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Geometric convergence of distributed gradient play in games with unconstrained action sets

IFAC-PapersOnLine 2020年第2期53卷 3367-3372页

作者： Tatiana Tatarenko Angelia Nedić Control Methods and Robotics Lab TU Darmstadt Germany School of Electrical Computer and Energy Engineering Arizona State University USA

We provide a distributed algorithm to learn a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings and unconstrained action sets. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. We consider a distributed communication-based gradient algorithm. For this procedure, we prove geometric convergence to a Nash equilibrium. In contrast to our previous works Tatarenko et al. (2018); Tatarenko et al. (2019), where the proposed algorithms required two parameters to be set up and the analysis was based on a so called augmented game mapping, the procedure in this work corresponds to a standard distributed gradient play and, thus, only one constant step size parameter needs to be chosen appropriately to guarantee fast convergence to a game solution. Moreover, we provide a rigorous comparison between the convergence rate of the proposed distributed gradient play and the rate of the GRANE algorithm presented in Tatarenko et al. (2019). It allows us to demonstrate that the distributed gradient play outperforms the GRANE in terms of convergence speed.

关键词： Game theory networked systems fast algorithms

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PARODIS: One MPC framework to control them all. Almost.

PARODIS: One MPC framework to control them all. Almost.

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control Technology and Applications (CCTA),

作者： Thomas Schmitt Jens Engel Matthias Hoffmann Tobias Rodemann Control Methods & Robotics Lab Technical University of Darmstadt Darmstadt Germany. Honda Research Institute Europe GmbH Offenbach Germany Systems Modeling and Simulation Systems Engineering Saarland University Germany

ISBN: (纸本)9781665436441

We introduce the MATLAB framework PARODIS, the Pareto optimal Model Predictive control framework for distributed Systems. It is a general-purpose, flexible and easy-to-use framework for discrete state space models. Special features are the support of distributed (hierarchical) systems, scenario-based optimization and built-in methods for determination of the Pareto front and selection of a solution. It uses the popular MATLAB framework YALMIP for the symbolic formulation of optimization problems and models.

关键词： Adaptation models Object oriented modeling Conferences Hierarchical systems Pareto optimization Mathematical models Optimization

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Gradient-tracking over directed graphs for solving leaderless multi-cluster games

arXiv

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arXiv 2021年

作者： Zimmermann, Jan Tatarenko, Tatiana Willert, Volker Adamy, Jürgen Control Methods and Robotics Lab Department of Electrical Engineering and Information Science Technical University of Darmstadt Darmstadt64283 Germany Faculty of Electrical Engineering University of Applied Sciences Würzburg-Schweinfurt Schweinfurt97421 Germany

We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to be virtual players that compete against each other in a non-cooperative game with respect to a coupled cost function. In such scenarios, the inner-cluster problem and the game between the clusters need to be solved simultaneously. Therefore, the resulting inter-cluster Nash Equilibrium should also be a minimizer of the social welfare problem inside the clusters. In this work, this setup is cast as a distributed optimization problem with sparse state information. Hence, critical information, such as the agent’s cost functions, remain private. We present a distributed algorithm that converges with a linear rate to the optimal solution. Furthermore, we apply our algorithm to an extended cournot game to verify our theoretical results. © 2021, CC BY.

关键词： Game theory

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Application of Pareto Optimization in an Economic Model Predictive controlled Microgrid

Application of Pareto Optimization in an Economic Model Pred...

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Mediterranean Conference on control and Automation (MED)

作者： Thomas Schmitt Jens Engel Tobias Rodemann Jürgen Adamy Honda Research Institute Europe GmbH Offenbach Germany Control Methods & Robotics Lab TU Darmstadt Darmstadt Germany

ISBN: (数字)9781728157429

ISBN: (纸本)9781728157436

This paper presents an economic model predictive control approach for a linear microgrid model. The microgrid in grid-connected mode represents a medium-sized company building including storage systems, renewable energies and couplings between the electrical and heat energy system. Economic model predictive control together with Pareto optimization is applied to find suitable compromises between two competing objectives, i.e. monetary costs and thermal comfort. Using realworld data from 2018 and 2019, the model is simulated with auto-detection of the Pareto solution which is closest to the Utopia point. The results show that the Pareto optimization can either be used in real-time control of the microgrid, or to obtain suitable weights from long term simulations. Both approaches result in significant cost reductions.

关键词： Microgrids Buildings Cogeneration Pareto optimization Economics Predictive control

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Domain mixture: An overlooked scenario in domain adaptation 18

Domain mixture: An overlooked scenario in domain adaptation

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18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019

作者： Schrom, Sebastian Hasler, Stephan Control Methods and Robotics Lab Tu Darmstadt Darmstadt Germany Honda Research Institute GmbH Offenbach/Main Germany

ISBN: (纸本)9781728145495

An image based object classification system trained on one domain usually shows decreased performance for other domains if data distributions differ significantly. There exist various domain adaptation approaches that improve generalization between domains. However, those approaches consider during transfer only the restricted setting where supervised samples of all competing classes are available from the source domain. We investigate here the more open and so far overlooked scenario, where during training only a subset of all competing classes is shown in one domain and another subset in another domain. We show the unexpected tendency of a deep learning classifier to use the domain origin as a prominent feature, which is resulting in a poor performance when testing on samples of unseen domain-class combinations. With an existing domain adaptation method this issue can be overcome, while additional unsupervised data of all unseen domain-class combinations is not essential. First results of this overlooked scenario are extensively discussed on a modified MNIST benchmark. © 2019 IEEE.

关键词： Mixtures

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An Open Data Set for Rail Vehicle Positioning Experiments

An Open Data Set for Rail Vehicle Positioning Experiments

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International Conference on Intelligent Transportation

作者： Michael Roth Hanno Winter Institute of Transportation Systems German Aerospace Center (DLR) Braunschweig Germany Control Methods and Robotics Laboratory Technische Universität Darmstadt Germany

ISBN: (数字)9781728141497

ISBN: (纸本)9781728141503

This paper describes an openly available data set for rail vehicle positioning experiments. The data were collected using the DLR research vehicle RailDriVE on a segment of the harbor railway of Braunschweig, Germany, in February 2019. Several sensors of the RailDriVE equipment and an additional self-sufficient system provided by Technische Universität Darmstadt were employed, including two GNSS receivers, two inertial measurement units (IMU), and several speed and distance sensors (radar, optical, odometer) from the rail domain. Front-facing camera data has been included for documentation purposes. In order to simplify its use, some pre-processing steps were applied to the data, mainly to have common time and coordinate frames. Furthermore, example and reference positioning solutions have been included. The data set is described in detail, with information about the individual sensors and the data set structure (with parameters, raw, pre-processed, and reference data). Our work should be seen as a step towards more open and data-driven research in the rail domain, where experiments are difficult and costly. It is our hope to provide a solid basis for many different research efforts that provide the required technological advances for the rail sector.

关键词： Sensors Rails Global navigation satellite system Optical sensors Receivers Sensor systems Radar tracking

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Convergence rate of a penalty method for strongly convex problems with linear constraints

arXiv

引用

arXiv 2020年

作者： Nedić, Angelia Tatarenko, Tatiana School of Electrical Computer and Energy Engineering Arizona State University United States Control Methods and Robotics Lab Technical University Darmstadt Darmstadt Germany

We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a version of the one-sided Huber losses. The smoothness properties of these functions allow us to choose time-varying penalty parameters in such a way that the incremental procedure with the diminishing step-size converges to the exact solution with the rate O(1/√k). To the best of our knowledge, we present the first result on the convergence rate for the penalty-based gradient method, in which the penalty parameters vary with time. Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

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Data-based Identifiability and Observability Assessment for Nonlinear control Systems using the Profile Likelihood Method

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IFAC-PapersOnLine 2020年第2期53卷 1114-1119页

作者： Thomas Schmitt Bastian Ritter Control Methods & Robotics Lab Technische Universität Darmstadt Landgraf Georg Str.4 64283 Darmstadt Germany Control Systems & Mechatronics Lab Technische Universität Darmstadt Landgraf Georg Str.4 64283 Darmstadt Germany

This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

关键词： Nonlinear systems identifiability analysis observability analysis parameter estimation profile likelihood

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Generating compact geometric track-maps for train positioning applications

arXiv

引用

arXiv 2019年

作者： Winter, Hanno Luthardt, Stefan Willert, Volker Adamy, Jürgen Control Methods and Robotics Laboratory TU Darmstadt Germany

In this paper, we present a method to generate compact geometric track-maps for train-borne localization applications. Therefore, we first give a brief overview on the purpose of track maps in train-positioning applications. It becomes apparent that there are hardly any adequate methods to generate suitable geometric track-maps. This is why we present a novel map generation procedure. It uses an optimization formulation to find the continuous sequence of track geometries that fits the available measurement data best. The optimization is initialized with the results from a localization filter [1] developed in our previous work. The localization filter also provides the required information for shape identification and measurement association. The presented approach will be evaluated on simulated data as well as on real measurements. Copyright © 2019, The Authors. All rights reserved.

关键词： Geometry

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Penalized Push-Sum Algorithm for Constrained Distributed Optimization with Application to Energy Management in Smart Grid

Penalized Push-Sum Algorithm for Constrained Distributed Opt...

引用

IEEE Annual Conference on Decision and control

作者： Tatiana Tatarenko Jan Zimmermann Volker Willert Jurgen Adamy Control Methods and Robotics Lab at TU Darmstadt Germany

ISBN: (数字)9781728113982

ISBN: (纸本)9781728113999

We study distributed convex constrained optimization on a time-varying multi-agent network. Each agent has access to its own local cost function, its local constraints, and its instant number of out-neighbors. The collective goal is to minimize the sum of the cost functions over the set of all constraints. We utilize the push-sum protocol to be able to solve this distributed optimization problem. We adapt the push-sum optimization algorithm, which has been studied in context of unconstrained optimization so far, to convex constrained optimization by introducing an appropriate choice of penalty functions and penalty parameters. Under some additional technical assumptions on the gradients we prove convergence of the distributed penalty-based push-sum algorithm to the optimal value of the global objective function. We apply the proposed penalty-based push-sum algorithm to the problem of distributed energy management in smart grid and discuss the advantages of this novel procedure in comparison with existing ones.

关键词： Optimization Convergence Signal processing algorithms Energy management Smart grids Protocols Linear programming

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