A theory for synchronization of dynamical systems

In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint and to multiple specific constraints is investigated. Finally, the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed briefly. The meaning of synchronization for dynamical systems with constraints is extended as a generalized, universal concept. The theory presented in this paper may be as a universal theory for dynamical systems. The paper provides a theoretic frame work in order to control slave systems which can be synchronized with master systems through specific constraints in a general sense.     

A model of general systems

In this paper a mathematical model of general systems with not only one, but also more than one relation between the objects of the systems, was introduced. Among others, the concepts of partial systems, similarity of systems, embeddability of systems and free sum of systems were introduced. The following theorem was proved: there is no system whose object set consists of all systems.     

自治Birkhoff系统的广义正则变换和辛算法研究

研究了自治Birkhoff系统的广义正则变换,将Hamilton系统的辛算法推广到Birkhoff系统,通过引入凯莱变换和生成函数法构造Birkhoff方程的Birkhoff的辛差分格式,同时讨论了Birkhoff差分格式的辛算法.     

时变离散大系统的稳定性

本文首先给出了线性时变离散系统稳定性的一个充分条件.然后研究当孤立子系统满足上述条件时的线性及非线性时变离散大系统的稳定性.利用向量李雅普诺夫函数法结合时变离散系统的比较原理,得到了时变离散大系统在稳定性中的集结模型.直接由集结系统的稳定性得到大系统稳定性的条件.     

Maximum principle of stochastic controlled systems of functional type

This paper studies the optimal controls of stochastic systems of functional type with end constraints. The systems considered may be degenerate and the control region may be nonconvex. A stochastic maximum principle is derived. The method is based on the idea that stochastic systems are essentially infinite dimensional systems. The Project Supported by National Natural Science Fundation of China.     

Representation of solutions of control hybrid differential-difference impulse systems

We consider linear nonstationary hybrid differential-difference controlled dynamical systems under the action of impulses. For such systems, we derive integral representations of solutions on the basis of the solution of dual (adjoint) systems. This is, in a sense, a generalization to these systems of the Cauchy formula for ordinary systems. This formula is refined in the stationary case. The results are illustrated by an example     

On symmetry classification of third-order evolutionary systems of divergent type

A symmetry classification is presented for integrable two-field third-order evolutionary systems of divergent type. The list contains thirteen exactly integrable systems. For eleven of them, differential substitutions that relate the systems with the known systems by Drinfeld-Sokolov, Ito, and Hirota-Satsuma are found. The two remaining systems seem to be new. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 141–161, 2006.     

Reconstruction of possibilistic behavior systems

Reconstructability analysis is viewed as a process of investigating the possibilities of reconstructing desirable properties of overall systems from the knowledge of the corresponding properties of their various subsystems. The reconstructability analysis consists of procedures for generating meaningful reconstruction hypotheses, procedures for the evaluation of the reconstruction hypotheses, and procedures for making various decisions regarding the acceptance of evaluated reconstruction hypotheses, generation of additional reconstruction hypotheses, termination of the analysis and the like.The paper discusses the evaluation of reconstruction hypotheses when the systems under consideration are possibilistic behavior systems. It is shown that a principle of maximum ambiguity, similar to the principle of maximum entropy for probabilistic systems, can be used for possibilistic systems. It is also shown that the unbiased (maximum ambiguity) reconstruction can be determined by a simple join procedure, in a similar fashion as for probabilistic systems. The join procedure for possibilistic systems turns out to be computationally simpler than the one for probabilistic systems. The paper also describes a general procedure for determining the reconstruction family.     

Ten years of genetic fuzzy systems: current framework and new trends

Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. Neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms.The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems. After a brief introduction to models and applications of genetic fuzzy systems, the field is overviewed, new trends are identified, a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated, and open questions that remain to be addressed in the future are raised. The paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems.     

相对论性Birkhoff系统动力学方程的代数结构与Poisson积分方法

定义相对论性Ｐｆａｆｆ作用量,得到相对论性Ｐｆａｆｆ Ｂｉｒｋｈｏｆｆ原理和相对论性Ｂｉｒｋｈｏｆｆ方程．证明了自治形式和半自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程具有相容代数结构和Ｌｉｅ代数结构;一般非 自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程没有代数结构．研究一种特殊的非自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程,它具有相容代数结构和Ｌｉｅ容许代数结构．给出相对论性Ｂｉｒｋｈｏｆｆ方程的Ｐｏｉｓｓｏｎ积分 方法．最后给出应用性实例．     

Controllability and observability of coordinated linear systems

This paper develops concepts of controllability and observability for the class of coordinated linear systems, a special class of linear hierarchical systems with a top-to-bottom information structure. The usual concepts of reachability and indistinguishability for linear systems are refined, taking into account the decentralized nature of coordinated linear systems. The corresponding controllability and observability decompositions are derived, and several concepts of controllability and observability for coordinated linear systems are introduced and discussed. These results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems.     

一类混沌系统的函数矩阵投影同步

研究了一类混沌系统的函数矩阵投影同步问题,基于函数矩阵方法,利用Lyapunov稳定性理论和极点配置理论,设计了两个连续混沌系统之间的同步方案,同时设计了两个离散混沌系统之间的同步方案,实现了驱动系统与动态系统按给定的函数矩阵投影同步,并给出了证明,通过对Lorenz混沌系统,和Henon系统的数值模拟,表明了该方法的有效性.     

Dynamics of controlled hybrid systems of aerial cable-ways

The dynamics of the hybrid systems of aerial cable-ways is investigated. The eigenvalue problems are considered for such hybrid systems with different assumptions. An overview of different methods for eigenvalue problems is given. In the research, the method of normal fundamental systems is applied, which turns out to be very effective for the considered problems. Changes in the dynamical characteristics of the systems depending on the controlled parameter are studied.     

A review of expert systems

Expert systems have recently become popular and are attracting more and more attention. The high quality performance achieved by some systems in areas previously not considered practical for computational solutions has lead to great interest from many different disciplines. Most expert systems use a subset of techniques from the general area of computer science research known as artificial intelligence. However, some expert systems have been developed that incorporate more traditional mathematical modeling techniques. The combination of artificial intelligence techniques and more traditional mathematical techniques has been shown to be quite effective in developing several high quality performance computer software systems. The techniques used in expert systems may be what is needed to bridge the gap between classical operational research modeling and human decision making processes. This paper addresses how expert systems techniques are being used in problem solving and why someone in operational research might want to use them.     

On Stability of Symplectic Algorithms

1.FundamentalDeflnitionsLemma1.Thesolutionofalinearoofinarydtherentialequationwithcon8tantcoeffcientY=AYissta6leifalleigenvalue8ofAhaven0nP6sitivercalpartsandtheeigenvalueswithnullrealpartaresingleroots0ftheminimalp0lynomial.,/P\ThelinearHamiltoniansystemcanbeden0tedasZ=JSZwhereZ=(q),J=(ELs),andtheHamiltonianfuncti0nH(z)=ty.Lemma2.Thesolution80flinearHamiltoniansy8temsarecmticallysta6leifalleigenvaluesofJShavenullrsalpartandaresinglerootsojtheminitnalp0lyno?nial.Definiti0n1.Whenthemo…     

Irreducible Lie-Yamaguti algebras of generic type

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their inner derivation algebras are the algebraic counterparts of the isotropy irreducible homogeneous spaces.These systems splits into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types were classified in a previous paper through a generalized Tits Construction of Lie algebras. In this paper, the Lie-Yamaguti algebras of generic type are classified by relating them to several other nonassociative algebraic systems: Lie and Jordan algebras and triple systems, Jordan pairs or Freudenthal triple systems.     

转动系统相对论性动力学方程的代数结构与Poisson积分

研究转动相对论系统动力学方程的代数结构,得到了完整保守转动相对论系统与特殊非完整转动相对论系统动力学方程具有Lie代数结构;一般完整转动相对论系统、一般非完整转动相对论系统动力学方程具有Lie容许代数结构。并给出转动相对论系统动力学方程的Poisson积分。     

Transformations of interval linear systems of equations and inequalities

Very recently, new results on transformation of interval linear systems and on generalizations of the Farkas lemma to interval systems appeared in the literature. They are by far not obvious since the standard transformations on linear systems are not easily adapted to interval system due to the dependency problem. The aim of this paper was to come up with new possible transformations and to extend the results to more general classes of AE interval systems and to linear parametric systems. We also show that the transformations can help in simplifying the proofs of some characterization theorems.     

Detection of structural inconsistency in systems of equations with degrees of freedom and its applications

The concept of structural inconsistency in systems of equations is generalized to systems in which the number of equations is not necessarily equal to that of unknowns, and efficient algorithms for detecting it are established. Some examples are presented to show that the present method is not only useful for detecting errors in the formulation of large-scale systems but also useful for analyzing some essential properties of various kinds of engineering systems.