Forschungsschwerpunkte

A. Fun­nel-Re­gel­ung

  • T. Berger, C. M. Hackl and S. Trenn
    Asymptotic tracking by funnel control with internal models
    to appear in: Proceedings of the European Control Conference 2024 [preprint]

  • T. Berger und L. Lanza
    Funnel control of linear systems with arbitrary relative degree under output measurement losses
    IMA Journal of Mathematical Control and Information 40 (4), 691-713, 2023 [preprint]
    doi: 10.1093/imamci/dnad029

  • T. Berger
    Fault tolerant funnel control for uncertain linear systems
    IEEE Transactions on Automatic Control 66 (9), 4349-4356, 2021 [preprint]
    doi: 10.1109/TAC.2020.3030759

  • T. Berger
    Tracking with prescribed performance for linear non-minimum phase systems
    Automatica 115, Article 108909, 2020 [preprint]
    doi: 10.1016/j.automatica.2020.108909

  • T. Berger und T. Reis
    Funnel control via funnel pre-compensator for minimum phase systems with relative degree two
    IEEE Transactions on Automatic Control 63 (7), 2264-2271, 2018 [preprint]
    doi: 10.1109/TAC.2017.2761020

Regelfehler und Eingangsgrößen für die Simulation eines Boeing 737-Modells unter fehlertoleranter Funnel-Regelung bei Beeinträchtigung des zweiten und vierten Aktuators
Darstellung eines Funnels (engl. für Trichter), welcher den Bewegungsbereich des Regelfehlers vorgibt
Snapshots der Lösung der Fokker-Planck-Gleichung unter Funnel-Regelung
Skizze eines rollenden Wassertanks

  • T. Berger, B. Besselink
    String stability and guaranteed safety via funnel cruise control for vehicle platoons
    eingereicht bei: IEEE Transactions on Automatic Control [pdf]

  • T. Berger, F. Nüske
    Funnel control for Langevin dynamics
    eingereicht bei: Automatica [pdf]

  • S. Drücker, L. Lanza, T. Berger, T. Reis, R. Seifried
    Experimental validation for the combination of funnel control with a feedforward control strategy
    Multibody System Dynamics 2024 [pdf]
    doi: 10.1007/s11044-024-09976-2 (open access)

  • Z. Guo, X. Gu, Y. Han, J. Guo, T. Berger
    Maneuvering tracking algorithm for reentry vehicles with guaranteed prescribed performance
    IEEE Transactions on Aerospace and Electronic Systems 60 (3), 3012-3020, 2024 [preprint]
    doi: 10.1109/TAES.2024.3357649

  • J. G. Lee, T. Berger, S. Trenn, H. Shim
    Edge-wise funnel output synchronization of heterogeneous agents with relative degree one
    Automatica 156, Article 111204, 2023 [preprint]
    doi: 10.1016/j.automatica.2023.111204 (open access)

  • T. Berger
    Feedback control of the COVID-19 pandemic with guaranteed non-exceeding ICU capacity
    Systems & Control Letters 160, Article 105111, 2022 [preprint]
    doi: 10.1016/j.sysconle.2021.105111

  • T. Berger, L. Lanza
    Output tracking for a non-minimum phase robotic manipulator
    IFAC-PapersOnLine 54 (9), 178-185, 2021 [preprint]
    doi: 10.1016/j.ifacol.2021.06.074

  • T. Berger, S. Drücker, L. Lanza, T. Reis, R. Seifried
    Tracking control for underactuated non-minimum phase multibody systems
    Nonlinear Dynamics 104 (4), 3671-3699, 2021 [preprint]
    doi: 10.1007/s11071-021-06458-4

  • T. Berger, A.-L. Rauert
    Funnel cruise control
    Automatica 119, Article 109061, 2020 [preprint]
    doi: 10.1016/j.automatica.2020.109061

  • T. Berger, S. Otto, T. Reis, R. Seifried
    Combined open-loop and funnel control for underactuated multibody systems
    Nonlinear Dynamics 95 (3), 1977-1998, 2019 [preprint]
    doi: 10.1007/s11071-018-4672-5

  • T. Berger, A.-L. Rauert
    A universal model-free and safe adaptive cruise control mechanism
    Proceedings of the MTNS 2018, Hong Kong, pp. 925-932, 2018 [pdf]
Darstellung der Entwicklung symptomatischer COVID-19-Patienten unter Regelung (mit zwei verschiedenen Parametern) und der Schranke gegeben durch die verfügbaren Intensivbetten (ICU beds)
Schematische Darstellung des Funnel Cruise Control-Mechanismus

B. Op­ti­mie­rung­s­ba­si­er­­te Re­ge­lung

  • L. Lanza, D. Dennstädt, T. Berger, K. Worthmann
    Safe continual learning in model predictive control with prescribed bounds on the tracking error
    eingereicht bei: International Journal of Robust and Nonlinear Control [pdf]

  • B. Oppeneiger, L. Lanza, M. Schell, D. Dennstädt, M. Schaller, B. Zamzow, T. Berger, K. Worthmann
    Model predictive control of a magnetic levitation system with prescribed output tracking performance
    Control Engineering Practice 151, Article 106018, 2024 
    doi: 10.1016/j.conengprac.2024.106018 (open access)

  • T. Berger, D. Dennstädt, L. Lanza, K. Worthmann
    Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance
    SIAM Journal on Control and Optimization 62 (4), 2071-2097, 2024 [preprint]
    doi: 10.1137/23M1551195

  • T. Berger, D. Dennstädt
    Funnel MPC for nonlinear systems with arbitrary relative degree
    Automatica 167, Article 111759, 2024 [preprint]
    doi: 10.1016/j.automatica.2024.111759 (open access)

  • T. Berger, D. Dennstädt, A. Ilchmann, K. Worthmann
    Funnel MPC for nonlinear systems with relative degree one
    SIAM Journal on Control and Optimization 60 (6), 3358-3383, 2022 [preprint]
    doi: 10.1137/21M1431655

  • T. Berger, D. Dennstädt
    Funnel MPC with feasibility constraints for nonlinear systems with arbitrary relative degree
    IEEE Control Systems Letters 6, 2804-2809, 2022 [preprint]
    doi: 10.1109/LCSYS.2022.3178478

  • T. Berger, C. Kästner, K. Worthmann
    Learning-based Funnel-MPC for output-constrained nonlinear systems
    IFAC-PapersOnLine 53 (2), 5177-5182, 2020 [preprint]
    doi: 10.1016/j.ifacol.2020.12.1186

Simulation mit Vergleich von MPC und Funnel-MPC für ein Tracking-Problem mit vorgegebenen Fehlerschranken
  • J. G. Lee, T. Berger, S. Trenn and H. Shim
    Utility of Edge-wise Funnel Coupling for Asymptotically Solving Distributed Consensus Optimization
    Proceedings of the European Control Conference 2020, Saint Petersburg, Russia, pp. 911-916, 2020 [preprint]
    doi: 10.23919/ECC51009.2020.9143983
Synchronisierung von Agenten zur Lösung eines verteilten Optimierungsproblems

C. Differentiell-algebraische Systeme

Dissertation: 

  • T. Berger
    On differential-algebraic control systems
    Universitätsverlag Ilmenau, 2014.
    ISBN: 978-3-86360-081-5
    [pdf]            official website

 

  • T. Berger, T. Reis, S. Trenn
    Observability of linear differential-algebraic systems - a survey
    In: Achim Ilchmann and Timo Reis (eds.) Surveys in Differential-Algebraic Equations IV, Differential-Algebraic Equations Forum, pp. 161-219. Springer, Berlin-Heidelberg, 2017 [preprint]
    doi: 10.1007/978-3-319-46618-7_4

  • T. Berger, T. Reis
    Controllability of linear differential-algebraic systems - a survey
    In: Achim Ilchmann and Timo Reis (eds.) Surveys in Differential-Algebraic Equations I, Differential-Algebraic Equations Forum, pp. 1-61. Springer, Berlin-Heidelberg, 2013 [preprint]
    doi: 10.1007/978-3-642-34928-7_1

  • T. Berger, A. Ilchmann, S. Trenn
    Quasi feedback forms for differential-algebraic systems
    IMA Journal of Mathematical Control and Information 39 (2), 533-563, 2022 [preprint]
    doi: 10.1093/imamci/dnab030

  • T. Berger
    The zero dynamics form for nonlinear differential-algebraic systems
    IEEE Transactions on Automatic Control 62 (8), 4131-4137, 2017 [preprint]
    doi: 10.1109/TAC.2016.2620561

  • T. Berger
    Zero dynamics and funnel control of general linear differential-algebraic systems
    ESAIM: Control, Optimisation and Calculus of Variations 22 (2), 371-403, 2016 [preprint]
    doi: 10.1051/cocv/2015010

  • T. Berger, C. Trunk, H. Winkler
    Linear relations and the Kronecker canonical form
    Linear Algebra and its Applications 488, 13-44, 2016 [preprint]
    doi: 10.1016/j.laa.2015.09.033

  • T. Berger, P. Van Dooren
    Computing the regularization of a linear differential-algebraic system
    Systems & Control Letters 86, 48-53, 2015 [preprint]
    doi: 10.1016/j.sysconle.2015.10.003

  • T. Berger, S. Trenn
    Kalman controllability decompositions for differential-algebraic systems
    Systems & Control Letters 71, 54-61, 2014 [preprint]
    doi: 10.1016/j.sysconle.2014.06.004

  • T. Berger, S. Trenn
    Addition to "The quasi-Kronecker form for matrix pencils"
    SIAM Journal on Matrix Analysis and Applications 34 (1), 94–101, 2013 [pdf]
    doi: 10.1137/120883244

  • T. Berger, A. Ilchmann
    On the standard canonical form of time-varying linear DAEs
    Quarterly of Applied Mathematics 71 (1), 69-87, 2013 [preprint]
    doi: 10.1090/S0033-569X-2012-01285-1

  • T. Berger, A. Ilchmann, T. Reis
    Normal forms, high-gain and funnel control for linear differential-algebraic systems
    In: L.T. Biegler, S.L. Campbell, V. Mehrmann (eds.) Control and Optimization with Differential-Algebraic Constraints, Advances in Design and Control, vol. 23, pp. 127–164. SIAM, Philadelphia, 2012 [preprint]
    doi: 10.1137/9781611972252.ch7

  • T. Berger, S. Trenn
    The quasi-Kronecker form for matrix pencils
    SIAM Journal on Matrix Analysis and Applications 33 (2), 336-368, 2012 [pdf]
    doi: 10.1137/110826278

  • T. Berger, A. Ilchmann, T. Reis
    Zero dynamics and funnel control of linear differential-algebraic systems
    Mathematics of Control, Signals and Systems 24 (3), 219-263, 2012 [preprint]
    doi: 10.1007/s00498-012-0085-z

  • T. Berger, A. Ilchmann, S. Trenn
    The quasi-Weierstraß form for regular matrix pencils
    Linear Algebra and its Applications 436 (10), 4052-4069, 2012 [preprint]
    doi: 10.1016/j.laa.2009.12.036

System Inversion Form eines singulären differentiell-algebraischen Systems
Ein elementares Werkzeug bei der Berechnung von Normalformen von Matrizen-Büscheln: die Wong-Sequenzen
Ein elektrischer Schaltkreis, welcher nicht mehr mithilfe regulärer differentiell-algebraischer Gleichungen modelliert werden kann, sondern singuläre Modelle benötigt

  • T. Berger, Le Huy Hoang, T. Reis
    Vector relative degree and funnel control for differential-algebraic systems
    In: Sara Grundel, Timo Reis, and Sebastian Schöps (eds.) Progress in Differential-Algebraic Equations II, Differential-Algebraic Equations Forum, pp. 213-255. Springer, Cham, 2020 [preprint]
    doi: 10.1007/978-3-030-53905-4_8

  • T. Berger
    Zero dynamics and funnel control of general linear differential-algebraic systems
    ESAIM: Control, Optimisation and Calculus of Variations 22 (2), 371-403, 2016 [preprint]
    doi: 10.1051/cocv/2015010

  • T. Berger, T. Reis
    Zero dynamics and funnel control for linear electrical circuits
    Journal of the Franklin Institute 351 (11), 5099–5132, 2014 [preprint]
    doi: 10.1016/j.jfranklin.2014.08.006

  • T. Berger, A. Ilchmann, T. Reis
    Normal forms, high-gain and funnel control for linear differential-algebraic systems
    In: L.T. Biegler, S.L. Campbell, V. Mehrmann (eds.) Control and Optimization with Differential-Algebraic Constraints, Advances in Design and Control, vol. 23, pp. 127–164. SIAM, Philadelphia, 2012 [preprint]
    doi: 10.1137/9781611972252.ch7

  • T. Berger, A. Ilchmann, T. Reis
    Zero dynamics and funnel control of linear differential-algebraic systems
    Mathematics of Control, Signals and Systems 24 (3), 219-263, 2012 [preprint]
    doi: 10.1007/s00498-012-0085-z

  • T. Berger, A. Ilchmann and T. Reis
    Funnel control for nonlinear functional differential-algebraic systems
    Proceedings of the MTNS 2014, Groningen, The Netherlands, pp. 46-53, 2014 [pdf]

Schaltkreis einer diskretisierten Übertragungsleitung (oben), Referenzsignal einer Sägezahnschwingung für die Messgrößen (Mitte) und tatsächliche Ausgänge bei Simulation des Modells unter Funnel-Regelung (unten)

  • J. Jaiswal, T. Berger, N. K. Tomar
    Partial causal detectability of linear descriptor systems and existence of functional ODE estimators
    eingereicht bei: SIAM Journal on Control and Optimization [pdf]

  • J. Jaiswal, T. Berger, N. K. Tomar
    Partial detectability and generalized functional observer design for linear descriptor systems
    eingereicht bei: Franklin Open [pdf]

  • J. Jaiswal, T. Berger, N. K. Tomar
    Existence conditions for functional ODE observer design of descriptor systems revisited
    Journal of the Franklin Institute 361 (8), Article 106848, 2024 [preprint]
    doi: 10.1016/j.jfranklin.2024.106848

  • J. Jaiswal, T. Berger, N. K. Tomar
    Partial impulse observability of linear descriptor systems
    Systems & Control Letters 168, Article 105352, 2022 [preprint]
    doi: 10.1016/j.sysconle.2022.105352

  • T. Berger, L. Lanza
    Observers for differential-algebraic systems with Lipschitz or monotone nonlinearities
    In: Sara Grundel, Timo Reis, and Sebastian Schöps (eds.) Progress in Differential-Algebraic Equations II, Differential-Algebraic Equations Forum, pp. 257-289. Springer, Cham, 2020 [preprint]
    doi: 10.1007/978-3-030-53905-4_9

  • T. Berger, T. Reis
    ODE observers for DAE systems
    IMA Journal of Mathematical Control and Information 36 (4), 1375-1393, 2019 [preprint]
    doi: 10.1093/imamci/dny032

  • T. Berger
    On observers for nonlinear differential-algebraic systems
    IEEE Transactions on Automatic Control 64 (5), 2150-2157, 2019 [preprint]
    doi: 10.1109/TAC.2018.2866438

  • T. Berger
    Disturbance decoupled estimation for linear differential-algebraic systems
    International Journal of Control 92 (3), 593-612, 2019 [preprint]
    doi: 10.1080/00207179.2017.1363411

  • T. Berger, T. Reis
    Observers and dynamic controllers for linear differential-algebraic systems
    SIAM Journal on Control and Optimization 55 (6), 3564-3591, 2017 [pdf]
    doi: 10.1137/15M1035355

Kopplung eines Beobachters mit einem differentiell-algebraischen System
Modell eines Beobachters für ein lineares differentiell-algebraisches System
Konstruktion eines dynamischen Feedback-Reglers für ein lineares differentiell-algebraisches System mithilfe eines Beobachters
Schematische Darstellung von Ergebnissen zur Störungsentkopplung für lineare differentiell-algebraische Systeme

  • T. Berger, N. Karcanias, M. Livada
    The pseudo-McMillan degree of implicit transfer functions of RLC networks
    Circuits, Systems, and Signal Processing 38 (3), 967-985, 2019 [preprint]
    doi: 10.1007/s00034-018-0921-6

  • T. Berger, G. Halikias, N. Karcanias
    Effects of dynamic and non-dynamic element changes in RC and RL networks
    International Journal of Circuit Theory and Applications 43 (1), 36-59, 2015 [preprint]
    doi: 10.1002/cta.1923

  • T. Berger, T. Reis
    Zero dynamics and funnel control for linear electrical circuits
    Journal of the Franklin Institute 351 (11), 5099-5132, 2014 [preprint]
    doi: 10.1016/j.jfranklin.2014.08.006

  • T. Berger, T. Reis
    Structural properties of positive real and reciprocal rational matrices
    Proceedings of the MTNS 2014, Groningen, The Netherlands, pp. 402-409, 2014 [pdf]

Schaltkreis mit unterschiedlichen McMillan- und Pseudo-McMillan-Graden