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The scenario approach meets uncertain variational inequalities and game theory

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arXiv 2019年

作者： Paccagnan, Dario Campi, Marco C. Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States Dipartimento di Ingegneria dell'Informazione Università di Brescia Italy

Variational inequalities are modelling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle stochastic optimization problems, take decisions based on historical data, and quantify their risk. The overarching goal of this manuscript is to bridge these two areas of research, and thus broaden the class of problems amenable to be studied under the lens of the scenario approach. First and foremost, we provide out-of-samples feasibility guarantees for the solution of variational and quasi variational inequality problems. Second, we apply these results to two classes of uncertain games. In the first class, the uncertainty enters in the constraint sets, while in the second class the uncertainty enters in the cost functions. Finally, we exemplify the quality and relevance of our bounds through numerical simulations on a demand-response model. Copyright © 2019, The Authors. All rights reserved.

关键词： Variational techniques

FULLY TRANSFORMER-BASED BIOMARKER PREDICTION FROM COLORECTAL CANCER HISTOLOGY: A LARGE-SCALE MULTICENTRIC STUDY

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arXiv 2023年

作者： Wagner, Sophia J. Reisenbüchler, Daniel West, Nicholas P. Niehues, Jan Moritz Veldhuizen, Gregory Patrick Quirke, Philip Grabsch, Heike I. van den Brandt, Piet A. Hutchins, Gordon G.A. Richman, Susan D. Yuan, Tanwei Langer, Rupert Jenniskens, Josien Christina Anna Offermans, Kelly Mueller, Wolfram Gray, Richard Gruber, Stephen B. Greenson, Joel K. Rennert, Gad Bonner, Joseph D. Schmolze, Daniel James, Jacqueline A. Loughrey, Maurice B. Salto-Tellez, Manuel Brenner, Hermann Hoffmeister, Michael Truhn, Daniel Schnabel, Julia A. Boxberg, Melanie Peng, Tingying Kather, Jakob Nikolas Helmholtz Munich German Research Center for Environment and Health Munich Germany School of Computation Information and Technology Technical University of Munich Munich Germany Technical University Dresden Dresden Germany Division of Pathology and Data Analytics Leeds Institute of Medical Research at St James’s University of Leeds Leeds United Kingdom Department of Pathology GROW School for Oncology and Developmental Biology Maastricht University Medical Center+ Maastricht Netherlands Department of Epidemiology Maastricht University Medical Center+ Maastricht Netherlands Heidelberg Germany Institute of Pathology und Molecular Pathology Johannes Kepler University Hospital Linz Linz Austria Gemeinschaftspraxis Pathologie Starnberg Germany Nuffield Department of Population Health University of Oxford Oxford United Kingdom Center for Precision Medicine Department of Medical Oncology City of Hope National Medical Center DuarteCA United States Department of Pathology City of Hope Comprehensive Cancer Center DuarteCA United States Department of Community Medicine & Epidemiology Lady Davis Carmel Medical Center Ruth & Bruce Rappaport Faculty of Medicine Technion-Israel Institute of Technology Israel Steve and Cindy Rasmussen Institute for Genomic Medicine Lady Davis Carmel Medical Center Technion Faculty of Medicine Clalit National Cancer Control Center Haifa Israel Precision Medicine Centre of Excellence Health Sciences Building The Patrick G Johnston Centre for Cancer Research Queen’s University Belfast Belfast United Kingdom Regional Molecular Diagnostic Service Belfast Health and Social Care Trust Belfast United Kingdom The Patrick G Johnston Centre for Cancer Research Queen’s University Belfast Belfast United Kingdom Department of Cellular Pathology Belfast Health and Social Care Trust Belfast United Kingdom Centre for Public Health Queen’s University Belfast Belfast United Kingdom Integrated Pathology Unit Institute for Cancer Research Royal Mars

Background: Deep learning (DL) can extract predictive and prognostic biomarkers from routine pathology slides in colorectal cancer. For example, a DL test for the diagnosis of microsatellite instability (MSI) in CRC has been approved in 2022. Current approaches rely on convolutional neural networks (CNNs). Transformer networks are outperforming CNNs and are replacing them in many applications, but have not been used for biomarker prediction in cancer at a large scale. In addition, most DL approaches have been trained on small patient cohorts, which limits their clinical utility. Methods: In this study, we developed a new fully transformer-based pipeline for end-to-end biomarker prediction from pathology slides. We combine a pre-trained transformer encoder and a transformer network for patch aggregation, capable of yielding single and multi-target prediction at patient level. We train our pipeline on over 9,000 patients from 10 colorectal cancer cohorts. Results: A fully transformer-based approach massively improves the performance, generalizability, data efficiency, and interpretability as compared with current state-of-the-art algorithms. After training on a large multicenter cohort, we achieve a sensitivity of 0.97 with a negative predictive value of 0.99 for MSI prediction on surgical resection specimens. We demonstrate for the first time that resection specimen-only training reaches clinical-grade performance on endoscopic biopsy tissue, solving a long-standing diagnostic problem. Interpretation: A fully transformer-based end-to-end pipeline trained on thousands of pathology slides yields clinical-grade performance for biomarker prediction on surgical resections and biopsies. Our new methods are freely available under an open source license. © 2023, CC BY.

关键词： Forecasting

Performance–guaranteed consensus control inspired by the mammalian limbic system for a class of nonlinear multi-agents ⁎

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IFAC-PapersOnLine 2020年第2期53卷 9496-9501页

作者： Ignacio Rubio Scola Luis Rodolfo Garcia Carrillo João P. Hespanha Rogelio Lozano CIFASIS (CONICET-UNR) and Department of Mathematics National University of Rosario Rosario 2000 Argentina. Unmanned Systems Laboratory. School of Engineering and Computer Sciences Texas A&M University - Corpus Christi TexasUSA. 78412-5797. Center for Control Dynamical Systems and ComputationUniversity of California Santa Barbara CA 93106 USA. Heuristique et Diagnostic des Systemes Complexes Universit é de Technologie de Compiègne UMR CNRS 7253 60200 CompiegneFrance

computational models of emotional learning observed in the mammalian brain have inspired diverse self-learning control approaches. These architectures are promising in terms of their fast learning ability and low computational cost. In this paper, the objective is to establish performance–guaranteed emotional learning–inspired control (ELIC) strategies for autonomous multi–agent systems (MAS), where each agent incorporates an ELIC structure to support the consensus controller. The objective of each ELIC structure is to identify and compensate model differences between the theoretical assumptions taken into account when tuning the consensus protocol, and the real conditions encountered in the real system to be stabilized. Stability of the closed-loop MAS is demonstrated using a Lyapunov analysis. Simulation results based on the consensus task of a group of inverted pendulums demonstrate the effectiveness of the proposed ELIC for stabilization of nonlinear MAS.

关键词： Multi-agents systems Biologically-inspired control Robust control Distributed control Nonlinear control

Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems

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Learning Deep Neural Network Representations for Koopman Ope...

American control Conference

作者： Enoch Yeung Soumya Kundu Nathan Hodas Biomolecular Science and Engineering Graduate Program Center for Dynamical Systems Control and Computation University of California Santa Barbara Energy and Environment Directorate Pacific Northwest National Laboratory National Security Directorate Pacific Northwest National Laboratory

ISBN: (纸本)9781538679012;9781538679265

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition;this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a computational framework for learning Koopman operators of nonlinear dynamical systems using deep learning. We show that this novel method automatically selects efficient deep dictionaries, requiring much lower dimensional dictionaries while outperforming state-of-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict on test data quantitatively 100 steps into the future, using only a single timepoint as an initial condition, and quantitative oscillatory behavior 400 steps into the future.

关键词： Nonlinear dynamical systems Dictionaries as Topic DYNAMICAL SYSTEMS System analyses INITIAL CONDITIONS Hydrodynamics complexity classes Learning

Small-signal stability of grid-tied inverter networks

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arXiv 2019年

作者： Jafarpour, Saber Purba, Victor Dhople, Sairaj V. Johnson, Brian Bullo, Francesco Department of Mechanical Engineering Center of Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States Department of Electrical and Computer Engineering University of Minnesota MinneapolisMN55414 United States Department of Electrical Engineering University of Washington SeattleWA98195 United States

This paper considers the small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We identify a suitable time-scale decomposition for the inverter dynamics and, using singular perturbation theory, we obtain an analytic sufficient condition for the small-signal stability of the network. In contrast to the alternative of performing an eigenvalue analysis of the full-order network dynamics, our analytic sufficient condition has the benefit of reducing computational complexity and yielding insights on the role of network topology and constitution as well as inverter filter and control parameters on small-signal stability. Our numerical analysis for an inverter network with radial topology validates the approach and illustrates the efficiency of our analytic conditions for designing/monitoring grid-tied inverter networks. Copyright © 2019, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Convergence Properties of the Heterogeneous Deffuant-Weisbuch Model

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arXiv 2019年

作者： Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco National Center for Mathematics and Interdisciplinary Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing100083 China Automatic Control Laboratory ETH Zurich8092 Switzerland Department of Mechanical Engineering The Center of Control Dynamical-Systems and Computation University of California Santa BarbaraCA93106-5070 United States

The Deffuant-Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence properties, easy to observe numerically, are only conjectures. This paper solves the convergence problem for the heterogeneous DW model with the weighting factor not less than 1/2. We establish that, for any positive confidence bounds and initial values, the opinion of each agent will converge to a limit value almost surely, and the convergence rate is exponential in mean square. Moreover, we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents. Finally, we provide some sufficient conditions for the heterogeneous DW model to reach *** Codes 93E03, 93A30, 91D30 Copyright © 2019, The Authors. All rights reserved.

关键词： Economic and social effects

Robotic surveillance based on the meeting time of random walks

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arXiv 2019年

作者： Duan, Xiaoming George, Mishel Patel, Rushabh Bullo, Francesco Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States DoorDash San FranciscoCA United States Systems Technology Inc. HawthorneCA United States

This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate optimization problems and design robotic strategies. First, by analyzing multiple random walks on a common graph as a single random walk on the Kronecker product graph, we provide the first closed-form expression for the expected meeting time in terms of the transition matrices of the moving agents. This novel expression leads to necessary and sufficient conditions for the meeting time to be finite and to insightful graph-theoretic interpretations. Second, based on the closed-form expression, we setup and study the minimization problem for the expected capture time for a pursuer/evader pair. We report theoretical and numerical results on basic case studies to show the effectiveness of the design. Copyright © 2019, The Authors. All rights reserved.

关键词： Random processes

Synchronization of Kuramoto oscillators: Inverse Taylor expansions

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arXiv 2018年

作者： Jafarpour, Saber Huang, Elizabeth Y. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara United States Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with arbitrary topology and heterogeneous edge weights. We propose a novel equivalent transcription for the equilibrium synchronization equation. Using this transcription, we develop a power series expansion to compute the synchronized solution of the Kuramoto model as well as a sufficient condition for the strong convergence of this series expansion. Truncating the power series provides (i) an efficient approximation scheme for computing the synchronized solution, and (ii) a simple-to-check, statistically-correct hierarchy of increasingly accurate synchronization tests. This hierarchy of tests provides a theoretical foundation for and generalizes the best-known approximate synchronization test in the literature. Our numerical experiments illustrate the accuracy and the computational efficiency of the truncated series approximation compared to existing iterative methods and existing synchronization tests. Copyright © 2018, The Authors. All rights reserved.

关键词： Synchronization

Analysis and design of quadratically bounded QPV control systems ⁎

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IFAC-PapersOnLine 2019年第28期52卷 76-81页

作者： Damiano Rotondo Marcin Witczak Institut de Robòtica i Informàtica Industrial CSIC-UPC Carrer de Llorens i Artigas 4-6 08028 Barcelona Spain Research Center for Supervision Safety and Automatic Control UPC Rambla Sant Nebridi s/n 08022 Terrassa Spain Institute of Control and Computation Engineering Univ. of Zielona Gora ul. Podgorna 50 65-246 Zielona Gora Poland

A nonlinear system is said to be quadratically bounded (QB) if all its solutions are bounded and this is guaranteed using a quadratic Lyapunov function. This paper considers the QB analysis and state-feedback controller design problems for quadratic parameter varying (QPV) systems. The developed approach, which relies on a linear matrix inequality (LMIs) feasibility problem, ensures that the QB property holds for an invariant ellipsoid which contains a predefined polytopic region of the state space. An example is used to illustrate the main characteristics of the proposed approach and to confirm the validity of the theoretical results.

关键词： Quadratic boundedness quadratic systems gain-scheduling linear matrix inequalities