Commuting and stable feedback design for switched linear systems

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.     

Fixed-point theorems for families of weakly non-expansive maps

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.     

Nonlinear modelling and control of a common rail injection system for diesel engines

Modern trends in designing mechatronic systems call for a synergic design of the separated subsystems (mechanic, electronic parts, control modules, etc.) concurring to the overall performance. Following this point of view, this paper presents a control oriented model and a nonlinear control design for a Common Rail injection system. First a model is developed, which is tuned in a virtual simulation environment, representing the injection system in details in a reliable replication of reality. Then a sliding mode control is developed. Both the model of the injection process and of the control law are validated by a virtual detailed simulation environment. The prediction capability of the model and the control efficiency are clearly shown.     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

基于FCS的海水痕量元素的通用测定平台

为了对海水痕量营养盐与重金属进行测定,基于FCS的设计思想,采用流动注射分光光度法研制了具有自适应外界设备、快速组建多种仪器及全数字化通信等特点的软硬件一体化的通用测定平台。平台以ARM(S3C2416)处理器为核心,Linux为操作系统,LCD作为人机交互显示,触摸屏或者USB鼠标完成输入控制,构成完整的嵌入式工控机系统;采用CAN总线并制定CAN应用层协议管理设备,提高了系统的可靠性及抗干扰能力。实际测试和应用证明,该平台自动化程度高,通用性、重用性及可扩展性均较强,可组建成亚硝氮、硝氮、氨氮、活性磷、铁等多种痕量元素的实验室、船载和原位分析系统,检测限为nmol/L级别。平台对样品的测试准确度与商品专用仪器无显著性差异。     

Computational modeling of Hg/Ni ions separation via MOF/LDH nanocomposite: Machine learning based modeling

Nowadays, sustainable supplement of water has recently been identified as a vital necessity due to the existence of limited drinkable water sources. To do this, various techniques are being developed to remove various types of pollutants from water/wastewater sources. Adsorption of common water pollutants using nanocomposite materials has been of great popularity in recent years due to its high efficiency. This paper aims to develop various models based on machine learning approach to study their efficiency on predicting the experimentally measured results of Hg/Ni ions removal from water sources. To do this, this study attempts regression on a small data set using two parameters as inputs and two parameters as outputs. In this dataset, the inputs are Ion and C0, and the outputs are Ce and Qe. AdaBoost (Adaptive Boosting), a well-known ensemble method, was applied on top of three different models, including Decision Tree Regression (DT), Gaussian Process Regression (GPR), and Linear Regression (LR). After fine-tuning their hyper-parameters, the optimized model was evaluated through various metrics. For example, the R² for ADA + GPR model has a score of 0.998 for Ce and 0.999 for Qe as the best model among these three models. This model in RMSE is the best and illustrates 0.1512 and 1.490 for Ce and Qe as error. Eventually, ADA + GPR has been selected as the optimized model with optimized dataset: (Ion = Ni, C0 = 250, Ce = 206.0). But for Qe, different amounts are illustrated: (Ion = Hg, C0 = 106.7, Ce = 577.35)     

Common complements of two subspaces of a Hilbert space

In this paper we find a necessary and sufficient condition for two closed subspaces, and , of a Hilbert space to have a common complement, i.e. a subspace having trivial intersection with and and such that .Unlike the finite-dimensional case the condition is significantly more subtle than simple equalities of dimensions and codimensions, and non-trivial examples of subspaces without a common complement are possible.     

An enhanced common path interference optic measurement system for refractive indices and thickness

This study proposes a common path interference optical system for the measurement of refractive indices and thickness of uniaxial crystal material. The measurement system comprises an accurate Mach–Zehnder laser interferometer, a single-axis rotary stepping motor, and a computer. The laser interferometer is composed of a single-frequency He–Ne laser, two-beam splitters and two reflectors. The Mach–Zehnder laser interferometer measures the optical length difference by using its linear measurement accuracy. The proposed solution procedure enables both the refractive indices and the thickness of the optical waveplate to be obtained. The proposed design differs from conventional designs in that it does not use a heterodyne modulator with a lock-in technique. It is shown that the refractive indices and thickness of the tested optical elements can be measured rapidly and accurately.