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Euclidean Contractivity of Neural Networks with Symmetric Weights

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arXiv 2023年

作者： Centorrino, Veronica Gokhale, Anand Davydov, Alexander Russo, Giovanni Bullo, Francesco Scuola Superiore Meridionale University of Naples Federico II Italy Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of symmetric matrices. Then, we give sufficient conditions for strong and weak Euclidean contractivity, i.e., contractivity with respect to the 2 norm, of both models with symmetric weights and (possibly) non-smooth activation functions. Our contraction analysis leads to contraction rates which are log-optimal in almost all symmetric synaptic matrices. Finally, we use our results to propose a firing-rate neural network model to solve a quadratic optimization problem with box constraints. © 2023, CC BY.

关键词： Matrix algebra

ONLINE FEEDBACK OPTIMIZATION AND SINGULAR PERTURBATION VIA CONTRACTION THEORY∗

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arXiv 2023年

作者： Cothren, Liliaokeawawa Bullo, Francesco Dall’Anese, Emiliano Department of Electrical Computer and Energy Engineering University of Colorado Boulder BoulderCO United States Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93101 United States Department of Electrical and Computer Engineering Boston University BostonMA02215 United States

In this paper, we provide a novel contraction-theoretic approach to analyze two-time scale systems, including those commonly encountered in Online Feedback Optimization (OFO). Our framework endows these systems with several robustness properties, enabling a more comprehensive characterization of their behaviors. The primary assumptions are the contractivity of the fast subsystem and the reduced model, along with an explicit upper bound on the time-scale parameter. For two-time scale systems subject to disturbances, we show that the distance between solutions of the nominal system and solutions of its reduced model is uniformly upper bounded by a function of contraction rates, Lipschitz constants, the time-scale parameter, and the variability of the disturbances over time. Applying these general results to the OFO context, we establish new individual tracking error bounds, showing that solutions converge to their time-varying optimizer, provided the plant and steady-state feedback controller exhibit contractivity and the controller gain is suitably bounded. Finally, we explore two special cases: for autonomous nonlinear systems, we derive sharper bounds than those in the general results, and for linear time-invariant systems, we present novel bounds based on induced matrix norms and induced matrix log norms. Copyright © 2023, The Authors. All rights reserved.

关键词： State feedback

Modeling and Contractivity of Neural-Synaptic Networks with Hebbian Learning

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arXiv 2022年

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

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian learning rules. To capture the synaptic sparsity of neural circuits we propose a low dimensional formulation. We then characterize certain key dynamical properties. First, we give biologically-inspired forward invariance results. Then, we give sufficient conditions for the non-Euclidean contractivity of the models. 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. For each model, we propose a contractivity test based upon biologically meaningful quantities, e.g., neural and synaptic decay rate, maximum in-degree, and the maximum synaptic strength. Then, we show that the models satisfy Dale's Principle. Finally, we illustrate the effectiveness of our results via a numerical example. Copyright © 2022, The Authors. All rights reserved.

关键词： Hopfield neural networks

Electroencephalogram and Event-Related Potential in Mild Cognitive Impairment: Recent Developments in Signal Processing, Machine Learning, and Deep Learning

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IEEE Journal of Selected Areas in Sensors

IEEE Journal of Selected Areas in Sensors 2025年 2卷 162-184页

作者： Azami, Hamed Mirjalili, Mina Rajji, Tarek K. Wu, Chien-Te Humeau-Heurtier, Anne Jung, Tzyy-Ping Wei, Chun-Shu Trinh, Thanh-Tung Liu, Yi-Hung University of Toronto Centre for Addiction and Mental Health TorontoONM5S 1A1 Canada University of Texas Southwestern Medical Center DallasTX75390 United States University of Florida Department of Occupational Therapy GainesvilleFL32611 United States University of Florida Center for Cognitive Aging and Memory McKnight Brain Institute GainesvilleFL32611 United States University of Angers LARIS SFR MATHSTIC AngersF-49000 France University of California Institute for Neural Computation Institute of Engineering in Medicine La Jolla CA92093 United States National Yang Ming Chiao Tung University Department of Computer Science Hsinchu City30010 Taiwan National Taipei University of Technology Graduate Institute of Manufacturing Technology College of Mechanical and Electrical Engineering Taipei10608 Taiwan Vietnam National University Department of Information and Communication Technology Faculty of Nontraditional Security HSB Hanoi720325 Viet Nam National Yang Ming Chiao Tung University Institute of Electrical and Control Engineering Hsinchu City30010 Taiwan

Mild cognitive impairment (MCI) is an early stage of non-age-related cognitive decline with an increased risk of progressing to dementia. Early detection of MCI is essential for implementing preventative strategies that can delay or prevent the onset of dementia, ultimately improving patient outcomes and reducing healthcare costs. Electroencephalograms (EEGs) and event-related potentials (ERPs) have shown significant promise in detecting MCI due to their affordability, real-time monitoring capabilities, and noninvasiveness. EEG provides continuous brain activity data, while ERPs offer insights into specific cognitive processes by analyzing brain responses to stimuli. These methods can complement each other in MCI diagnosis by providing a comprehensive view of overall brain function and detailed information on specific cognitive processes. However, EEG and ERP are susceptible to noise and interindividual variability, which can hinder their reliability. In addition, applying machine learning models on EEG or ERP for MCI detection presents challenges such as the risk of overfitting and difficulties in interpreting the underlying decision-making process. This review emphasizes recent advancements in signal processing and feature extraction methods applied to EEG and ERP data and explores the use of machine learning and deep learning techniques to enhance diagnostic accuracy and interpretative depth. By integrating these methodologies, the review highlights how EEG and ERP can contribute to a more effective understanding and monitoring of cognitive changes associated with MCI, underscoring the importance of early diagnosis for timely intervention and improved patient care. Finally, the review focuses on future research directions, including the development of advanced analytical techniques and multimodal integration approaches involving EEG and ERP to further improve diagnostic accuracy and clinical application. © 2024 IEEE.

关键词： Deep learning

Design and experimental implementation of multi-loop LQR, PID, and LQG controllers for the trajectory tracking control of twin rotor MIMO system 3rd

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Design and experimental implementation of multi-loop LQR, PI...

3rd International Conference on Intelligent Communication, control and Devices, ICICCD 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Ayush Dharavath, Abhiraj Department of Electrical Engineering Incubation Center for Control Dynamical Systems and Computation Delhi Technological University New DelhiDelhi110042 India

ISBN: (纸本)9789811386176

One DOF (degree of freedom) Twin Rotor multi-input multi-output system (TRMS) is one of the benchmarked dynamical systems which has striking comparability with Helicopter. Design of controllers for such complex air vehicle is a daunting task as it has inherent nonlinearities and cross-coupling between its main and tail rotors. Therefore, it is an interesting laboratory benchmarked control problem, to test the performance of various controllers. The control techniques focused in this paper are the experimental implementation of multi-loop controllers such as Linear Quadratic Regulator (LQR), linear proportional integral derivative (L-PID), and Linear Quadratic Gaussian (LQG) controllers on TRMS system to verify the performance of these controllers. © Springer Nature Singapore Pte Ltd. 2020.

关键词： controllers

Experimental validation of fully informed particle swarm optimization tuned multi-loop L-PID controllers for stabilization of gantry crane system 3rd

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Experimental validation of fully informed particle swarm opt...

3rd International Conference on Intelligent Communication, control and Devices, ICICCD 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Dobhal, Daksh Kartikeya, Kumar Kaur, Manpreet Goel, Arnav Department of Electrical Engineering Incubation Center for Control Dynamical Systems and Computation Delhi Technological University New DelhiDelhi110042 India

ISBN: (纸本)9789811386176

Linear PID controllers are commonly used as an electrical component to decrease the error between anticipated set value and actual measured values for control of various benchmarked systems. The Multi-Loop Linear PID (ML-PID) controller, gives a robust and efficient performance in most of the situations. This paper presents the implementation of linear PID controller to stabilize and control the Gantry Crane System. Optimal performance is obtained for a few specific combinations of the proportional, integral, and derivative gains, which makes it essential to tune these values through Optimization techniques. The Fully Informed Particle Swarm Optimizer (FIPSO) is used to tune the gain values of the ML-PID controlled Gantry Crane System. These values are validated experimentally, and obtained results prove that the FIPSO tuned multi-loop linear PID controller quickly stabilizes the system subjected to external disturbances. © Springer Nature Singapore Pte Ltd. 2020.

关键词： controllers

Newton and interior-point methods for (constrained) nonconvex-nonconcave minmax optimization with stability and instability guarantees

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arXiv 2022年

作者： Chinchilla, Raphael Yang, Guosong Hespanha, João P. Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States Department of Electrical and Computer Engineering Rutgers University New BrunswickNJ08854 United States

We address the problem of finding a local solution to a nonconvex-nonconcave minmax optimization using Newton type methods, including primal-dual interior-point ones. The first step in our approach is to analyze the local convergence properties of Newton’s method in nonconvex minimization. It is well established that Newton’s method iterations are attracted to any point with a zero gradient, irrespective of it being a local minimum. From a dynamical system standpoint, this occurs because every point for which the gradient is zero is a locally asymptotically stable equilibrium point. We show that by adding a multiple of the identity such that the Hessian matrix is always positive definite, we can ensure that every non-local-minimum equilibrium point becomes unstable (meaning that the iterations are no longer attracted to such points), while local minima remain locally asymptotically stable. Building on this foundation, we develop Newton-type algorithms for minmax optimization, conceptualized as a sequence of local quadratic approximations for the minmax problem. Using a local quadratic approximation serves as a surrogate for guiding the modified Newton’s method towards a solution. For these local quadratic approximations to be well-defined, it is necessary to modify the Hessian matrix by adding a diagonal matrix. We demonstrate that, for an appropriate choice of this diagonal matrix, we can guarantee the instability of every non-local-minmax equilibrium point while maintaining stability for local minmax points. Using numerical examples, we illustrate the importance of guaranteeing the instability property. While our results are about local convergence, the numerical examples also indicate that our algorithm enjoys good global convergence properties. © 2022, CC BY.

关键词： Stability

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

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Non-Euclidean Monotone Operator Theory with Applications to ...

IEEE Conference on Decision and control

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

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces ℓ 1 and ℓ ∞ . We first establish properties of mappings which are monotone with respect to the non-Euclidean norms ℓ 1 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.

关键词： Casting Analytical models Recurrent neural networks Machine learning Aerospace electronics control systems Robustness

Extending dynamic mode decomposition to data from multiple outputs

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arXiv 2021年

作者： Boddupalli, Nibodh Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA United States

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system. Estimation of these spectral objects has become widely accessible with the numerous algorithms developed in recent years. We show how one such algorithm – extended dynamic mode decomposition – can be used on data from multiple outputs of a system. These outputs that are functions of state are called observables in the literature and could be known outputs like the state itself or unknown outputs like data from sensors used in systems of biological interest. To this end, we approximate the desired observables and their iterates in time using minimizers of regularized least-squares problems which have analytic solutions with heuristic provisions for expected estimates. © 2021, CC BY-SA.

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