Data-Driven Control of Linear Time-Varying Systems

An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. This data-driven system representation is used to classify control laws yielding trajectories which satisfy a certain bound and to solve the linear quadratic regulator problem - both using data-dependent linear matrix inequalities only. The results are illustrated by means of a numerical example

The GTC exoplanet transit spectroscopy survey X. Stellar spots versus Rayleigh scattering: the case of HAT-P-11b

Rayleigh scattering in a hydrogen-dominated exoplanet atmosphere can be detected from ground or space based telescopes, however, stellar activity in the form of spots can mimic Rayleigh scattering in the observed transmission spectrum. Quantifying this phenomena is key to our correct interpretation of exoplanet atmospheric properties. We obtained long-slit optical spectroscopy of two transits of HAT-P-11b with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at Gran Telescopio Canarias (GTC) on August 30 2016 and September 25 2017. We integrated the spectrum of HAT-P-11 and one reference star in several spectroscopic channels across the $\lambda\sim$ 400-785 nm region, creating numerous light curves of the transits. We fit analytic transit curves to the data taking into account the systematic effects and red noise present in the time series in an effort to measure the change of the planet-to-star radius ratio ($R_\mathrm{p}/R_\mathrm{s}$) across wavelength. By fitting both transits together, we find a slope in the transmission spectrum showing an increase of the planetary radius towards blue wavelengths. A closer inspection to the transmission spectrum of the individual data sets reveals that the first transit presents this slope while the transmission spectrum of the second data set is flat. Additionally we detect hints of Na absorption in the first night, but not in the second. We conclude that the transmission spectrum slope and Na absorption excess found in the first transit observation are caused by unocculted stellar spots. Modeling the contribution of unocculted spots to reproduce the results of the first night we find a spot filling factor of $\delta=0.62^{+0.20}_{-0.17}$ and a spot-to-photosphere temperature difference of $\Delta T = 429^{+184}_{-299}$ K.Comment: Accepted for publication in Astronomy & Astrophysics, 13 page

Direct data-driven control of linear time-varying systems

An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. Subsequently, controllers guaranteeing bounded closed-loop trajectories, optimal performance and robustness to process and measurement noise are designed via convex feasibility and optimisation problems involving purely data-dependent linear matrix inequalities. For the special case of periodically time-varying systems, performance guarantees are achieved over an infinite horizon, based on data collected over a single, finite duration experiment. The results are demonstrated by means of an illustrative academic example and a practically motivated example involving a voltage source converter.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

The GTC exoplanet transit spectroscopy survey. VII. Detection of sodium in WASP-52b's cloudy atmosphere

We report the first detection of sodium absorption in the atmosphere of the hot Jupiter WASP-52b. We observed one transit of WASP-52b with the low-resolution Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at the 10.4 m Gran Telescopio Canarias (GTC). The resulting transmission spectrum, covering the wavelength range from 522 nm to 903 nm, is flat and featureless, except for the significant narrow absorption signature at the sodium doublet, which can be explained by an atmosphere in solar composition with clouds at 1 mbar. A cloud-free atmosphere is stringently ruled out. By assessing the absorption depths of sodium in various bin widths, we find that temperature increases towards lower atmospheric pressure levels, with a positive temperature gradient of 0.88 +/- 0.65 K/km, possibly indicative of upper atmospheric heating and a temperature inversion.Comment: 6 pages, 5 figures, accepted for publication in A&A Lette

Detection of sodium in the atmosphere of WASP-69b

Transit spectroscopy is one of the most commonly used methods to characterize exoplanets atmospheres. From the ground, these observations are very challenging due to the terrestrial atmosphere and its intrinsic variations, but high-spectral resolution observations overcome this difficulty by resolving the spectral lines and taking advantage of the different Doppler velocities of the Earth, the host star and the exoplanet. We analyze the transmission spectrum around the Na I doublet at 589 nm of the exoplanet WASP-69b, a hot Jupiter orbiting a K-type star with a period of 3.868 days, and compare the analysis to that of the well-know hot Jupiter HD 189733b. We also present the analysis of the Rossiter-McLaughlin effect for WASP-69b. Two transits of WASP-69b were observed with the HARPS-North spectrograph (R = 115 000) at the TNG telescope. We perform a telluric contamination subtraction based on the comparison between the observed spectra and a telluric water model. Then, the common steps of the differential spectroscopy are followed to extract the transmission spectrum. The method is tested with archival transit data of the extensively studied exoplanet HD 189733b, obtained with the HARPS-South spectrograph at ESO 3.6m telescope, and then applied to WASP-69b data. For HD 189733b, we spectrally resolve the Na I doublet and measure line contrasts of $0.72\pm0.05\%$ (D2) and $0.51\pm0.05\%$ (D1), and FWHMs of $0.64\pm0.04${\AA} (D2) and $0.60\pm0.06${\AA} (D1), in agreement with previously published results. A net blueshift of ${\sim}0.04${\AA} is measured. For WASP-69b only the contrast of the D2 line is measured ($5.8\pm0.3\%$). Even if this corresponds to a detection at the $5\sigma$-level of excess absorption of $0.5\pm0.1\%$ in a passband of $1.5${\AA}, more transits are needed to fully characterize the lines profiles and retrieve accurate atmospheric properties.Comment: 15 pages, 14 figure

The GTC exoplanet transit spectroscopy survey. VII. An optical transmission spectrum of WASP-48b

We obtained long-slit optical spectroscopy of one transit of WASP-48b with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) spectrograph at the 10.4 m Gran Telescopio Canarias (GTC). We integrated the spectrum of WASP-48 and one reference star in several channels with different wavelength ranges, creating numerous color light curves of the transit. We fit analytic transit curves to the data taking into account the systematic effects present in the time series in an effort to measure the change of the planet-to-star radius ratio ($R_p/R_s$) across wavelength. After removing the transit model and systematic trends to the curves we reached precisions between 261 ppm and 455-755 ppm for the white and spectroscopic light curves, respectively. We obtained $R_p/R_s$ uncertainty values between $0.8 \times 10^{-3}$ and $1.5\times 10^{-3}$ for all the curves analyzed in this work. The measured transit depth for the curves made by integrating the wavelength range between 530 nm and 905 nm is in agreement with previous studies. We report a relatively flat transmission spectrum for WASP-48b with no statistical significant detection of atmospheric species, although the theoretical models that fit the data more closely include of TiO and VO.Comment: 8 pages, 8 figures. Accepted for publication in Astronomy and Astrophysic

The GTC exoplanet transit spectroscopy survey. VI. A spectrally-resolved Rayleigh scattering slope in GJ 3470b

Aims. As a sub-Uranus-mass low-density planet, GJ 3470b has been found to show a flat featureless transmission spectrum in the infrared and a tentative Rayleigh scattering slope in the optical. We conducted an optical transmission spectroscopy project to assess the impacts of stellar activity and to determine whether or not GJ 3470b hosts a hydrogen-rich gas envelop. Methods. We observed three transits with the low-resolution OSIRIS spectrograph at the 10.4 m Gran Telescopio Canarias, and one transit with the high-resolution UVES spectrograph at the 8.2 m Very Large Telescope. Results. From the high-resolution data, we find that the difference of the Ca II H+K lines in- and out-of-transit is only 0.67 +/- 0.22%, and determine a magnetic filling factor of about 10-15%. From the low-resolution data, we present the first optical transmission spectrum in the 435-755 nm band, which shows a slope consistent with Rayleigh scattering. Conclusions. After exploring the potential impacts of stellar activity in our observations, we confirm that Rayleigh scattering in an extended hydrogen/helium atmosphere is currently the best explanation. Further high-precision observations that simultaneously cover optical and infrared bands are required to answer whether or not clouds and hazes exist at high-altitude.Comment: 12 pages, 11 figures, accepted for publication in A&

The eclipsing post-common envelope binary CSS21055: a white dwarf with a probable brown-dwarf companion

We report photometric observations of the eclipsing close binary CSS21055 (SDSS J141126+200911) that strongly suggest that the companion to the carbon-oxygen white dwarf is a brown dwarf with a mass between 0.030 and 0.074 Msun. The measured orbital period is 121.73min and the totality of the eclipse lasts 125s. If confirmed, CSS21055 would be the first detached eclipsing WD+BD binary. Spectroscopy in the eclipse could provide information about the companion's evolutionary state and atmospheric structure.Comment: 6 pages, 5 figure