5 research outputs found

    Identifying Single-Input Linear System Dynamics from Reachable Sets

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    This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the reachable sets are known from partially transparent manufacturer specifications or observations of the collective behavior of adversarial agents, we aim to utilize such sets to determine the unknown system's dynamics. This paper has two contributions. Firstly, we show that the sequence of the system's reachable sets can be used to uniquely determine the system's dynamics for asymmetric input sets under some generic assumptions, regardless of the system's dimensions. We also prove the same property holds up to a sign change for two-dimensional systems where the input set is symmetric around zero. Secondly, we present an algorithm to determine these dynamics. We apply and verify the developed theory and algorithms on an unknown band-pass filter circuit solely provided the unknown system's reachable sets over a finite observation period.Comment: 8 pages, 1 figure, published at the 62nd Conference on Decision and Control (CDC 2023

    Online Learning and Control Synthesis for Reachable Paths of Unknown Nonlinear Systems

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    In this paper, we present a novel method to drive a nonlinear system to a desired state, with limited a priori knowledge of its dynamic model: local dynamics at a single point and the bounds on the rate of change of these dynamics. This method synthesizes control actions by utilizing locally learned dynamics along a trajectory, based on data available up to that moment, and known proxy dynamics, which can generate an underapproximation of the unknown system's true reachable set. An important benefit to the contributions of this paper is the lack of knowledge needed to execute the presented control method. We establish sufficient conditions to ensure that a controlled trajectory reaches a small neighborhood of any provably reachable state within a short time horizon, with precision dependent on the tunable parameters of these conditions

    Guaranteed Reachability on Riemannian Manifolds for Unknown Nonlinear Systems

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    Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the dynamics are unknown, so we calculate underapproximations of such sets using local dynamics at a single point and bounds on the rate of change of the dynamics determined from known physical laws. Motivated by scenarios where an adverse event causes an abrupt change in the dynamics, we attempt to determine a provably reachable set of states without knowledge of the dynamics. This paper considers systems which are known to operate on a manifold. Underapproximations are calculated by utilizing the aforementioned knowledge to derive a guaranteed set of velocities on the tangent bundle of a complete Riemannian manifold that can be reached within a finite time horizon. We then interpret said set as a control system; the trajectories of this control system provide us with a guaranteed set of reachable states the unknown system can reach within a given time. The results are general enough to apply on systems that operate on any complete Riemannian manifold. To illustrate the practical implementation of our results, we apply our algorithm to a model of a pendulum operating on a sphere and a three-dimensional rotational system which lives on the abstract set of special orthogonal matrices

    Comparison the Effects of Ephedrine and Lidocaine in Treatment of Intraoperative Hiccups in Gynecologic Surgery under Sedation

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    Background: This study aimed to evaluate and compare the therapeutic effects of ephedrine and lidocaine in treatment of intraoperative hiccups in gynecologic surgery under sedation. Materials and Methods: This randomized clinical trial in Isfahan was done on fifty female patients referring to Shahid Beheshti Hospital who needed to have sedation for medical interventions and they afflicted hiccups during surgery or sedation. Patients divided into two groups of 25 randomly assigned to one of the two groups of ephedrine or lidocaine. Ephedrine group received 5 mg/kg of medicine, while the lidocaine group was under treatment with 1 mg/kg lidocaine. Patients were monitored about systolic and diastolic blood pressure, MAP, heart rate, duration of hiccup, frequency of betterment, duration of intervention, and recovery at 15-min intervals of surgery and recovery. Results: Hiccups were resolved in 14 cases (56%) in the lidocaine group, while the improvement of such problem was achieved in 24 cases (96%) in ephedrine group (P < 0.001), so that the two groups did not have any significant difference in terms of the time of onset but the stop time of hiccups (relative to its start time) in the ephedrine group with the mean value of (2.40 ± 1.16) was significantly lower than the lidocaine group with the mean of 19.64 ± 22.76 min (P = 0.014). In addition, no complications were observed in the two groups. Conclusion: Ephedrine has been more successful than lidocaine as a stimulant in controlling hiccups, and it has been able to suppress hiccups in a higher percentage of patients at a shorter time
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