Prescribed performance control of underactuated surface vessels' trajectory using a neural network and integral time-delay sliding mode

summary:To tackle the underactuated surface vessel (USV) trajectory tracking challenge with input delays and composite disturbances, an integral time-delay sliding mode controller based on backstepping is discussed. First, the law of virtual velocity control is established by coordinate transformation and the position error is caused to converge utilizing the performance function. At the same time, based on the estimation of velocity vector by the high-gain observer (HGO), radial basis function (RBF) neural network is applied to compensate for both the uncertainty of model parameters and external disturbances. The longitudinal and heading control laws are presented in combination with the integral time-delay sliding mode control. Then, on the basis of Lyapunov - Krasovskii functional and stability proof, virtual velocity error is guaranteed to converge to 0 in finite time. Finally, the outcomes of the numerical simulation demonstrate the reliability and efficiency of the proposed approach

Chromopolarizability of charmonium and ππ\pi\pi final state interaction revisited

The chromopolarizability of a quarknonium describes the quarknonium's interaction with soft gluonic fields and can be measured in the heavy quarkonium decays. Within the framework of dispersion theory which consider the $\pi\pi$ final state interaction (FSI) model-independently, we analyze the transition $\psi^\prime\to J/\psi\pi^+\pi^-$ and obtain the chromopolarizability $\alpha_{\psi^\prime \psi}$ and the parameter $\kappa$. It is found that the $\pi\pi$ FSI plays an important role in extracting the chromopolarizability from the experimental data. The obtained chromopolarizability with the FSI is reduced to about 1/2 of that without the FSI. With the FSI, we determine the chromopolarizability $|\alpha_{\psi^\prime\psi}|=(1.44\pm 0.02)$ GeV$^{-3}$ and the parameter $\kappa=0.139\pm 0.005.$ Our results could be useful in studying the interactions of charmonium with light hadrons.Comment: 8 pages, 1 figur

Analyses of pion-nucleon elastic scattering amplitudes up to O(p4)O(p^4) in extended-on-mass-shell subtraction scheme

We extend the analysis of elastic pion-nucleon scattering up to $O(p^4)$ level using extended-on-mass-shell subtraction scheme within the framework of covariant baryon chiral perturbation theory. Numerical fits to partial wave phase shift data up to $\sqrt{s}=1.13$ GeV are performed to pin down the free low energy constants. A good description to the existing phase shift data is achieved. We find a good convergence for the chiral series at $O(p^4)$, considerably improved with respect to the $O(p^3)$-level analyses found in previous literature. Also, the leading order contribution from explicit $\Delta(1232)$ resonance and partially-included $\Delta(1232)$ loop contribution are included to describe phase shift data up to $\sqrt{s}=1.20$ GeV. As phenomenological applications, we investigate chiral correction to the Goldberger-Treiman relation %$\Delta_{GT}$ and find that it converges rapidly, and the $O(p^3)$ correction is found to be very small: $\simeq 0.2$. We also get a reasonable prediction of pion-nucleon sigma term $\sigma_{\pi N}$ up to $O(p^4)$ by performing fits including both the pion-nucleon partial wave phase shift data and the lattice QCD data. We report that $\sigma_{\pi N}=52\pm7$ MeV from the fit without $\Delta(1232)$, and $\sigma_{\pi N}=45\pm6$ MeV from the fit with explicit $\Delta(1232)$.Comment: The final version published in Phys.Rev. D 87, 054019 (2013

Momentum-dependence of ρ−ω\rho-\omega mixing in the pion vector form factor and its effect on (g−2)μ(g-2)_\mu

The inclusion of the $\rho-\omega$ mixing effect is crucial for a good description of the pion electromagnetic form factor in the $e^+e^- \rightarrow \pi^+\pi^-$ process, which quantifies the two-pion contribution to the anomalous magnetic moment of the muon $a_\mu$. In this paper, we try to analyze the impact of the momentum-dependence of the $\rho-\omega$ mixing within the framework of resonance chiral theory. The momentum-dependence of the $\rho-\omega$ mixing is incorporated due to the calculation of loop contributions at the next-to-leading order in the $1/N_C$ expansion. The work of {[}Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69 (2018) 1{]} is revisited taking into account the contribution due to the kaon mass splitting in the kaon loops and the latest experimental data. We perform two kinds of fits (with momentum-independent or momentum-dependent $\rho-\omega$ mixing amplitude) describing the $e^+e^-\rightarrow \pi^+\pi^-$ and $\tau\rightarrow \nu_{\tau}2\pi$ data in the energy region of 600$\sim$900 MeV and the decay width of $\omega \rightarrow \pi^+\pi^-$, and compare their results. It is found that taking account of the momentum-dependence of $\rho-\omega$ mixing can describe the pion vector form factor data a little better. For the contribution to the anomalous magnetic moment of the muon $a_\mu^{\pi\pi}|_{[0.6,0.9]\text{GeV}}$, the values of the results in the fits considering the momentum-dependent $\rho-\omega$ mixing amplitude are agree well with those in the fits without including the momentum-dependence of the $\rho-\omega$ mixing within errors. In addition, based on the fitted values of the involved parameters, we find that in the decay width of $\omega \rightarrow \pi^+\pi^-$ the contribution from the direct $\omega_I\pi\pi$ coupling is comparable with the contribution due to the $\rho-\omega$ mixing.Comment: 21 pages, 4 figures. arXiv admin note: text overlap with arXiv:1710.1144