A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

Copper–4,4′-dipyridyl coordination compound as solid reagent for spectrophotometric determination of reducing sugar employing a multicommutation approach

In this work a multicommuted flow system employing copper–4,4′- dipyridyl coordination compound as the solid-phase reagent for the spectrophotometric determination of reducing sugar was developed. The coordination compound was synthesized through a reaction of the 4,4′-dipyridyl and copper (II) nitrate, under hydrothermal conditions. The complex was characterized by infrared spectroscopy (FTIR), power X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and thermogravimetric analysis (TGA). Based on the characterization, a multicommuted spectrophotometric procedure for the determination of reducing sugar using copper (II) complex as solid reagent is proposed. The proposed method was based on the redox reaction between a monosaccharide, such as fructose and glucose (reducing sugar) and Cu(II). This reaction, mediated in an alkaline medium, produces a yellow compound that can be determined by absorption electronic spectroscopy (λ_ABS = 420 nm). Under optimum experimental conditions, a linear response ranging from 1.0 to 20.0 g L⁻¹ (R = 0.9978 and n = 5), a detection (3σ criterion) and quantification (10σ criterion) limit estimated at 0.23 and 0.75 g L⁻¹, respectively, a standard deviation relative of 4.7% (n = 7), for a reference solution of 10.0 g L⁻¹ reducing sugar, and a sampling rate of 75 determinations per hour were achieved. The proposed system was applied to the determination of reducing sugars in coconut water and juices. The analysis of ten samples and the application of the t-test to the results found, and those obtained using reference procedures (AOAC), provided no significant differences at a 95% confidence level. This system enabled the analysis of reducing sugar with ease and simplicity, providing a significant economy of the solid reagent (600 μg per determination) and reducing effluent generation.     

马尔可夫跳变线性系统最优控制的研究现状与进展

马尔可夫跳变线性系统（MJLS）是一种具有多个模态的随机系统，系统在各个模态之间的跳变转移由一组马尔可夫链来决定。MJLS模型因其在表示过程中可以产生突变而更能精确的描述实际工程应用中的系统。近年来，MJLS的最优控制问题成为了研究的热点，动态规划、极大值原理以及线性矩阵不等式等成为了解决此类问题的主流方法。本文对MJLS最优控制领域的研究现状进行了综述。分别对一般情况下、带有噪声的情况下、带有时滞的情况下以及某些特定情况下的MLJS最优控制问题的国内外研究现状进行论述。最后进行了总结并提出MJLS最优控制领域未来值得关注的研究方向。     

Nonuniform linear array DOA estimation using EM criterion

In this letter, we address the problem of Direction of Arrival (DOA) estimation with nonuniform linear array in the context of sparse Bayesian learning (SBL) framework. The nonuniform array output is deemed as an incomplete-data observation, and a hypothetical uniform linear array output is treated as an unavailable complete-data observation. Then the Expectation-Maximization (EM) criterion is directly utilized to iteratively maximize the expected value of the complete-data log likelihood under the posterior distribution of the latent variable. The novelties of the proposed method lie in its capability of interpolating the actual received data to a virtual uniform linear array, therefore extending the achievable array aperture. Simulation results manifests the superiority of the proposed method over off-the-shelf algorithms, specially on circumstances such as low SNR, insufficient snapshots, and spatially adjacent sources.     

The generalized discrete ‐centroid problem

The ‐centroid problem or leader–follower problem is generalized considering different customer choice rules where a customer may use facilities belonging to different firms, if the difference in travel distance (or time) is small enough. Assuming essential goods, some particular customer choice rules are analyzed. Linear programming formulations for the generalized ‐medianoid and ‐centroid problems are presented and an exact solution approach is applied. Some computational examples are included.     

Improved Input and State Estimation for Linear Stochastic Systems with Direct Feedthrough

This paper is concerned with the problem of joint input and state estimation for linear stochastic systems with direct feedthrough. Based on the fact that each unknown input between any two time steps is always bounded, a novel improved algorithm is proposed. Compared with existing results, this algorithm can effectively enhance estimation accuracy. Moreover, the stability of the algorithm is also discussed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Using electroencephalogram to continuously discriminate feelings of personal thermal comfort between uncomfortably hot and comfortable environments

Thermal comfort is an important factor for the design of buildings. Although it has been well recognized that many physiological parameters are linked to the state of thermal comfort or discomfort of humans, how to use physiological signal to judge the state of thermal comfort has not been well studied. In this paper, the feasibility of continuously determining feelings of personal thermal comfort was discussed by using electroencephalogram (EEG) signals in private space. In the study, 22 subjects were exposed to thermally comfortable and uncomfortably hot environments, and their EEG signals were recorded. Spectral power features of the EEG signals were extracted, and an ensemble learning method using linear discriminant analysis or support vector machine as a sub-classifier was used to build the discriminant model. The results show that an average discriminate accuracy of 87.9% can be obtained within a detection window of 60 seconds. This study indicates that it is feasible to distinguish whether a person feels comfortable or too hot in their private space by multi-channel EEG signals without interruption and suggests possibility for further applications in neuroergonomics.