A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

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.     

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。     

基于时频域的卷积神经网络运动想象脑电信号识别方法

针对目前运动想象脑电（EEG）信号识别率较低的问题，考虑到脑电信号蕴含着丰富的时频信息，提出一种基于时频域的卷积神经网络（CNN）运动想象脑电信号识别方法。首先，利用短时傅里叶变换（STFT）对脑电信号的相关频带进行预处理，并将多个电极的时频图组合构造出一种二维时频图；然后，针对二维时频图的时频特性，通过一维卷积的方法设计了一种新颖的CNN结构；最后，通过支持向量机（SVM）对CNN提取的特征进行分类。基于BCI数据集的实验结果表明，所提方法的平均识别率为86.5%，优于其他传统运动想象脑电信号识别方法；同时将该方法应用在智能轮椅上，验证了其有效性。     

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.     

Robust Control of Permanent Magnet Synchronous Motors

In this paper, permanent magnet synchronous motors (PMSMs) are investigated. According to the feature of PMSMs, a novel state equation of PMSMs is obtained by choosing suitable state variables. Based on the state equation, robust controllers are designed via interval matrix and PI control idea. In terms of bilinear matrix inequations, sufficient conditions for the existence of the robust controller are derived. In order to reduce the conservation and the dependence on parameter, the control inputs of PMSMs are divided into two parts, a feedforward control input and a feedback control input, and relevant sufficient conditions for the existence of the controller are obtained. Because of the suitable choice of state variables, the proposed control strategies can cope with the load uncertainty and have robustness for disturbance. Finally, simulations are carried out via Matlab/Simulink soft to verify the effectiveness of the proposed control strategies. The performance of the proposed control strategies are demonstrated by the simulation results.