We present the Young Exoplanet Transit Initiative (YETI), in which we use several 0.2 to 2.6-m telescopes around the world to monitor continuously young (≤100 Myr), nearby (≤1 kpc) stellar clusters mainly to detect young transiting planets (and to study other variability phenomena on time-scales from minutes to years). The telescope network enables us to observe the targets continuously for several days in order not to miss any transit. The runs are typically one to two weeks long, about three runs per year per cluster in two or three subsequent years for about ten clusters. There are thousands of stars detectable in each field with several hundred known cluster members, e.g. in the first cluster observed, Tr-37, a typical cluster for the YETI survey, there are at least 469 known young stars detected in YETI data down to R = 16.5 mag with sufficient precision of 50 millimag rms (5 mmag rms down to R = 14.5 mag) to detect transits, so that we can expect at least about one young transiting object in this cluster. If we observe ∼10 similar clusters, we can expect to detect ∼10 young transiting planets with radius determinations. The precision given above is for a typical telescope of the YETI network, namely the 60/90-cm Jena telescope (similar brightness limit, namely within ±1 mag, for the others) so that planetary transits can be detected. For targets with a periodic transit-like light curve, we obtain spectroscopy to ensure that the star is young and that the transiting object can be sub-stellar; then, we obtain Adaptive Optics infrared images and spectra, to exclude other bright eclipsing stars in the (larger) optical PSF; we carry out other observations as needed to rule out other false positive scenarios; finally, we also perform spectroscopy to determine the mass of the transiting companion. For planets with mass and radius determinations, we can calculate the mean density and probe the internal structure. We aim to constrain planet formation models and their time-scales by discovering planets younger than ∼100 Myr and determining not only their orbital parameters, but also measuring their true masses and radii, which is possible so far only by the transit method. Here, we present an overview and first results.

Control Barrier Functions (CBFs) have become popular for enforcing — via barrier constraints — the safe operation of nonlinear systems within an admissible set. For systems with input delay(s) of the same length, constrained control has been achieved by combining a CBF for the delay free system with a state predictor that compensates the single input delay. Recently, this approach was extended to multi input systems with input delays of different lengths. One limitation of this extension is that barrier constraint adherence can only be guaranteed after the longest input delay has been compensated and all input channels become available for control. In this paper, we consider the problem of enforcing constraint adherence when only a subset of input delays have been compensated. In particular, we propose a new barrier constraint formulation that ensures that when possible, a subset of input channels with shorter delays will be utilized for keeping the system in the admissible set even before longer input delays have been compensated. We include a numerical example to demonstrate the effectiveness of the proposed approach.

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