A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

Special issue on system identification and estimation

It is our great pleasure and honor to organize this special issue“System Identification and Estimation”.System identification has been a surprisingly lively and resilient area of research in the control community for many years.It grew out of statisticians’interest in time series analysis beginning in the 1940s and became a“regular control topic”in the 1960s,as indicated by thefirst IFAC Symposium on System Identification held in Prague,Czech Republic,in 1967.Sixty years later,it is still an important area of research in thefield of control.It is relevant to ask why the interest in system identification has remained so intense.One answer might be that more and more applications in engineering require mathematical models and the combined use of system identification and physical modeling is the basic way to obtain reliable models.This special issue is focusing on the latest development,trends,and novel methods for system identification and estimation and these contributions will give interesting and inspiring insights into the current status of the area.

Modulating effects of Astragalus polysaccharide on immune disorders via gut microbiota and the TLR4/NF-κB pathway in rats with syndrome of dampness stagnancy due to spleen deficiency

The syndrome of dampness stagnancy due to spleen deficiency(DSSD)is relatively common globally.Although the pathogenesis of DSSD remains unclear,evidence has suggested that the gut microbiota might play a significant role.Radix Astragali,used as both medicine and food,exerts the effects of tonifying spleen and qi.Astragalus polysaccharide(APS)comprises a macromolecule substance extracted from the dried root of Radix Astragali,which has many pharmacological functions.However,whether APS mitigates the immune disorders underlying the DSSD syndrome via regulating gut microbiota and the relevant mechanism remains unknown.Here,we used DSSD rats induced by high-fat and low-protein(HFLP)diet plus exhaustive swimming,and found that APS of moderate molecular weight increased the body weight gain and immune organ indexes,decreased the levels of interleukin-1β(IL-1β),IL-6,and endotoxin,and suppressed the Toll-like receptor 4/nuclear factor-κB(TLR4/NF-κB)pathway.Moreover,a total of 27 critical genera were significantly enriched according to the linear discriminant analysis effect size(LEfSe).APS increased the diversity of the gut microbiota and changed its composition,such as reducing the relative abundance of Pseudoflavonifractor and Paraprevotella,and increasing that of Parasutterella,Parabacteroides,Clostridium XIVb,Oscillibacter,Butyricicoccus,and Dorea.APS also elevated the contents of short-chain fatty acids(SCFAs).Furthermore,the correlation analysis indicated that 12 critical bacteria were related to the body weight gain and immune organ indexes.In general,our study demonstrated that APS ameliorated the immune disorders in DSSD rats via modulating their gut microbiota,especially for some bacteria involving immune and inflammatory response and SCFA production,as well as the TLR4/NF-κB pathway.This study provides an insight into the function of APS as a unique potential prebiotic through exerting systemic activities in treating DSSD.

Copper-catalyzed asymmetric 1,3-dipolar cycloaddition of azomethine ylides withβ-trifluoromethyl-substituted alkenyl heteroarenes

Copper-catalyzed asymmetric 1,3-dipolar cycloaddition of azomethine ylides andβ-trifluoromethyl-substituted alkenyl heteroarenes was developed for the first time.A wide range of enantioenriched pyrrolidines containing both heteroarenes and trifluoromethyl group with multiple stereogenic centers could be readily accessible by this method with good to high yields and excellent levels of both stereo-and regioselectivity(up to 99%yield,>20:1 rr,>20:1 dr,and up to 95%ee).Notably,substratecontrolled umpolung-type dipolar cycloaddition was also disclosed in this protocol to achieve regiodivergent synthesis withα-aryl substituted aldimine esters as the dipole precursors.Systematic DFT studies were conducted to explore the origin of the stereo-and regioselectivity of this 1,3-dipolar cycloaddition,and suggest that copper(Ⅱ)salt utilized in this catalytic system could be reduced in-situ to the active copper(Ⅰ)species and might be responsible for the observed high stereo-and regioselectivity.

Sparse parameter identification of stochastic dynamical systems

Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control[1-4],signal processing[5,6],statistics[7,8],and machine learning[9,10]since it provides a way to discover a parsimonious model that leads to more reliable and robust prediction.Classical system identification theory has been a well-developed field[11,12].It usually characterizes the identification error between the estimates and the unknown parameters using different criteria such as randomness of noises,frequency domain sample data。

Variable selection in identification of a high dimensional nonlinear non-parametric system

The problem of variable selection in system identification of a high dimensional nonlinear non-parametric system is described. The inherent difficulty, the curse of dimensionality, is introduced. Then its connections to various topics and research areas are briefly discussed, including order determination, pattern recognition, data mining, machine learning, statistical regression and manifold embedding. Finally, some results of variable selection in system identification in the recent literature are presented.

Distributed dynamic stochastic approximation algorithm over time-varying networks

In this paper,a distributed stochastic approximation algorithm is proposed to track the dynamic root of a sum of time-varying regression functions over a network.Each agent updates its estimate by using the local observation,the dynamic information of the global root,and information received from its neighbors.Compared with similar works in optimization area,we allow the observation to be noise-corrupted,and the noise condition is much weaker.Furthermore,instead of the upper bound of the estimate error,we present the asymptotic convergence result of the algorithm.The consensus and convergence of the estimates are established.Finally,the algorithm is applied to a distributed target tracking problem and the numerical example is presented to demonstrate the performance of the algorithm.