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arXiv 2021年

作者： Lederer, Armin Umlauft, Jonas Hirche, Sandra Chair of Information-oriented Control Department of Electrical and Computer Engineering Technical University of Munich Munich Germany

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of performance guarantees using probabilistic model error bounds. To make these approaches applicable in practice, two open challenges must be solved i) Existing error bounds rely on prior knowledge, which might not be available for many real-world tasks. (ii) The relationship between training data and the posterior variance, which mainly drives the error bound, is not well understood and prevents the asymptotic analysis. This article addresses these issues by presenting a novel uniform error bound using Lipschitz continuity and an analysis of the posterior variance function for a large class of kernels. Additionally, we show how these results can be used to guarantee safe control of an unknown dynamical system and provide numerical illustration examples. Copyright © 2021, The Authors. All rights reserved.

关键词： Gaussian distribution

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On the Existence and Uniqueness of Steady State Solutions of a Class of Dynamic Hydraulic Networks via Actuator Placement

On the Existence and Uniqueness of Steady State Solutions of...

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IEEE Conference on Decision and control

作者： Mark Jeeninga Juan E. Machado Michele Cucuzzella Giacomo Como Jacquelien Scherpen Department of Automatic Control Lund University Lund Sweden Chair of Control Systems and Network Control Technology Faculty 3 Mechanical Engineering Electrical and Energy Systems Brandenburg University of Technology Cottbus - Senftenberg Cottbus Germany Department of Electrical Computer Science and Biomedical Engineering Univeristy of Pavia Pavia Italy Department of Mathematical Science “G.L. Lagrange” Politecnico di Torino Torino Italy Department of Automatic Control Lund University Faculty of Science and Engineering Jan C. Willems Center for Systems and Control ENTEG University of Groningen Groningen the Netherlands

In this paper, using tools from graph theory we provide verifiable necessary and sufficient conditions for the existence of a unique hydraulic equilibrium in district heating systems of meshed topology and containing multiple heat sources. Even though numerous publications have addressed the design of efficient algorithms for numerically finding hydraulic equilibria in the general context of water distribution networks, this is not the case for the analysis of existence and uniqueness. Moreover, most of the existing work dealing with these aspects exploit the equivalence between the nonlinear algebraic equations describing the hydraulic equilibria and the KKT conditions of a suitably defined nonlinear convex optimization problem. Differently, this paper proposes necessary and sufficient graph-theoretic conditions on the actuator placement for the existence and uniqueness of a hydraulic equilibrium, independent of the actuators' control objective. An example based on a representative district heating network is considered to illustrate the key aspects of our contribution, and an explicit formulation of the steady state solution is given for the case in which pressure drops through pipes are linear with respect to the flow rate.

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Distributed Optimal control with Recovered Robustness for Uncertain Network Systems: A Complementary Design Approach

arXiv

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arXiv 2022年

作者： Li, Zhongkui Jiao, Junjie Chen, Xiang The State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science College of Engineering Peking University Beijing100871 China The Chair of Information-oriented Control Department of Electrical and Computer Engineering Technical University of Munich Munich80333 Germany The Department of Electrical and Computer Engineering University of Windsor Canada

This paper considers the distributed robust suboptimal consensus control problem of linear multi-agent systems, with both H2 and H∞ performance requirements. A novel two-step complementary design approach is proposed. In the first step, a distributed control law is designed for the nominal multi-agent system to achieve consensus with a prescribed H2 performance. In the second step, an extra control input, depending on some carefully chosen residual signals indicating the modeling mismatch, is designed to complement the H2 performance by providing robustness guarantee in terms of H∞ requirement with respect to disturbances or uncertainties. The proposed complementary design approach provides an additional degree of freedom for design, having two separate controls to deal with the H2 performance and the robustness of consensus, respectively. Thereby, it does not need to make much trade-off, and can be expected to be much less conservative than the trade-off design such as the mixed H2/H∞ control method. Besides, this complementary approach will recover the achievable H2 performance when external disturbances or uncertainties do not exist. The effectiveness of the theoretical results and the advantages of the complementary approach are validated via numerical simulations. Copyright © 2022, The Authors. All rights reserved.

关键词： Robust control

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Constrained Visual-Inertial Localization With Application And Benchmark in Laparoscopic Surgery

Constrained Visual-Inertial Localization With Application An...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： Regine Hartwig Daniel Ostler Jean-Claude Rosenthal Hubertus Feuß ner Dirk Wilhelm Dirk Wollherr Surgical Department Research Group MITI Technical University of Munich (TUM) Germany Department of Electrical and Computer Engineering Chair of Automatic Control Engineering Technical University of Munich (TUM) Germany Fraunhofer HHI Berlin Germany

We propose a novel method to tackle the visual-inertial localization problem for constrained camera movements. We use residuals from the different modalities to jointly optimize a global cost function. The residuals emerge from IMU measurements, stereoscopic feature points, and constraints on possible solutions in SE(3). In settings where dynamic disturbances are frequent, the residuals reduce the complexity of the problem and make localization feasible. We verify the advantages of our method in a suitable medical use case and produce a dataset capturing a minimally invasive surgery in the abdomen. Our novel clinical dataset MITI is comparable to state-of-the-art evaluation datasets, contains calibration and synchronization and is available at [1].

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Towards Data-driven LQR with Koopmanizing Flows ⋆

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IFAC-PapersOnLine 2022年第15期55卷 13-18页

作者： Petar Bevanda Max Beier Shahab Heshmati-Alamdari Stefan Sosnowski Sandra Hirche Chair of Information-oriented Control (ITR) Department of Electrical and Computer Engineering Technical University of Munich D-80333 Munich Germany Department of Electronic Systems Aalborg University Fredrik Bajers Vej 7K 9220 Aalborg Denmark

We propose a novel framework for learning linear time-invariant (LTI) models for a class of continuous-time non-autonomous nonlinear dynamics based on a representation of Koopman operators. In general, the operator is infinite-dimensional but, crucially, linear. To utilize it for effcient LTI control design, we learn a finite representation of the Koopman operator that is linear in controls while concurrently learning meaningful lifting coordinates. For the latter, we rely on Koopmanizing Flows - a diffeomorphism-based representation of Koopman operators and extend it to systems with linear control entry. With such a learned model, we can replace the nonlinear optimal control problem with quadratic cost to that of a linear quadratic regulator (LQR), facilitating efficacious optimal control for nonlinear systems. The superior control performance of the proposed method is demonstrated on simulation examples.

关键词： Machine learning Koopman operators Learning for control Representation Learning Neural networks Learning Systems

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FLEXIBLE-STEP MPC FOR SWITCHED LINEAR SYSTEMS WITH NO QUADRATIC COMMON LYAPUNOV FUNCTION

arXiv

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arXiv 2024年

作者： Fürnsinn, Annika Ebenbauer, Christian Gharesifard, Bahman Department of Mathematics and Statistics Queen's University KingstonONK7L 3N6 Canada Chair of Intelligent Control Systems RWTH Aachen University Aachen52062 Germany Department of Electrical and Computer Engineering University of California at Los Angeles Los AngelesCA90095 United States

In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive control (MPC) scheme, recently introduced in [3], when restricted to the class of linear systems. Specifically, we show that a set of Linear Matrix Inequalities (LMIs) can be used for this purpose, demonstrating its tractability. The main consequence of this LMI formulation is that, when combined with flexible-step MPC, we can effectively stabilize switched control systems, for which no quadratic common Lyapunov function exists. © 2024, CC BY.

关键词： Model predictive control

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Network Traffic Co-Movement Assessment via Oriented Basis Signal Processing and Ensemble Decision Trees

Network Traffic Co-Movement Assessment via Oriented Basis Si...

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International Conference on Intelligent Transportation

作者： Mohammad Reza Mohebbi Mohammad Javad Hassan Zada Majid Rostami-Shahrbabaki Mario Döller Iuliia Yamnenko Josef Ressel Center Vision2Move project University of Applied Sciences Kufstein Tirol Austria Department of Computer Science University of Passau Germany Chair of Traffic Engineering and Control Technical University of Munich Germany Department of Electronic Devices and Systems National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” Kyiv Ukraine

ISBN: (数字)9798331505929

ISBN: (纸本)9798331505936

Accurate short-term network-wide traffic prediction is essential to guarantee high service quality in urban traffic control systems. Nevertheless, traffic state time series represent network-scale spatiotemporal co-movement patterns and location-specific features. Therefore, hybrid statistical machine learning (ml) algorithms could be utilized to accommodate the aforementioned characteristics. In this paper, a hybrid random forest (rf) and extreme gradient boosting tree (XGBoost) model is introduced for network-wide traffic prediction. Moreover, a multi-noise oriented basis wavelet transform (OBT) filter is employed to pre-process the original time series, and improve the predictive accuracy. The RF model captures the traffic co-movements and the XGBoost extracts the local information. Comparative analysis of the hybrid algorithm and deep learning-based benchmarks indicate better performance of the proposed methodology in hourly traffic state prediction of 30 loop detectors, located in the paris city center. Hence, the hybrid decision-tree-based mechanism is a useful framework for real-time network traffic forecasting offering fewer trainable (hyper-)parameters, and thus, lower computational cost.

关键词： Wavelet transforms Radio frequency Accuracy Machine learning algorithms Urban areas Signal processing algorithms Detectors Prediction algorithms Decision trees Random forests

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Cooperative Learning with Gaussian Processes for Euler-Lagrange Systems Tracking control Under Switching Topologies

Cooperative Learning with Gaussian Processes for Euler-Lagra...

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American control Conference (ACC)

作者： Zewen Yang Songbo Dong Armin Lederer Xiaobing Dai Siyu Chen Stefan Sosnowski Georges Hattab Sandra Hirche Center for Artificial Intelligence in Public Health Research (ZKI - PH) Robert Koch Institute Berlin Germany Chair of Information-oriented Control (ITR) TUM School of Computation Information and Technology Technical University of Munich Munich Germany Department of Computer Science ETH Zurich Zurich Switzerland Walker Department of Mechanical Engineering University of Texas at Austin Austin TX USA Department of Mathematics and Computer Science Freie Universität Berlin Berlin Germany

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

This work presents an innovative learning-based approach to tackle the tracking control problem of Euler-Lagrange multi-agent systems with partially unknown dynamics operating under switching communication topologies. The approach leverages a correlation-aware cooperative al-gorithm framework built upon Gaussian process regression, which adeptly captures inter-agent correlations for uncertainty predictions. A standout feature is its exceptional efficiency in deriving the aggregation weights achieved by circumventing the computationally intensive posterior variance calculations. Through Lyapunov stability analysis, the distributed control law ensures bounded tracking errors with high probability. Simulation experiments validate the protocol's efficacy in effectively managing complex scenarios, establishing it as a promising solution for robust tracking control in multi-agent systems characterized by uncertain dynamics and dynamic communication structures.

关键词： Uncertainty Protocols Correlation Decentralized control Switches Gaussian processes Topology

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Estimation of Involuntary Impedance in Multi-joint Arm Movements

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IFAC-PapersOnLine 2019年第34期51卷 220-226页

作者： Börner, Hendrik Endo, Satoshi Hirche, Sandra Chair of Information-oriented Control Department of Electrical and Computer Engineering Technical University of Munich Munich80333 Germany

Stability analysis in physical human-robot interaction requires consideration of human feedback behavior. In unpredictable scenarios, where voluntary cognitive feedback is too slow to guarantee desired task execution, the central nervous system relies on intrinsic and involuntary reflexive feedback. In this work, we present a method for the estimation of the combined effects of intrinsic and involuntary reflexive feedback in multi-joint arm movements, termed involuntary impedance. We apply external force perturbations that are specifically designed to evoke feedback jerk, which can be isolated by application of a high pass filter, and limit the duration of the estimation interval to guarantee the exclusion of voluntary feedback. The isolation of the feedback behavior is validated in simulation and the estimation of the involuntary impedance components is evaluated in an experiment with human participants. © 2019

关键词： Feedback Behavioral research High pass filters Human robot interaction Robotics Central nervous systems Cognitive feedback Combined effect Human motor control Impedance estimation Physical human robot interactions Stability analysis Task executions

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Uncertainty-based Human Motion Tracking with Stable Gaussian Process State Space Models

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IFAC-PapersOnLine 2019年第34期51卷 8-14页

作者： Pöhler, Lukas Umlauft, Jonas Hirche, Sandra Chair of Information-oriented Control Department of Electrical and Computer Engineering Technical University of Munich MunichD-80333 Germany

Data-driven approaches are well suited to represent human motion because arbitrary complex trajectories can be captured. Gaussian process state space models allow to encode human motion while quantifying uncertainty due to missing data. Such human motion models are relevant for many application domains such as learning by demonstration and motion prediction in human-robot collaboration. For goal-directed tasks it is essential to impose stability constraints on the model representing the human motion. Motivated by learning by demonstration applications, this paper proposes an uncertainty-based control Lyapunov function approach for goal-directed path tracking. We exploit the model fidelity which is related to the location of the training and test data: Our approach actively strives into regions with more demonstration data and thus higher model certainty. This achieves accurate reproduction of the human motion independent of the initial condition and we show that generated trajectories are uniformly globally asymptotically stable. The approach is validated in a nonlinear learning by demonstration task where human-demonstrated motions are reproduced by the learned dynamical system, and higher precision than competitive state of the art methods is achieved. © 2019

关键词： Motion tracking Cell proliferation Demonstrations Dynamical systems Gaussian distribution Gaussian noise (electronic) Learning systems Lyapunov functions Lyapunov methods Motion estimation Nonlinear systems Social robots State space methods Uncertainty analysis control Lyapunov function Human performance Human centered automation Human robot collaboration Learning by demonstration Path tracking State of the art methods Uniformly globally asymptotically stables

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