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1. Robust Analysis of Linear Systems with Uncertain Delays using PIEs

   https://doi.org/10.1016/j.ifacol.2021.11.133  

   Wu, S.; Peet, M.; Sun, F.; Hua, C. (January 2021, IFACPapersOnLine)

   Appeared in the proceedings of the 2021 IFAC Workshop on Time-Delay Systems This paper establishes a PIE (Partial Integral Equation)-based technique for the robust stability and H∞ performance analysis of linear systems with interval delays. The delays considered are time-invariant but uncertain, residing within a bounded interval excluding zero. We first propose a structured class of PIE systems with parametric uncertainty, then propose a Linear PI Inequality (LPI) for robust stability and H∞ performance of PIEs with polytopic uncertainty. Next, we consider the problem of robust stability and H∞ performance of multidelay systems with interval uncertainty in the delay parameters and show this problem is equivalent to robust stability and performance of a given PIE with parametric uncertainty. The robust stability and H∞ performance of the uncertain time-delay system are then solved using the LPI solver in the MATLAB PIETOOLS toolbox. Numerical examples are given to prove the effectiveness and accuracy of the method. This paper adds to the expanding field of PIE approach and can be extended to linear partial differential equations. 

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2. A dead time compensation approach for multirate observer design with large measurement delays

   https://doi.org/10.1002/aic.16445  

   Ling, Chen; Kravaris, Costas (November 2018, AIChE Journal)

   In our previous work, we developed a multirate observer design method in linear systems with asynchronous sampling based on a Luenberger observer design coupled with inter‐sample predictors. In this article, the problem of multirate multidelay observer design is addressed where both asynchronous sampling and possible measurement delays are accounted for. The proposed observer adopts an available multirate observer design in the time interval between two consecutive delayed measurements. A dead time compensation approach is developed to compensate for the effect of delay and update past estimates when a delayed measurement arrives. The stability and robustness properties of the multirate observer will be preserved under nonconstant, arbitrarily large measurement delays. A mathematical example and a gas‐phase polyethylene reactor example demonstrate good performance of the proposed observer in the presence of nonuniform sampling and nonconstant measurement delays. © 2018 American Institute of Chemical EngineersAIChE J, 65: 562–570, 2019 

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3. Constrained Control of Input Delayed Systems With Partially Compensated Input Delays

   https://doi.org/10.1115/DSCC2020-3271  

   Abel, Imoleayo; Janković, Mrdjan; Krstić, Miroslav (October 2020, ASME 2020 Dynamic Systems and Control Conference)

   null (Ed.)

   Abstract 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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4. Near-Equivalence Between Bounded Regret and Delay Robustness in Interactive Decision Making

   Kang, E H; Kumar, P R (October 2023, NeurIPS 2023 Workshop on Adaptive Experimental Design and Active Learning in the Real World)

   Interactive decision making, encompassing bandits, contextual bandits, and reinforcement learning, has recently been of interest to theoretical studies of experimentation design and recommender system algorithm research. Recently, it has been shown that the wellknown Graves-Lai constant being zero is a necessary and sufficient condition for achieving bounded (or constant) regret in interactive decision making. As this condition may be a strong requirement for many applications, the practical usefulness of pursuing bounded regret has been questioned. In this paper, we show that the condition of the Graves-Lai constant being zero is also necessary to achieve delay model robustness when reward delays are unknown (i.e., when feedbacks are anonymous). Here, model robustness is measured in terms of ✏-robustness, one of the most widely used and one of the least adversarial robustness concepts in the robust statistics literature. In particular, we show that ✏-robustness cannot be achieved for a consistent (i.e., uniformly sub-polynomial regret) algorithm however small the nonzero ✏ value is when the Grave-Lai constant is not zero. While this is a strongly negative result, we also provide a positive result for linear rewards models (Linear contextual bandits, Reinforcement learning with linear MDP) that the Grave-Lai constant being zero is also sufficient for achieving bounded regret without any knowledge of delay models, i.e., the best of both the efficiency world and the delay robustness world. 

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5. Astrometric requirements for strong lensing time-delay cosmography

   https://doi.org/10.1093/mnras/stz2254  

   Birrer, Simon; Treu, Tommaso (October 2019, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT The time-delay between the arrival of photons of multiple images of time-variable sources can be used to constrain absolute distances in the Universe, and in turn obtain a direct estimate of the Hubble constant and other cosmological parameters. To convert the time-delay into distances, it is well known that the gravitational potential of the main deflector and the contribution of the matter along the line of sight need to be known to a sufficient level of precision. In this paper, we discuss a new astrometric requirement that is becoming important, as time-delay cosmography improves in precision and accuracy with larger samples, and better data and modelling techniques. We derive an analytic expression for the propagation of astrometric uncertainties on the multiple image positions into the inference of the Hubble constant and derive requirements depending on image separation and relative time-delay. We note that this requirement applies equally to the image position measurements and to the accuracy of the model in reproducing them. To illustrate the requirement, we discuss some example lensing configurations and highlight that, especially for time-delays of order 10 d or shorter, the relative astrometric requirement is of order milliarcseconds, setting a tight requirement on both measurements and models. With current optical infrared technology, astrometric uncertainties may be the dominant limitation for strong lensing cosmography in the small image-separation regime when high-precision time-delays become accessible. 

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