Systems and Scholarship: The Need to Do Better

Although conscious organized systems thinking stems only from the 1940s, and is hence a very young field, it is more primitive than it ought or needs to be. Evidence for this is given in three areas: the exposition of systems ideas; the relation between systems epistemology and ontology; and the style and tone of presentation of systems work. The first area can be improved rather easily; the second defines the work systems thinkers ought to be doing; the third will be improved only by the adoption of a more modest mien.     

Symplectic Transformations and a Reduction Method for Asymptotically Linear Hamiltonian Systems

In many fields of applications, especially in applications from mechanics, many equations of motion can be written as Hamiltonian systems. In this paper, we study a class of asymptotically linear Hamiltonian systems. We construct a symplectic transformation which reduces the linear systems of the Hamiltonian systems. This reduction method can be applied to study the existence of periodic solutions for a class of asymptotically linear Hamiltonian systems under weaker conditions on the linear systems of the Hamiltonian systems.     

Survey of research in the design and control of automated guided vehicle systems

Automated guided vehicles (AGVs) are used for the internal and external transport of materials. Traditionally, AGVs were mostly used at manufacturing systems. Currently, AGVs are also used for repeating transportation tasks in other areas, such as warehouses, container terminals and external (underground) transportation systems. This paper discusses literature related to design and control issues of AGV systems at manufacturing, distribution, transshipment and transportation systems. It is concluded that most models can be applied for design problems at manufacturing centres. Some of these models and new models already proved to be successful in large AGV systems. In fact, new analytical and simulation models need to be developed for large AGV systems to overcome large computation times, NP-completeness, congestion, deadlocks and delays in the system and finite planning horizons. We specify more specific research perspectives in the design and control of AGV systems in distribution, transshipment and transportation systems.     

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.     

Controller design for stabilizing bilinear systems with state-based switching

Some nonlinear systems can be approximated by switching bilinear systems. In this paper, we proposed a method to design state-based stabilizing controller for switching bilinear systems. Based on the similarity between switching bilinear systems and switching linear systems, corresponding switching linear systems are obtained for switching bilinear systems by applying state-based feedback control laws. Instead, we consider asymptotically stabilizing the corresponding switching linear system through solving a number of relaxed LMI conditions. Stabilizing controllers for switching bilinear systems can be derived based on the results of the corresponding switching linear systems. The stability of the controller is proved step by step through the decreasing of the multiple Lyapunov functions along the state trajectory. The effectiveness of the method is demonstrated by both a theoretical example and an example of urban traffic network with traffic signals.     

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.     

时变退化时滞微分系统的变易公式

本文将研究时变退化时滞微分系统.给出了该类系统的变易公式.这将在进一步研究退化时滞微分系统时十分有用.     

Q_p上的共轭温度系

本文用于构造p-adic共轭温度系.首先,说明了热核及其Hilbert变换所适合的估计,描述了它们的正则性.并且对热核及其Hilbert变换在各个方向的导数进行了估计.然后,利用热核的卷积理论,得到了共轭温度系的边值特性.最后,通过共轭温度系解释了Hardy空间.     

Stability and chaos in a class of 2-dimensional spatiotemporal discrete systems

This paper is concerned with a class of 2-dimensional spatiotemporal discrete systems (2d spatiotemporal discrete systems), or 2-dimensional and 2-directional discrete systems (2d-2D discrete systems). Some sufficient conditions for this system to be stable and some illustrative examples for this system to be chaotic in the sense of Devaney and of Li-Yorke are derived and discussed.     

Analysis of stochastic min-max-plus systems: Results and conjectures

Systems in which the operations min, max and addition appear simultaneously are called min-max-plus systems. Such systems, which are extensions of timed discrete event systems (which on their turn are based on the max-plus algebra, i.e., on the operations max and addition only), have been studied for some years now [1–3]. In these references only deterministic systems were studied. In the current paper, some stochastic extensions will be considered. It will be shown that extensions of eigenvalues, Lyapunov coefficients, exist for these stochastic systems. Some conjectures will be given which are supported by characteristic examples.     

A unified theory for coherent systems in reliability part III: Two special cases for multinary systems—binary-type coherence and homogeneous coherence

As shown in a companion-paper,¹ binary and multinary coherent systems can be studied with unified arguments, through monotone binary coherent systems. These are binary coherent systems submitted to some monotone constraint and generalize the classic theory of free binary coherent systems. By considering the unified point of view thus obtained, this paper gives what is perhaps the most suggestive representation for multinary coherent systems, since this extends the definition of binary coherent systems in terms of series-parallel (parallel-series) structures. Then, this paper examines the special case of multinary systems that can be studied directly with the classic theory of free binary coherent systems. It thus enlarges and complements, in a shorter unified manner, the particular cases considered in earlier studies.     

Contributions to flatness‐based control of systems with input‐dependent delays

Flatness‐based control of nonlinear systems has been generalized in [1] to systems with time‐delays of constant amplitude. Continuous stirred tank chemical reactors with recycle provide examples of such systems. However, if the volume flow‐rate in the recycle is used as control input the time delay depends on control. This can be avoided by a proper choice of the independent variable, i.e., time transformation: Transported volume is used instead of time. This leads to systems with a time delay of constant amplitude belonging to a class of systems which can be called a generalized type of π‐flat systems [2], barely studied so far. Motion planning and tracking control can be achieved by flatness‐based methods.     

Robustness analysis for parameter matrices of global exponential stable stochastic time varying delay systems

In this paper, we analyze the robustness of global exponential stable stochastic delayed systems subject to the uncertainty in parameter matrices. Given a globally exponentially stable systems, the problem to be addressed here is how much uncertainty in parameter matrices the systems can withstand to be globally exponentially stable. The upper bounds of the parameter uncertainty intensity are characterized by using transcendental equation for the systems to sustain global exponential stability. Moreover, we prove theoretically that, the globally exponentially stable systems, if additive uncertainties in parameter matrices are smaller than the upper bounds arrived at here, then the perturbed systems are guaranteed to also be globally exponentially stable. Two numerical examples are provided here to illustrate the theoretical results.     

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.     

On the solution of inequality systems relevant to IC-layout

Many problems arising in CAD systems for VLSI design, such as layout computation and compaction as well as channel routing, can be reduced to the solution of a certain class of systems of linear inequalities. The complexity of the solution of such systems is studied. The results show that CAD systems manipulating merely the geometry of the layout without changing its topology can be efficiently implemented. However, systems that are also able to change the topology of the layout have to solve hard, i.e., NP-complete, problems.     

On the basis property of a two-part trigonometric series

Conditions are presented under which two-part trigonometric systems arising in mixed type equations form a Riesz basis in the space of Lebesgue square integrable functions. For such systems, biorthogonal systems can be obtained in explicit form. As a result, an integral representation of the solution to the Frankl problem in a special domain can be found. The results are extended to two-part systems of broader functions.     

Fourier coefficients of continuous functions

It is well known that the Fourier coefficients of continuous functions with respect to classical orthogonal systems (trigonometric, Haar, and Walsh) can be estimated via the moduli of continuity of the functions. However, not all orthonormal systems possess this property. We obtain necessary and sufficient conditions on orthonormal systems such that the Fourier coefficients of continuous functions with respect to these orthonormal systems can be estimated via the moduli of continuity in a certain sense.     

大系统试验选优理论研究

针对某些高维动态、大型线性、复杂非线性、复杂模拟仿真和定性知识模型，该文全面总结了作者采用数学模型、知识模型和试验选优理论相结合的方法而提出的试验选优理论，该理论体系可以使一些目前无法求解或很难求解的大型问题获得近似解。并在复杂水资源系统的优化中取得了良好的效果。     

Robust synchronization of perturbed Chen’s fractional-order chaotic systems

In this paper, based on a stability theorem proved for linear fractional-order systems, a scheme for robust synchronization of two perturbed fractional-order Chen systems is proposed. In the proposed scheme, both master and slave systems are considered to be involved with external disturbances having unknown values. It is analytically shown that any set of bounded external disturbances can be damped by the proposed method, where synchronization error will be forced and then kept inside a ball around the origin. Since during the design procedure the radius of this ball could be easily chosen by the designer, the synchronization can be done with any desired accuracy. The proposed method can be easily extended to synchronize other fractional-order chaotic systems. Numerical simulation results are presented to show the effectiveness of the proposed method.     

Disturbance decoupling and model matching problems for discrete-time systems with time-varying delays

In this paper, the disturbance decoupling problem and the model matching problem for discrete-time linear systems with time-varying delays are considered. Solvability of the above problems is characterized by means of structural necessary and sufficient conditions that can be checked by algorithmic procedures. The basic method used to analyze the considered problems consists in representing the discrete-time linear systems with time-varying delays as switching linear systems, whose properties can be studied by a powerful structural approach. In this way, the considered control problems can be reduced to the corresponding problems for switched linear systems, whose solvability has been recently characterized.