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1. Nonlinear observer design for two‐time‐scale systems

   https://doi.org/10.1002/aic.16956  

   Duan, Zhaoyang; Kravaris, Costas (March 2020, AIChE Journal)

   Abstract A two‐time‐scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two‐time‐scale systems and presents two alternative nonlinear observer design approaches, one full‐order and one reduced‐order. The full‐order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced‐order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow‐motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced‐order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties. 

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2. Observer-Aware Legibility for Social Navigation

   https://doi.org/10.1109/RO-MAN53752.2022.9900676  

   Taylor, Ada V.; Mamantov, Ellie; Admoni, Henny (August 2022, EEE International Conference on Robot and Human Interactive Communication (RO-MAN))

   We designed an observer-aware method for creating navigation paths that simultaneously indicate a robot’s goal while attempting to remain in view for a particular observer. Prior art in legible motion does not account for the limited field of view of observers, which can lead to wasted communication efforts that are unobserved by the intended audience. Our observer-aware legibility algorithm directly models the locations and perspectives of observers, and places legible movements where they can be easily seen. To explore the effectiveness of this technique, we performed a 300-person online user study. Users viewed first-person videos of restaurant scenes with robot waiters moving along paths optimized for different observer perspectives, along with a baseline path that did not take into account any observer’s field of view. Participants were asked to report their estimate of how likely it was the robot was heading to their table versus the other goal table as it moved along each path. We found that for observers with incomplete views of the restaurant, observer-aware legibility is effective at increasing the period of time for which observers correctly infer the goal of the robot. Non-targeted observers have lower performance on paths created for other observers than themselves, which is the natural drawback of personalizing legible motion to a particular observer. We also find that an observer’s relationship to the environment (e.g. what is in their field of view) has more influence on their inferences than the observer’s relative position to the targeted observer, and discuss how this implies knowledge of the environment is required in order to effectively plan for multiple observers at once. 

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3. 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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4. Estimator-Based Output-Feedback Stabilization of Linear Multi-Delay Systems using SOS

   Wu, S.; Peet, M. (January 2019, Proceedings of the IEEE Conference on Decision & Control)

   In this paper, we investigate the estimator-based output feedback control problem of multi-delay systems. This work is an extension of recently developed operator-value LMI framework for infinite-dimensional time-delay systems. Based on the optimal convex state feedback controller and generalized Luenberger observer synthesis conditions we already have, the estimator-based output feedback controller is designed to contain the estimates of both the present state and history of the state. An output feedback controller synthesis condition is proposed using SOS method, which is expressed in a set of LMI/SDP constraints. The simulation examples are displayed to demonstrate the effectiveness and advantages of the proposed results. 

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5. Variational Observer Designs on Lie Groups, with Applications to Rigid Body Motion Estimation

   https://doi.org/10.1109/CDC56724.2024.10886160  

   Srinivasu, Neon; Dongare, Abhijit; Sanyal, Amit K (December 2024, IEEE)

   Variational estimation of a mechanical system is based on the application of variational principles from mechanics to state estimation of the system evolving on its configuration manifold. If the configuration manifold is a Lie group, then the underlying group structure can be used to design nonlinearly stable observers for estimation of configuration and velocity states from measurements. Measured quantities are on a vector space on which the Lie group acts smoothly. We formulate the design of variational observers on a general finite-dimensional Lie group, followed by the design and experimental evaluation of a variational observer for rigid body motions on the Lie group SE(3). 

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