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arXiv 2022年

作者： Davydov, Alexander Jafarpour, Saber Abate, Matthew Bullo, Francesco Coogan, Samuel The Center for Control Dynamical Systems and Computation University of California Santa Barbara United States The School of Electrical and Computer Engineering Georgia Institute of Technology United States

We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable benefits over traditional deep neural networks. We first establish that tight inclusion functions of neural networks, which provide the tightest rectangular over-approximation of an input-output map, lead to sharper robustness guarantees than the well-studied robustness measures of local Lipschitz constants. Like Lipschitz constants, tight inclusions functions are computationally challenging to obtain, and we thus propose using mixed monotonicity and contraction theory to obtain computationally efficient estimates of tight inclusion functions for INNs. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs. We design a novel optimization problem for training robust INNs and we provide empirical evidence that suitably-trained INNs can be more robust than comparably-trained feedforward networks. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep neural networks

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Synchronization of Switched Complex Dynamical Networks with Impulses: State-Dependent Switching Approach

SSRN

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SSRN 2023年

作者： Yang, Dan Li, Xiaodi Song, Shiji School of Mathematics and Statistics Shandong Normal University Jinan250014 China Center for Control and Engineering Computation Shandong Normal University Jinan250014 China Shandong Normal University China

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method. © 2023, The Authors. All rights reserved.

关键词： Synchronization

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Diversity and Suitability of the State-of-the-Art Wearable and Wireless EEG Systems Review

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IEEE Journal of Biomedical and Health Informatics 2023年第8期27卷 3830-3843页

作者： He, Congying Chen, Yu-Yi Phang, Chun-Ren Stevenson, Cory Chen, I-Ping Jung, Tzyy-Ping Ko, Li-Wei Institute of Bioinformatics and Systems Biology National Yang Ming Chiao Tung University Hsinchu30010 Taiwan Institute of Applied Arts National Yang Ming Chiao Tung University Hsinchu30010 Taiwan International Ph.D. Program in Interdisciplinary Neuroscience National Yang Ming Chiao Tung University Hsinchu30010 Taiwan Institute for Neural Computation and Institute of Engineering in Medicine University of California San DiegoCA90093 United States National Yang Ming Chiao Tung University Hsinchu30010 Taiwan Institute of Electrical and Control Engineering Department of Electronics and Electrical Engineering Department of Biological Science and Technology National Yang Ming Chiao Tung University Hsinchu30010 Taiwan Department of Biomedical Science and Environment Biology Drug Development and Value Creation Research Center Kaohsiung Medical University Kaohsiung80708 Taiwan

Wireless electroencephalography (EEG) systems have been attracting increasing attention in recent times. Both the number of articles discussing wireless EEG and their proportion relative to general EEG publications have increased over years. These trends indicate that wireless EEG systems could be more accessible to researchers and the research community has recognized the potential of wireless EEG systems. To explore the development and diverse applications of wireless EEG systems, this review highlights the trends in wearable and wireless EEG systems over the past decade and compares the specifications and research applications of the major wireless systems marketed by 16 companies. For each product, five parameters (number of channels, sampling rate, cost, battery life, and resolution) were assessed for comparison. Currently, these wearable and portable wireless EEG systems have three main application areas: consumer, clinical, and research. To address this multitude of options, the article also discussed the thought process to find a suitable device that meets personalization and use cases specificities. These investigations suggest that low-price and convenience are key factors for consumer applications, wireless EEG systems with FDA or CE-certification may be more suitable for clinical settings, and devices that provide raw EEG data with high-density channels are important for laboratory research. This article presents an overview of the current state of the wireless EEG systems specifications and possible applications and serves as a guide point as it is expected that more influential and novel research will cyclically promote the development of such EEG systems. © 2023 IEEE.

关键词： Electroencephalography

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State Estimation for Asynchronously Switched Sampled-Data Systems

State Estimation for Asynchronously Switched Sampled-Data Sy...

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IEEE Conference on Decision and control

作者： Sharad C. Shankar Guosong Yang João P. Hespanha Center for Control Dynamical Systems and Computation University of California Santa Barbara CA USA Department of Electrical and Computer Engineering Rutgers University–New Brunswick Piscataway NJ USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Asynchronously switched sampled-data systems can help model power systems and vehicles that evolve in continuous-time with switching behavior and discrete time measurements. We address the problem of jointly estimating a switching signal, with uncertainty in the exact switching times, as well as the continuous states of the system. We prove stability of the standard Kalman Filter under uncertainty in the switching times, with statistical bounds relating to the sampling period. We then propose a method for estimation of switching times as well as a method for efficient joint estimation of the state and switching signal inspired by the interacting multiple-model extended-Viterbi algorithm. We validate our algorithms in simulation for a power converter and a maneuvering vehicle.

关键词： Uncertainty Heuristic algorithms Power system dynamics Switches Power system stability Filtering algorithms Sampled data systems

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Data-Driven Distributionally Robust Coverage control by Mobile Robots

Data-Driven Distributionally Robust Coverage Control by Mobi...

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IEEE Conference on Decision and control

作者： Dimitris Boskos Jorge Cortes Sonia Martinez Delft Center for Systems and Control TU Delft Department of Mechanical and Aerospace Engineering University of California San Diego

This paper provides a data-driven solution to the problem of coverage control by which a team of robots aims to optimally deploy in a spatial region where certain event of interest may occur. This event is random and described by a probability density function, which is unknown and can only be learned by collecting data. In this work, we hedge against this uncertainty by designing a distributionally robust algorithm that optimizes the locations of the robots against the worst-case probability density from an ambiguity set. This ambiguity set is constructed from data initially collected by the agents, and contains the true density function with prescribed confidence. However, the objective function that the robots seek to minimize is non-smooth. To address this issue, we employ the so-called gradient sampling algorithm, which approximates the Clarke generalized gradient by sampling the derivative of the objective function at nearby locations and stabilizes the choice of descent directions around points where the function may fail to be differentiable. This enables us to prove that the algorithm converges to a stationary point from any initial location of the robots, in analogy to the well-known Lloyd algorithm for differentiable costs when the spatial density is known.

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Hierarchical Event-Triggered Systems: Safe Learning of Quasi-Optimal Deadline Policies

Hierarchical Event-Triggered Systems: Safe Learning of Quasi...

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IEEE Conference on Decision and control

作者： Pio Ong Manuel Mazo Aaron D. Ames Department of Mechanical and Civil Engineering California Institute of Technology Pasadena CA USA Delft Center for Systems and Control Faculty of Mechanical Engineering Delft University of Technology The Netherlands

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

We present a hierarchical architecture to improve the efficiency of event-triggered control (ETC) in reducing resource consumption. This paper considers event-triggered systems generally as an impulsive control system in which the objective is to minimize the number of impulses. Our architecture recognizes that traditional ETC is a greedy strategy towards optimizing average inter-event times and introduces the idea of a deadline policy for the optimization of long-term discounted inter-event times. A lower layer is designed employing event-triggered control to guarantee the satisfaction of control objectives, while a higher layer implements a deadline policy designed with reinforcement learning to improve the discounted inter-event time. We apply this scheme to the control of an orbiting spacecraft, showing superior performance in terms of actuation frequency reduction with respect to a standard (one-layer) ETC while maintaining safety guarantees.

关键词： Space vehicles Event detection Transfer learning Optimal control Stochastic processes Reinforcement learning Trajectory Safety Optimization Standards

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Multidimensional Opinion Dynamics with Heterogeneous Bounded Confidences and Random Interactions

arXiv

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arXiv 2024年

作者： Cheng, Jiangjiang Chen, Ge Mei, Wenjun Bullo, Francesco School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mechanics and Engineering Science Peking University Beijing100871 China Department of Mechanical Engineering The Center of Control Dynamical-Systems and Computation University of California Santa BarbaraCA93106-5070 United States

This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other’s opinions with a specific probability. This revised model is motivated by the observation that the standard Hegselmann-Krause (HK) dynamics requires unrealistic all-to-all interactions at certain configurations. For this randomized BC opinion dynamics, regardless of initial opinions and positive confidence bounds, we show that the agents’ states converge to fixed final opinions in finite time almost surely and that the convergence rate follows a negative exponential distribution in mean square. Furthermore, we establish sufficient conditions for the heterogeneous BC opinion dynamics with random interactions to achieve consensus in finite time. Copyright © 2024, The Authors. All rights reserved.

关键词： Random processes

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Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach

arXiv

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arXiv 2022年

作者： Jafarpour, Saber Davydov, Alexander Abate, Matthew Bullo, Francesco Coogan, Samuel School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta United States Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural network as a reachability problem and use (i) the `∞-norm input-output Lipschitz constant and (ii) the tight inclusion function of the network to over-approximate its reachable sets. First, for a given implicit neural network, we use `∞-matrix measures to propose sufficient conditions for its well-posedness, design an iterative algorithm to compute its fixed points, and provide upper bounds for its `∞-norm input-output Lipschitz constant. Second, we introduce a related embedded network and show that the embedded network can be used to provide an `∞-norm box over-approximation of the reachable sets of the original network. Moreover, we use the embedded network to design an iterative algorithm for computing the upper bounds of the original system’s tight inclusion function. Third, we use the upper bounds of the Lipschitz constants and the upper bounds of the tight inclusion functions to design two algorithms for the training and robustness verification of implicit neural networks. Finally, we apply our algorithms to train implicit neural networks on the MNIST dataset and compare the robustness of our models with the models trained via existing approaches in the literature. Copyright © 2022, The Authors. All rights reserved.

关键词： Iterative methods

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Probing Rotational Decoherence with a Trapped-Ion Planar Rotor

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Physical Review Letters 2025年第3期134卷 033601-033601页

作者： Neil Glikin Benjamin A. Stickler Ryan Tollefsen Sara Mouradian Neha Yadav Erik Urban Klaus Hornberger Hartmut Häffner Department of Physics University of California Berkeley Berkeley California 94720 USA Challenge Institute for Quantum Computation University of California Berkeley Berkeley California 94720 USA Institute for Complex Quantum Systems and Center for Integrated Quantum Science and Technology Ulm University Albert-Einstein-Allee 11 89069 Ulm Germany Department of Electrical and Computer Engineering University of Washington Seattle Washington 98195 USA Present address: Exponent Inc. Electrical Engineering and Computer Science Practice Warrenville Illinois USA. University of Duisburg-Essen Faculty of Physics Lotharstraße 1 47057 Duisburg Germany

The quantum rotor is one of the simplest model systems in quantum mechanics, but only in recent years has theoretical work revealed general fundamental scaling laws for its decoherence. For example, a superposition of orientations decoheres at a rate proportional to the sine squared of the angle between them. Here, we observe scaling laws for rotational decoherence dynamics for the first time, using a 4 μm diameter planar rotor composed of two Paul-trapped ions. We prepare the rotational motion of the ion crystal into superpositions of angular momentum with well-defined differences ranging from 1−3ℏ, and measure the rate of decoherence. We also tune the system-environment interaction strength by introducing resonant electric field noise. The observed scaling relationships for decoherence are in excellent agreement with recent theoretical work, and are directly relevant to the growing development of rotor-based quantum applications.

关键词： Trapped ions

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Using EEG Signals to Assess Workload during Memory Retrieval in a Real-world Scenario

arXiv

引用

arXiv 2023年

作者： Chiang, Kuan-Jung Dong, Steven Cheng, Chung-Kuan Jung, Tzyy-Ping Department of Computer Science and Engineering University of California San Diego United States Human Factors Center of Excellence Microsoft Corporation United States Institute for Neural Computation Institute of Engineering in Medicine University of California San Diego United States

Objective: The Electroencephalogram (EEG) is gaining popularity as a physiological measure for neuroergonomics in human factor studies because it is objective, less prone to bias, and capable of assessing the dynamics of cognitive states. This study investigated the associations between memory workload and EEG during participants’ typical office tasks on a single-monitor and dual-monitor arrangement. We expect a higher memory workload for the single-monitor arrangement. Approach: We designed an experiment that mimics the scenario of a subject performing some office work and examined whether the subjects experienced various levels of memory workload in two different office setups: 1) a single-monitor setup and 2) a dual-monitor setup. We used EEG band power, mutual information, and coherence as features to train machine learning models to classify high versus low memory workload states. Main results: The study results showed that these characteristics exhibited significant differences that were consistent across all participants. We also verified the robustness and consistency of these EEG signatures in a different data set collected during a Sternberg task in a prior study. Significance: The study found the EEG correlates of memory workload across individuals, demonstrating the effectiveness of using EEG analysis in conducting real-world neuroergonomic studies. © 2023, CC BY-NC-ND.

关键词： Electroencephalography

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