arXiv subjects

Xiao-Yu Sun

Publications and source records attributed to Xiao-Yu Sun.

5 recordsLinked to original sources

arXiv2024

Switching Event-Triggered Control of Nonlinear Parabolic PDE Systems via Galerkin/Neural-Network-Based Modeling Approach

This paper focuses on switching event-triggered output feedback control for a class of parabolic partial differential equation (PDE) systems subject to unknown nonlinearities and external bounded disturbance. Initially, the PDE systems is properly separated into a finite-dimensional ordinary differential equation (ODE) slow system and an infinite-dimensional ODE fast system based on Galerkin technique, especially the slow system can characterize the dominated dynamics. Then, a three-layer neural network is employed to approximate the unknown nonlinearities, and Levenberg-Marquardt algorithm is adopted to get a relative accurate slow system. Subsequentaly, a switching event-triggered control scheme is developed, and a waiting time subject to the triggered condition is implemented to avoid the Zeno behavior and convert the slow system into a switching system. In the following, the stability and $\textbf{\textit{H}}_\infty$ performance issues of the closed-loop system are discussed, and the controllers are displayed in terms of bilinear matrix inequalities (BMIs). Novel algorithms are proposed to convert the BMIs into linear matrix inequalities (LMIs). Additionally, a sub-optimal switching event-triggered controller is obtained using an iterative optimization approach based on LMIs. Finally, simulation on the catalytic rod reaction model and traffic flow model demonstrate the effectiveness of switching event-triggered control strategy.

math.OC↗

arXiv2023

On the four-quark operator matrix elements for the lifetime of $Λ_{b}$

Heavy quark expansion can nicely explain the lifetime of $Λ_{b}$. However, there still exist sizable uncertainties from the four-quark operator matrix elements of $Λ_{b}$ in $1/m_{b}^{3}$ corrections, which describe the spectator effects. In this work, these four-quark operator matrix elements are investigated using full QCD sum rules for the first time. At the QCD level, contributions from up to dimension-6 four-quark operators are considered. Our method of calculating high-dimensional operator matrix elements is promising to be used to resolve the $Ω_{c}$ lifetime puzzle.

hep-ph↗

arXiv2023

Semi-leptonic form factors of $Ξ_{c}\toΞ$ in QCD sum rules

There exists a significant deviation between the most recent Lattice QCD simulation and experimental measurement by Belle for $Ξ_{c}^{0}\toΞ^{-}\ell^{+}ν_{\ell}$. In this work, we investigate the $Ξ_{c}\toΞ$ form factors in QCD sum rules. To this end, the two-point correlation functions of $Ξ_{c}$ and $Ξ$, and the three-point correlation functions of $Ξ_{c}\toΞ$ are calculated. At the QCD level, contributions from up to dimension-6 four-quark operators are considered, and the leading order results of the Wilson coefficients are obtained. For the form factors, relatively stable Borel windows can be found. Our form factors are comparable with those of Lattice QCD, except for $f_{\perp}$. The obtained form factors are then used to predict the branching ratios of $Ξ_{c}\toΞ\ell^{+}ν_{\ell}$, and our predictions are consistent with the most recent data of ALICE and Belle, and those of Lattice QCD within error. Given that the branching ratios only contain limited information, we suggest the experimentalists directly measure the form factors of $Ξ_{c}\toΞ$.

hep-ph↗

arXiv2023

Revisiting $Ξ_{Q}-Ξ_{Q}^{\prime}$ mixing in QCD sum rules

In this work, we perform a QCD sum rules analysis on the $Ξ_{Q}-Ξ_{Q}^{\prime}$ mixing. Contributions from up to dimension-6 four-quark operators are considered. However, it turns out that, only dimension-4 and dimension-5 operators contribute, which reveals the non-perturbative nature of mixing. Especially we notice that only the diagrams with the two light quarks participating in gluon exchange contribute to the mixing. Our results indicate that the mixing angle $θ_{c}=(1.2\sim2.8)^{\circ}$ for the $Q=c$ case and $θ_{b}=(0.28\sim0.34)^{\circ}$ for the $Q=b$ case. Our prediction of $θ_{c}$ is consistent with the most recent Lattice QCD result within error. Such a small mixing angle seems unlikely to resolve the tension between the recent experimental measurement from Belle and Lattice QCD calculation for the semileptonic decay $Ξ_{c}^{0}\toΞ^{-} e^{+}ν_{e}$.

hep-ph↗

arXiv2012

Conditions and instability in $f(R)$ gravity with non-minimal coupling between matter and geometry

In this paper on the basis of the generalized $f(R)$ gravity model with arbitrary coupling between geometry and matter, four classes of $f(R)$ gravity models with non minimal coupling between geometry and matter will be studied. By means of conditions of power law expansion and the equation of state of matter less than -1/3, the relationship among p, w and n, the conditions and the candidate for late time cosmic accelerated expansion will be discussed in the four classes of $f(R)$ gravity models with non minimal coupling. Furthermore, in order to keep considering models to be realistic ones, the Dolgov Kawasaki instability will be investigated in each of them.

gr-qc↗