Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point

Phoebe's orbit from ground-based and space-based observations

The ephemeris of Phoebe, the ninth satellite of Saturn, is not very accurate. Previous dynamical models were usually too simplified, the astrometry is heterogeneous and, the Saturn's ephemeris itself is an additionnal source of error. The aim is to improve Phoebe's ephemeris by using a large set of observations, correcting some systematic errors and updating the dynamical model. The dynamical model makes use of the most recent ephemeris of planets and Saturnian satellites. The astrometry of Phoebe is improved by using a compilation of ground-based and space-based observations and by correcting the bias in stellar catalogues used for the reduction. We present an accurate ephemeris of Phoebe with residuals of 0.45 arcsec and with an estimated accuracy of Phoebe's position of less that 100 km on 1990-2020 period.Comment: 10 pages, 9 figures, accepted by A&

Magnon dark modes and gradient memory

Extensive efforts have been expended in developing hybrid quantum systems to overcome the short coherence time of superconducting circuits by introducing the naturally long-lived spin degree of freedom. Among all the possible materials, single-crystal yttrium iron garnet has shown up very recently as a promising candidate for hybrid systems, and various highly coherent interactions, including strong and even ultra-strong coupling, have been demonstrated. One distinct advantage of these systems is that the spins are in the form of well-defined magnon modes, which allows flexible and precise tuning. Here we demonstrate that by dissipation engineering, a non-Markovian interaction dynamics between the magnon and the microwave cavity photon can be achieved. Such a process enables us to build a magnon gradient memory to store information in the magnon dark modes, which decouple from the microwave cavity and thus preserve a long life-time. Our findings provide a promising approach for developing long-lifetime, multimode quantum memories.Comment: 18 pages, 12 figure

Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters

Single-point zeroth-order optimization (SZO) is useful in solving online black-box optimization and control problems in time-varying environments, as it queries the function value only once at each time step. However, the vanilla SZO method is known to suffer from a large estimation variance and slow convergence, which seriously limits its practical application. In this work, we borrow the idea of high-pass and low-pass filters from extremum seeking control (continuous-time version of SZO) and develop a novel SZO method called HLF-SZO by integrating these filters. It turns out that the high-pass filter coincides with the residual feedback method, and the low-pass filter can be interpreted as the momentum method. As a result, the proposed HLF-SZO achieves a much smaller variance and much faster convergence than the vanilla SZO method and empirically outperforms the residual-feedback SZO method, which is verified via extensive numerical experiments

A fault diagnosis approach of reciprocating compressor gas valve based on local mean decomposition and autoregressive-generalized autoregressive conditional heteroscedasticity model

Vibration signal of reciprocating compressor gas valve represents nonlinear, non-stationary and multiple impulse characteristics. To extract the features of the signal, an integration approach based on local mean decomposition (LMD) method and autoregressive-generalized autoregressive conditional heteroscedasticity (AR-GARCH) model is proposed. First, the property of LMD is investigated in the paper, which indicates that LMD method not only can effectively alleviate non-stationary feature and restrain the end effect of non-stationary signal, but also can accurately improve the resolution of time-frequency analysis. Then, the first five PF components of gas valve signal are modeled by AR(1)-GARCH(1, 1) model as the feature vectors without any prior knowledge about the fault mechanism. Finally, the BP neural networks are applied to diagnose the faults of reciprocating compressor gas valve based on the feature vectors above. The results indicate that high diagnosis accuracy can be obtained by integrating LMD method and AR-GARCH model. So the approach proposed in the paper provides an effective measure to extract the fault feature of reciprocating compressor gas valve