Functionally redundant constraints for Boolean quadratic-type optimization problems

A method of construction of functionally redundant quadratic constraints is proposed for Boolean quadratic-type optimization problems. The method is based on an extension of a set of Boolean variables and formation of functionally redundant constraints that relate the initial and added variables. Examples of improvement of Lagrangian dual quadratic estimates obtained by using the constructed redundant constraints are given. This work was carried out thanks to partial financial support under grant UM2-2547-KV-03 (CRDF Cooperative Grants Program.). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 168–172, November–December 2005.     

Solving Optimal Control Problems on the Class of Step Functions

Linear optimal control problems with multipoint non-separated conditions with a quadratic performance criterion of control are analyzed. An approach with a violation of intermediate conditions is proposed. The original problem is reduced to the classical quadratic programming problem with the dimension determined by the number of intermediate points. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 153–162, July–August 2005.     

求解线性约束的二次规划神经网络学习新算法

提出了一种基于0.618法求解具有线性约束的二次规划问题的神经网络学习新算法。与已有的求解线性约束的二次规划问题的神经网络学习算法相比,该算法的适用范围更广,计算精度更高。其目的是为具有线性约束的二次规划问题的求解提供一种新方法。仿真实验验证了新算法的有效性。     

On the lower bound for a quadratic problem on the Stiefel manifold

We study the problem of finding the global minimum of a homogeneous quadratic function of special kind over the Stiefel manifold. For two variants of this problem, a low bound is proposed that is the dual Lagrange bound in the quadratic statement obtained using a family of redundant restrictions. The dual bound is proved to be exact in the case where the problem is considered over Boolean variables. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 95–103, September–October 2008.     

首系数奇异的二阶系统解耦

针对首系数奇异的二阶系统的解耦问题,提出了一种奇异二阶系统的同谱构造解耦方法。引入了对逆二阶系统,将难以描述的二阶系统无穷大特征值转化为其对逆二阶系统的零特征值来加以描述,分析了奇异二阶系统可对角化应该满足的条件及其相应的证明,并且给出了一种具体的奇异二阶系统的同谱构造解耦方法,从而实现了奇异二阶系统解耦,即将奇异二阶系统的3个参数矩阵同时对角化。数值试验中将一个三自由度的奇异质量弹簧二阶系统解耦成3个无关的单自由度二阶子系统,而且解耦前后系统不仅保持了相同的有限特征值及其重复度结构,还保持了相同的无限特征值及其重复度结构。工程应用前景十分广泛。     

模糊神经网络补偿的伺服系统二次型最优控制

针对伺服系统二次型最优控制存在的问题,提出了基于模糊神经网络补偿的二次型最优控制方法,该控制方法利用模糊神经网络的实时学习能力,能够及时补偿被控对象建模不准确、参数摄动和外界干扰等非线性因素对控制系统性能的影响,增强控制系统的自适应能力,有效提高控制系统的跟踪性能和抗干扰鲁棒性能.仿真试验结果验证了该控制方法的有效性.     

基于T-S模型的模糊系统的二次镇定

针对一类由T-S模糊模型描述的非线性系统,利用这类系统模型表示上的特点, 研究了二次镇定问题,提出了模糊系统二次镇定律存在的充分条件,给出并讨论了控制律的 求解步骤．     

An approach to determining Shor’s dual quadratic estimates

For a general quadratic problem, an analog is formulated as a homogeneous quadratic problem. The estimates ψ* constructed based on Shor’s dual quadratic estimates for these problems are proved to be equal. It is shown that, for the case of a homogeneous quadratic problem, finding ψ* is reduced to an unconstraint minimization problem for a convex function. The study was partially sponsored by the grant UKM2-2812-KV-06 (CRDF Cooperative Grants Program). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 89–99, March–April 2008.     

A generalized sector‐bound approach to feedback stabilization of nonlinear control systems

This paper proposes and develops a generalized sector‐bound approach to feedback stabilization of nonlinear control systems described by state–space models. This approach is inherited from the methodology of the sector‐bounded or passive nonlinearities and influenced by the concept of absolute and quadratic stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. More importantly, it has a close connection to gain scheduling and switching control. A path of equilibria is programmed on the basis of the assumption of centered‐ ε‐cover, which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. Simulation results are worked out to illustrate our proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.     

On classical state space realisability of quadratic input–output differential equations

This article studies the realisability property of continuous-time quadratic input–output (i/o) equations in the classical state space form. Constraints on the parameters of the quadratic i/o model are suggested that lead to realisable models. The complete list of second- and third-order realisable i/o quadratic models is given and two subclasses of the n-th order realisable i/o quadratic systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit state equations for realisable second-order quadratic i/o equations, and for one realisable subclass of quadratic i/o equations of arbitrary order.     

Analysis of stability of stochastic dynamic systems under Poisson perturbations. II. Stability of solutions in quadratic mean of systems of linear stochastic differential equations under Poisson perturbations

Necessary and sufficient conditions of asymptotic stability in quadratic mean are obtained for trivial solutions of systems of linear stochastic differential equations under Poisson perturbations. Model problems are analyzed. Part I of this article is published in No. 4 (2005). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 50–66, November–December 2005.     

A computational study on the quadratic knapsack problem with multiple constraints

The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint.In this paper we provide a comparison of quadratic and linear representations of QKP based on test problems with multiple knapsack constraints and up to eight hundred variables. For the linear representations, three standard linearizations are investigated. Both the quadratic and linear models are solved by standard branch-and-cut optimizers available via CPLEX. Our results show that the linear models perform well on small problem instances but for larger problems the quadratic model outperforms the linear models tested both in terms of solution quality and solution time by a wide margin. Moreover, our results demonstrate that QKP instances larger than those previously addressed in the literature as well as instances with multiple constraints can be successfully and efficiently solved by branch and cut methodologies.     

New designing of cryptosystems based on quadratic fields

This paper proposes a method to construct new kind of non-maximal imaginary quadratic order （NIQO＊） by combining the technique of Diophantine equation and the characters of non-maximal imaginary quadratic order. It is proved that in the class group of this new kind of NIQO＊, it is very easy to design provable secure cryptosystems based on quadratic field （QF）. With the purpose to prove that this new kind of QF-based cryptosystems are easy to implement, two concrete schemes are presented, i.e., a Schnorr-like signature and an EIGamel-like encryption, by using the proposed NIQO＊. In the random oracle model, it is proved that： （1） under the assumption that the discrete logarithm problem over class groups （CL-DLP） of this new kind of NIQO＊ is intractable, the proposed signature scheme is secure against adaptive chosen-message attacks, i.e., achieving UF-CMA security; （2） under the assumption that the decisional Diffie-Hellman problem over class groups （CL-DDH） of this new kind of NIQO＊ is intractable, the enhanced encryption in this paper is secure against adaptive chosen-ciphertext attacks, i.e., reaching IND-CCA2 security.     

Rough‐fuzzy quadratic minimum spanning tree problem

A quadratic minimum spanning tree problem determines a minimum spanning tree of a network whose edges are associated with linear and quadratic weights. Linear weights represent the edge costs whereas the quadratic weights are the interaction costs between a pair of edges of the graph. In this study, a bi‐objective rough‐fuzzy quadratic minimum spanning tree problem has been proposed for a connected graph, where the linear and the quadratic weights are represented as rough‐fuzzy variables. The proposed model is formulated by using rough‐fuzzy chance‐constrained programming technique. Subsequently, three related theorems are also proposed for the crisp transformation of the proposed model. The crisp equivalent models are solved with a classical multi‐objective solution technique, the epsilon‐constraint method and two multi‐objective evolutionary algorithms: (a) nondominated sorting genetic algorithm II (NSGA‐II) and (b) multi‐objective cross‐generational elitist selection, heterogeneous recombination, and cataclysmic mutation (MOCHC) algorithm. A numerical example is provided to illustrate the proposed model when solved with different methodologies. A sensitivity analysis of the example is also performed at different confidence levels. The performance of NSGA‐II and MOCHC are analysed on five randomly generated instances of the proposed model. Finally, a numerical illustration of an application of the proposed model is also presented in this study.     

基于二次稳定的仿真转台鲁棒控制器设计

针对摩擦力矩干扰,系统参数摄动等非线性扰动环节对仿真转台控制系统的影响,提出了基于二次稳定理论的仿真转台鲁棒控制器设计思想。分析了二次稳定理论的基本原理及设计方法,给出了某型飞行仿真转台基于二次稳定的状态反馈控制器和PID鲁棒控制器设计实例。仿真结果表明,基于二次稳定理论的控制器克服了摩擦力矩干扰以及转动惯量摄动对仿真转台的影响,实现了转台转角的精确控制,动态指标优越,满足了高精度飞行仿真转台系统的鲁棒控制要求。     

Optimal control of the dynamic state of a thin compound plate

This paper addresses new optimal control problems for dynamic deflections of a thin compound plate with quadratic cost functionals. Theorems on the existence of optimal controls are proved for all the cases considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 151–175, July–August 2006.     

A meta-heuristic algorithm to solve quadratic assignment formulations of cell formation problems without presetting number of cells

The purpose of cellular manufacturing (CM) is to find part-families and machine cells which form self-sufficient units of production with a certain amount of autonomy that result in easier control (Kusiak, 1987, 1990). One of the most important steps in CM is to optimally identify cells from a given part-machine incidence matrix. Several formulations of various complexities are proposed in the literature to deal with this problem. One of the mostly known formulations for CM is the quadratic assignment formulation (Kusiak and Chow, 1988). The problem with the quadratic assignment based formulation is the difficulty of its solution due to its combinatorial nature. The formulation is also known as NP-hard (Kusiak and Chow, 1988). In this paper a novel simulated annealing based meta-heuristic algorithm is developed to solve quadratic assignment formulations of the manufacturing cell formation problems. In the paper a novel solution representation scheme is developed. Using the proposed solution representation scheme, feasible neighborhoods can be generated easily. Moreover, the proposed algorithm has the ability to self determine the optimal number of cell during the search process. A test problem is solved to present working of the proposed algorithm.     

基于状态反馈的预测二次稳定系统设计

基于广义预测的状态空间形式，提出了一种新的鲁棒预测控制设计方法—预测二次稳定控制器。利用Riccati方程给出了最优控制律，并在理论上给出了严格的证明。这种控制算法可以保证控制系统的稳定性。与广义预测控制方法进行比较，仿真结果表明该鲁棒预测控制方法是有效的，其控制性能明显优于常规的广义预测控制。     

Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

广义不确定系统鲁棒稳定性及鲁棒镇定的矩阵不等式方法

考虑广义不确定系统的鲁棒稳定性及鲁棒镇定问题.提出了广义不确定系统'广义二 次稳定'及'广义二次可镇定'的概念,利用矩阵不等式,分别得到了所考虑广义不确定系统广义 二次稳定及广义二次可镇定的充要条件,而且,使广义不确定系统鲁棒镇定的状态反馈控制律 的设计可通过求解一给定的矩阵不等式而得到.