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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

Contraction Analysis of Hopfield Neural Networks with Hebbian Learning

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Contraction Analysis of Hopfield Neural Networks with Hebbia...

IEEE Conference on Decision and control

作者： Veronica Centorrino Francesco Bullo Giovanni Russo Scuola Superiore Meridionale University of Naples Federico II Italy Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa Barbara USA Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Motivated by advances in neuroscience and machine learning, this paper is concerned with the modeling and analysis of Hopfield neural networks with dynamic recurrent connections undergoing Hebbian learning. To capture the synaptic sparsity of neural circuits, we propose a low dimensional formulation for the model and then characterize its key dynamical properties. First, we give a biologically-inspired forward invariance result. Then, we give sufficient conditions for the non-Euclidean contractivity of the model. Our contraction analysis leads to stability and robustness of time-varying trajectories – for networks with both excitatory and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. Our proposed contractivity test is based upon biologically meaningful quantities, e.g., neural and synaptic decay rate, maximum out-degree, and the maximum synaptic strength. Finally, we show that the model satisfies Dale’s principle. The effectiveness of our results is illustrated via a numerical example.

关键词： Sufficient conditions Biological system modeling Hopfield neural networks Stability analysis Robustness Trajectory Integrated circuit modeling

Non-Euclidean Contraction Theory for Robust Nonlinear Stability

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arXiv 2021年

作者： Davydov, Alexander Jafarpour, Saber Bullo, Francesco The Department of Mechanical Engineering The Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to arbitrary norms, and characterize their properties. We introduce and study the sign and max pairings for the `1 and `∞ norms, respectively. Using weak pairings, we establish five equivalent characterizations for contraction, including the one-sided Lipschitz condition for the vector field as well as logarithmic norm and Demidovich conditions for the corresponding Jacobian. Third, we extend our contraction framework in two directions: we prove equivalences for contraction of continuous vector fields and we formalize the weaker notion of equilibrium contraction, which ensures exponential convergence to an equilibrium. Finally, as an application, we provide (i) incremental input-to-state stability and finite input-state gain properties for contracting systems, and (ii) a general theorem about the Lipschitz interconnection of contracting systems, whereby the Hurwitzness of a gain matrix implies the contractivity of the interconnected system. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems

Learning Robust Data-based LQG controllers from Noisy Data

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arXiv 2023年

作者： Liu, Wenjie Sun, Jian Wang, Gang Bullo, Francesco Chen, Jie The National Key Lab of Autonomous Intelligent Unmanned Systems School of Automation Beijing Institute of Technology Beijing100081 China The Beijing Institute of Technology Chongqing Innovation Center Chongqing401120 China The Mechanical Engineering Department The Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States The Department of Control Science and Engineering Tongji University Shanghai201804 China The National Key Lab of Autonomous Intelligent Unmanned Systems Beijing Institute of Technology Beijing100081 China

This paper addresses the joint state estimation and control problems for unknown linear time-invariant systems subject to both process and measurement noise. The aim is to redesign the linear quadratic Gaussian (LQG) controller based solely on data. The LQG controller comprises a linear quadratic regulator (LQR) and a steady-state Kalman observer;while the data-based LQR design problem has been previously studied, constructing the Kalman gain and the LQG controller from noisy data presents a novel challenge. In this work, a data-based formulation for computing the steady-state Kalman gain is proposed based on semi-definite programming (SDP) using some noise-free input-state-output data. Additionally, a data-based LQG controller is developed, which is shown to be equivalent to the model-based LQG controller. For cases where offline data are corrupted by noise, a robust data-based observer gain is constructed by tackling a relaxed SDP. The proposed controllers are proven to achieve robust global exponential stability (RGES) for state estimation and input-to-state practical stability (ISpS) under standard conditions. Finally, numerical tests are conducted to validate the proposed controllers' correctness and effectiveness. © 2023, CC BY.

关键词： Linear time-invariant system

Multistability and anomalies in oscillator models of lossy power grids

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arXiv 2022年

作者： Delabays, Robin Jafarpour, Saber Bullo, Francesco Center for Control Dynamical Systems and Computation Uc Santa Barbara Santa BarbaraCA93106-5070 United States School of Electrical and Computer Engineering Georgia Institute of Technology AtlantaGA30332-0250 United States

The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate a close correspondence between stable synchronous states in dissipatively coupled oscillators, and the winding partition of their state space, a geometric notion induced by the network topology. Leveraging this winding partition, we accompany this article with an algorithms to compute all synchronous solutions of complex networks of dissipatively coupled oscillators. These geometric and computational tools allow us to identify anomalous behaviors of lossy networked systems. Counterintuitively, we show that loop flows and dissipation can increase the system's transfer capacity, and that dissipation can promote multistability. We apply our geometric framework to compute power flows on the IEEE RTS-96 test system, where we identify two high voltage solutions with distinct loop flows. © 2022, CC BY.

关键词： Complex networks

Topological entropy of switched nonlinear and interconnected systems

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arXiv 2023年

作者： Yang, Guosong Liberzon, Daniel Hespanha, João P. The Department of Electrical and Computer Engineering Rutgers University PiscatawayNJ08854 United States The Coordinated Science Laboratory University of Illinois Urbana-Champaign UrbanaIL61801 United States The Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa BarbaraCA93106 United States

A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their active rates. A general lower bound is constructed as well, using a similar weighted average of lower limits of the traces of these Jacobian matrices. In a case of interconnected structure, the general upper bound is readily applied to derive upper bounds for entropy that depend only on "network-level" information. In a case of block-diagonal structure, less conservative upper and lower bounds for entropy are constructed. In each case, upper bounds for entropy that require less information about the switching signal are also derived. The upper bounds for entropy and their relations are illustrated by numerical examples of a switched Lotka–Volterra ecosystem *** Codes 37B40, 93C30 (Primary) 93C57 (Secondary) © 2023, CC BY-NC-ND.

关键词： Jacobian matrices

Non-Euclidean Monotone Operator Theory and Applications

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arXiv 2023年

作者： Davydov, Alexander Jafarpour, Saber Proskurnikov, Anton V. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa BarbaraCA93106-5070 United States Department of Electrical Computer and Energy Engineering University of Colorado BoulderCO80309-0020 United States Department of Electronics and Telecommunications Politecnico di Torino Turin10129 Italy

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as diagonally-weighted 1 or ∞ norms. This paper provides a natural generalization of monotone operator theory to finite-dimensional non-Euclidean spaces. The key tools are weak pairings and logarithmic norms. We show that the resolvent and reflected resolvent operators of non-Euclidean monotone mappings exhibit similar properties to their counterparts in Hilbert spaces. Furthermore, classical iterative methods and splitting methods for finding zeros of monotone operators are shown to converge in the non-Euclidean case. We apply our theory to equilibrium computation and Lipschitz constant estimation of recurrent neural networks, obtaining novel iterations and tighter upper bounds via forward-backward splitting. © 2023, CC BY.

关键词： Recurrent neural networks

Game Theory for Autonomy: From Min-Max Optimization to Equilibrium and Bounded Rationality Learning

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Game Theory for Autonomy: From Min-Max Optimization to Equil...

American control Conference (ACC)

作者： Kyriakos G. Vamvoudakis Filippos Fotiadis João P. Hespanha Raphael Chinchilla Guosong Yang Mushuang Liu Jeff S. Shamma Lacra Pavel Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta GA USA Center for Control Dynamical Systems and Computation University of California Santa Barbara CA Department of Electrical and Computer Engineering Rutgers University Piscataway NJ USA Department of Mechanical and Aerospace Engineering University of Missouri Columbia MO USA Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign IL USA Department of Electrical and Computer Engineering University of Toronto Canada

Finding Nash equilibria in non-cooperative games can be, in general, an exceptionally challenging task. This is owed to various factors, including but not limited to the cost functions of the game being nonconvex/nonconcave, the players of the game having limited information about one another, or even due to issues of computational complexity. The present tutorial draws motivation from this harsh reality and provides methods to approximate Nash or min-max equilibria in non-ideal settings using both optimization- and learning-based techniques. The tutorial acknowledges, however, that such techniques may not always converge, but instead lead to oscillations or even chaos. In that respect, tools from passivity and dissipativity theory are provided, which can offer explanations about these divergent behaviors. Finally, the tutorial highlights that, more frequently than often thought, the search for equilibrium policies is simply vain; instead, bounded rationality and non-equilibrium policies can be more realistic to employ owing to some players’ learning imperfectly or being relatively naive – "bounded rational." The efficacy of such plays is demonstrated in the context of autonomous driving systems, where it is explicitly shown that they can guarantee vehicle safety.

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Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks

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arXiv 2022年

作者： Davydov, Alexander Jafarpour, Saber Proskurnikov, Anton V. Bullo, Francesco The Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States The School of Electrical and Computer Engineering Georgia Institute of Technology United States The Department of Electronics and Telecommunications Politecnico di Torino Turin Italy

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces l1 and l∞. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms l1 or l∞. In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates. Copyright © 2022, The Authors. All rights reserved.

关键词： Recurrent neural networks