processing times are uncertain and they are specified as a discrete scenario set. For this uncertainty representation, the min-max and min-max regret criteria are adopted. The min-max regret version of the problem is known to be weakly NP-hard even for two processing time scenarios. In this paper, it is shown that the min-max and min-max regret versions of the problem are strongly NP-hard even for two scenarios. Furthermore, the min-max version admits a polynomial time approximation scheme if the number of scenarios is constant and it is approximable with performance ratio of 2 and not (4/3 − ?)-approximable for any ? > 0 unless P = NP if the number of scenarios is a part of the input. On the other hand, the min-max regret version is not at all approximable even for two scenarios.     

Complexity of the min-max and min-max regret assignment problems

This paper investigates the complexity of the min-max and min-max regret assignment problems both in the discrete scenario and interval data cases. We show that these problems are strongly NP-hard for an unbounded number of scenarios. We also show that the interval data min-max regret assignment problem is strongly NP-hard.     

Bounds for min-max heaps

Very recently a new data structure, called a min-max heap, was presented for implementing the double-ended priority queue. A min-max heap onn keys is constructed inO(n) time; the minimum and maximum keys are found in constant time, and the operations of deleting the minimum, deleting the maximum and inserting a new key into the heap are performed inO(logn) time. In addition, the data structure can be stored implicitly, i.e. in an array ofn elements without using any additional pointers.In this paper, we present lower bound results on the number of comparisons required, in the worst case, for the operations i) to construct a min-max heap on a given set of keys; ii) to convert a min-max heap into a max-min heap; and iii) to merge two min-max heaps into one min-max heap. New upper bounds for the convert and merge operations are also derived. It is found that the main difference between traditional heaps and min-max heaps lies in the time needed to perform the merge operation. While traditional heaps can be merged efficiently, it is shown that min-max heaps are not sublinearly mergeable. Even the seemingly simple task of converting a min-max heap into a max-min heap cannot be performed in less than linear time.This research was supported by the Natural Science and Engineering Council of Canada under Grant No. A0392. (A preliminary version of this paper was presented at the 24th Annual Allerton Conference on Communication, Control and Computing.)