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This work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

 

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization approach to augmenting model-free RL. In particular, we regularize the behavior of the deep policy to be similar to a control prior, i.e., we regularize in function space. We show that functional regularization yields a bias-variance trade-off, and propose an adaptive tuning strategy to optimize this trade-off. When the prior policy has control-theoretic stability guarantees, we further show that this regularization approximately preserves those stability guarantees throughout learning. We validate our approach empirically on a wide range of settings, and demonstrate significantly reduced variance, guaranteed dynamic stability, and more efficient learning than deep RL alone. 

In 2019 September, a sudden flare of the 6.7 GHz methanol maser was observed toward the high-mass young stellar object (HMYSO) G24.33+0.14. This may represent the fourth detection of a transient mass accretion event in an HMYSO after S255IR NIRS3, NGC 6334I-MM1, and G358.93−0.03-MM1. G24.33+0.14 is unique among these sources as it clearly shows a repeating flare with an 8 yr interval. Using the Atacama Large Millimeter/submillimeter Array (ALMA), we observed the millimeter continuum and molecular lines toward G24.33+0.14 in the pre-flare phase in 2016 August (ALMA Cycle 3) and the mid-flare phase in 2019 September (ALMA Cycle 6). We identified three continuum sources in G24.33+0.14, and the brightest source, C1, which is closely associated with the 6.7 GHz maser emission, shows only a marginal increase in flux density with a flux ratio (Cycle 6$/$Cycle 3) of 1.16 ± 0.01, considering an additional absolute flux calibration uncertainty of $10\%$. We identified 26 transitions from 13 molecular species other than methanol, and they exhibit similar levels of flux differences with an average flux ratio of 1.12 ± 0.15. In contrast, eight methanol lines observed in Cycle 6 are brighter than those in Cycle 3 with an average flux ratio of 1.23 ± 0.13, and the higher excitation lines tend to show a larger flux increase. If this systematic increasing trend is real, it would suggest radiative heating close to the central HMYSO due to an accretion event which could expand the size of the emission region and/or change the excitation conditions. Given the low brightness temperatures and small flux changes, most of the methanol emission is likely to be predominantly thermal, except for the 229.759 GHz (8−1–70 E) line known as a class I methanol maser. The flux change in the millimeter continuum of G24.33+0.14 is smaller than in S255IR NIRS3 and NGC 6334I-MM1 but is comparable with that in G358.93−0.03-MM1, suggesting different amounts of accreted mass in these events.