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Publikationen

 


Editorial Boards


  1. Dynamics of Continuous, Discrete & Impulsive Systems, Series B: Applications & Algorithms
  2. Differential-Algebraic Equations Forum, Springer

Books


  1. M. Gerdts, F. Lempio: Mathematische Optimierungsverfahren des Operations Research, DeGruyter, 2011, ISBN 978-3-11-024994-1
  2. M. Gerdts: Optimal Control of ODEs and DAEs, DeGruyter, 2011, ISBN 978-3-11-024995-8

Habilitation


  1. M. Gerdts: Optimal Control of Ordinary Differential Equations and Differential-Algebraic Equations, Fakultät für Mathematik und Physik, Universität Bayreuth, Bayreuth, 2006. 

Publications


  1. S. Erschen, F. Duddeck, M. Gerdts, M. Zimmermann: On the optimal decomposition of high-dimensional solution spaces of complex systems, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part B: Mechanical Engineering, Vol. 4(2),  doi: 10.1115/1.4037485, 2017.
  2. V. Gaitsgory, M. Gerdts: On Numerical Solution of Singularly Perturbed Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 174(3), pp. 762{784, DOI 10.1007/s10957-017-1138-8, 2017.
  3. A. Dreves, M. Gerdts: A generalized Nash equilibrium approach for optimal control problems of autonomous cars, Optimal Control, Applications and Methods, DOI 10.1002/oca.2348, 2017.
  4. M. Burger, M. Gerdts: A survey on numerical methods for the simulation of initial value problems with DAEs, Surveys in Di erential-Algebraic Equations IV, Di erential-Algebraic Equations Forum 2017, Editors: A. Ilchmann, T. Reis, Springer, pp. 221-300, 2017.
  5. M. Gerdts, S. Horn, S. J. Kimmerle: Line search globalization of a semismooth Newton method for operator equations in Hilbert spaces with applications in optimal control, Journal of Industrial and Management Optimization, Vol. 13(1), pp. 47{62, 2017.
  6. A. Huber, M. Gerdts: A dynamic programming MPC approach for automatic driving along tracks and its
    realization with online steering controllers, IFAC PapersOnLine, Vol. 50(1), pp. 86868691, 2017.
  7. A. Dreves, M. Gerdts, M. Sama, A. D'Ariano: Free
    flight trajectory optimization and generalized Nash equilibria in conicting situations, Lecture Notes in Mobility, Springer volume dedicated to the KoMSO
    Challenge Workshop on  Mathematical Modeling, Simulation and Optimization for Air Trac Management, 2017.
  8. K. Palagachev, M. Gerdts: Numerical approaches towards bilevel optimal control problems with scheduling tasks, in: Math for the Digital Factory, Editors: L. Ghezzi, D. Homberg, C. Landry, Springer, Berlin, to appear 2017.
  9. M. Sama, A. D'Ariano, D. Pacciarelli, K. Palagachev, M. Gerdts: Optimal aircraft scheduling and flight trajectory in terminal control areas, 2017 5th IEEE International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), pp. 285-290, DOI: 10.1109/MTITS.2017.8005681, 2017
  10. K. Palagachev, M. Gerdts: Necessary conditions for a class of bilevel optimal control problems exploiting the value function, Pure and Applied Functional Analysis, Vol. 1(4), pp. 505-524, 2016.
  11. S. J. Kimmerle, M. Gerdts: Necessary optimality conditions and a semi-smooth Newton approach for an optimal control problem of a coupled system of Saint-Venant equations and ordinary differential equations, Pure and Applied Functional Analysis, Vol. 1(2), pp. 231-256, 2016.
  12. C. Landry, W. Welz, M. Gerdts: Combining discrete and continuous optimization to solve kinodynamic motion planning problems, accepted for publication in Optimization and Engineering, Vol. 17(3), pp. 533-556, 2016, DOI 10.1007/s11081-015-9291-0.
  13. M. Rieck, G. P. Falconi, M. Gerdts, F. Holzapfel: Periodic Full Circuit Race Line Optimization under
    Consideration of a Dynamic Model with Gear Changes, 2016 IEEE Multi-Conference on Systems and
    Control, Buenos Aires, Argentina, 2016.
  14. M. Sama, K. Palagachev, A. D'Ariano, M. Gerdts, D. Pacciarelli: Terminal Control Area Aircraft Scheduling and Trajectory Optimization Approaches, Proceedings of the Applied mathematical programming
    and Modelling (APMOD 2016) conference, Brno, Czech Republic, 2016.
  15. J. J. Kiam, A. Schulte, M. Gerdts: Fast Subset Path Planning/Replanning to Avoid Obstacles with Time-Varying Probabilistic Motion Patterns, STAIRS 2016 IOS Proceedings.
  16. M. Burger, M. Gerdts, S. Gottlich, M. Herty: Dynamic programming approach for discrete-valued time discrete optimal control problems with dwell time constraints, Springer series: IFIP Advances in Information and Communication Technology (IFIP AICT Series), System Modeling and Optimization (CSMO 2015), Editors: Lorena Bociu, J.A. Desideri and A. Habbal.
  17. K. Palagachev, M. Gerdts: Exploitation of the value function in a bilevel optimal control problem, Springer series: IFIP Advances in Information and Communication Technology (IFIP AICT Series), System Modeling and Optimization (CSMO 2015), Editors: Lorena Bociu, J.A. Desideri and A. Habbal.
  18. J. Michael, M. Gerdts: Pro-active optimal control for semi-active vehicle suspension based on sensitivity updates, Vehicle System Dynamics, Vol. 53(12), pp. 1721-1741, 2015, DOI 10.1080/00423114.2015.1081953.
  19. J. Michael, M. Gerdts: A method to model impulsive Multi-Body-Dynamics using Riemann-Stieltjes-Integrals, IFAC-PapersOnline, Vol. 48(1), pp. 629{634, 2015.
  20. M. Gerdts, S.-J. Kimmerle: Numerical optimal control of a coupled ODE-PDE model of a truck with a fluid basin, AIMS 2015 Proceedings, pp. 515-524, 2015.
  21. K. Palagachev, M. Gerdts: Mathematical Programs with Blocks of Vanishing Constraints Arising in Discretized Mixed-Integer Optimal Control Problems, Set-Valued and Variational Analysis, Vol. 23(1), pp. 149-167, 2015, DOI 10.1007/s11228-014-0297-0
  22. M. Gerdts: A survey on optimal control problems with differential-algebraic equations, Differential-Algebraic Equations Forum 2015, Editors: A. Ilchmann, T. Reis, pp. 103-161, 2015.

  23. J. Pannek, T. Sprodowski, M. Gerdts, J. Michael: Kooperative Regelung vernetzter Fahrzeuge: Hierarchische und verhandlungsbasierte Strategien im Straßenverkehr, Industrie 4.0 Management, Vol. 2/2015, 2015.

  24. M. Gerdts, M. Kunkel: Convergence Analysis of Euler Discretization of Control-State Constrained Optimal Control Problems with Controls of Bounded Variation, Journal of Industrial and Management Optimization, Vol. 10(1), pp. 311-336, 2014.
  25. J. Pannek, T. Naundorf, M. Gerdts: Autonomous Control Strategy for High Precision Marking of Drill
    Holes using a Mobile Robot, Dynamics in Logistics, Proceedings of the 4th International Conference on
    Dynamics in Logistics { LDIC, 2014 Bremen. In: Lecture Notes in Logistics, pp. 69-78, 2015, Editors: H.
    Kotzab, J. Pannek, K.-D. Thoben.
  26. K. Palagachev, M. Gerdts: A time transformation technique for Switched Systems Optimal Control Problems with fixed sequence of phases, PAMM 14(1), 2014.
  27. J. Michael, M. Gerdts: Optimal Control in Proactive Chassis Dynamics - A xed step size time-stepping
    scheme for complementarity problems, In: Progress in Industrial Mathematics at ECMI 2012, Editors: M.
    Fontes, M. Gunther, N. Marheineke, Springer, pp. 271-276, 2014.
  28. J. Pannek, M. Gerdts: Performance of Sensitivity Based NMPC Updates in Automotive Applications,
    In: Progress in Industrial Mathematics at ECMI 2012, Editors: M. Fontes, M. Gunther, N. Marheineke,
    Springer, pp. 265-270, 2014.
  29. C. Landry, M. Gerdts, R. Henrion, D. Hömberg, W.Welz: Collision-Free Path Planning of Welding Robots, In: Progress in Industrial Mathematics at ECMI 2012, Editors: M. Fontes, M. Gunther, N. Marheinke, Springer, pp. 251-256, 2014.
  30. K. Palagachev, M. Rieck, M. Gerdts: A Mixed-Integer Optimal Control Approach for Aircraft Landing Model, 10 pages, Proceedings of the 3rd International Conference on Models and Technologies for Intelligent Transportation Systems, TU Dresden, 2013, Editors: T. Albrecht, B. Jaekel, M. Lehnert, Tudpress Verlag Der Wissenschaften Gmbh, 2013.

  31. J. Michael, K. Chudej, M. Gerdts, J. Pannek: Optimal Rendezvous Path Planning to an Uncontrolled
    Tumbling Target, Proceedings of the 19th IFAC Symposium on Automatic Control in Aerospace, September 2-6, 2013, University of Würzburg, Würzburg, Germany.

  32. R. Baier, M. Gerdts, I. Xausa: Approximation of reachable sets using optimal control algorithms, Numerical Algebra, Control and Optimization, Vol. 3(3), pp. 519-548, 2013.

  33. M. Schlueter, S. O. Erb, M. Gerdts, S. Kemble, J.-J. Rückmann: MIDACO on MINLP Space Applications, Advances in Space Research, Vol. 51(7), pp. 1116-1131, 2013, DOI 10.1016/j.asr.2012.11.006
  34. W. Alt, R. Baier, F. Lempio, M. Gerdts: Approximation of Linear Control Problems with Bang-Bang Solutions, Optimization: A Journal of Mathematical Programming and Operations Research, Vol. 62(1), pp. 9-32, 2013, DOI: 10.1080/02331934.2011.568619
  35. M. Gerdts, I. Xausa: Avoidance Trajectories Using Reachable Sets and Parametric Sensitivity Analysis, System Modeling and Optimization, Editors: D. Hömberg et al., 25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 1216, 2011. Revised Selected Papers. Heidelberg: Springer (ISBN 978-3-642-36061-9/hbk; 978-3-642-36062-6/ebook). IFIP Advances in Information and Communication Technology 391, 491-500 (2013).

  36. C. Landry, M. Gerdts, R. Henrion, D. HömbergPath-Planning with Collision Avoidance in Automotive Industry, System Modeling and Optimization, Editors: D. Hömberg et al., 25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 1216, 2011. Revised Selected Papers. Heidelberg: Springer (ISBN 978-3-642-36061-9/hbk; 978-3-642-36062-6/ebook). IFIP Advances in Information and Communication Technology 391, 102-111 (2013).

  37. I. Xausa, R. Baier, M. Gerdts, M. Gonter, C. Wegwerth: Avoidance Trajectories for Driver Assistance Systems via Solvers for Optimal Control Problems, 8 pages, Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, July 2012.

  38. I. Kornienko, M. Gerdts, MdR de Pinho: A new version of necessary conditions for optimal control problems with differential-algebraic equations, 8 pages, Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, July 2012.

  39. J. Pannek, M. Gerdts: Robust Stability and Performance Bounds for NMPC with Abstract Updates, Proceedings of the 4th IFAC Nonlinear Model Predictive Control Conference, Noordwijk, 2012.

  40. M. Gerdts, S. Sager: Mixed-Integer DAE Optimal Control Problems: Necessary Conditions and Bounds, in Control and Optimization with Differential-Alebraic Equations. Editors:L. T. Biegler, S. L. Campbell, V. Mehrmann, Advances in Design and Control 23, SIAM, Philadelphia, 2012, pp. 189-212.
  41. J. Chen, M. Gerdts: Smoothing technique of nonsmooth Newton methods for control-state constrained optimal control problems, SIAM Journal on Numerical Analysis, Vol. 50(4), pp. 1982-2011, 2012.
  42. C. Landry, M. Gerdts, R. Henrion, D. Hömberg: Path planning and Collision avoidance for robots, Numerical Algebra, Control and Optimization, Vol. 2(3), pp. 437-463, 2012.
  43. W. Alt, R. Baier, M. Gerdts, F. Lempio: Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions, Numerical Algebra, Control and Optimization, Vol. 2(3), pp. 547-570,  2012.
  44. M. Schlüter, M. Gerdts, J. J. Rückmann: A Numerical Study of MIDACO on 100 MINLP Benchmarks, Optimization, Vol. 61(7), pp. 873-900, 2012.
  45. J. Chen, M. Gerdts: Numerical solution of control-state constrained optimal control problems with an inexact smoothing Newton method, IMA Journal of Numerical Analysis, 31(4), 2011.
  46. M. Gerdts, B. Hüpping: Virtual control regularization of state constrained linear quadratic optimal control problem, Computational Optimization and Applications, Vol. 51(2), pp. 867-882, 2012. DOI: 10.1007/s10589-010-9353-3
  47. C. Landry, M. Gerdts, R. Henrion, D. Hömberg: A time optimal control problem for the collision-free robot motion planning, PAMM, 11 (1), pp. 725-726, 2011.
  48. M. Gerdts, B. Hüpping: A linear-quadratic model-predictive controller for control and state constrained nonlinear control problems, Recent Trends in Optimization and its Applications in Engineering. Editors:M. Diehl, F. Glineur, E. Jarlebring, W. Michiels, Springer, 2010, Part 5, 319-328, DOI: 10.1007/978-3-642-12598-0_28 .
  49. M. Schlüter, M. Gerdts: The oracle penalty method, Journal of Global Optimization, Vol. 47(2), pp. 293-325, 2010. DOI 10.1007/s10898-009-9477-0.
  50. S. Hoffmann, A.S. Funke, K. Wiesehan, S. Moedder, J. Glück, S. Feuerstein, M. Gerdts, J. Mötter, D. Willbold: Competitively selected protein ligands pay theirs increase in specificity by a decrease in affinity, Molecular Biosystems, Vol. 6, pp. 126-133, 2010. DOI: 10.1039/b910945e
  51. R. Baier, M. Gerdts: A computational method for non-convex reachable sets using optimal control, Proceedings of the European Control Conference 2009, Budapest, Hungary, August 23-26, pp. 97-102, 2009.
  52. M. Gerdts, M. Kunkel: A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems, Computational Optimization and Applications, Vol. 48(3), pp. 601-633, DOI 10.1007/s10589-009-9275-0, 2011.
  53. M. Gerdts: Global Convergence of a Nonsmooth Newton's Method for Control-State Constrained Optimal Control Problems, SIAM Journal on Optimization, 19 (1), pp. 326-350, 2008. The original contains a mistake (Lemma 2.5 (i) is wrong). Here is a corrected version.
  54. M. Gerdts, S. Karrenberg, B. Müller-Beßler, G. Stock: Generating Optimal Trajectories for an Automatically Driven Car, Optimization and Engineering, 10(4), pp. 439-463, 2009
  55. M. Gerdts, M. Kunkel: A Nonsmooth Newton's Method for Discretized Optimal Control Problems with State and Control Constraints Journal of Industrial and Management Optimization, 4 (2), pp. 247-270, 2008
  56. M. Gerdts: A nonsmooth Newton's method for control-state constrained optimal control problems, Mathematics and Computers in Simulation, Vol. 79 (4), pp. 925-936, 2008
  57. M. Gerdts, G. Greif, H. J. Pesch: Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time, Mathematics and Computers in Simulation, Vol. 79 (4), pp. 1020-1032, 2008
  58. R. Baier, C. Büskens, I. A. Chahma, M. Gerdts: Approximation of Reachable Sets by Direct Solution Methods of Optimal Control Problems, Optimization Methods and Software, 22 (3), pp. 433-452, 2007
  59. M. Gerdts: Representation of Lagrange multipliers for optimal control problems subject to index-two differential-algebraic equations, Journal of Optimization Theory and Applications, 130 (2), pp. 231-251, 2006
  60. M. Gerdts: Local Minimum principle for optimal control problems subject to index-two differential-algebraic equations, Journal of Optimization Theory and Applications, 130 (3), pp. 443-462, 2006
  61. M. Gerdts: A variable time transformation method for mixed-integer optimal control problems, Optimal Control, Applications and Methods, Vol. 27 (3), pp. 169-182, 2006
  62. C. Büskens, M. Gerdts: Differentiability of Consistency Functions for DAE Systems, Journal of Optimization Theory and Applications, 125 (1), pp. 37-61, 2005
  63. M. Gerdts: Solving Mixed-Integer Optimal Control Problems by Branch & Bound: A Case Study from Automobile Test-Driving with Gear Shift, Optimal Control, Applications and Methods, Vol. 26 (1), pp. 1-18, 2005
  64. M. Gerdts: On the convergence of Linearized Implicit Runge-Kutta Methods and their Use in Parameter Optimization , Mathematica Balkanica, New Series, Vol. 19 (1-2), pp. 75-83, 2005
  65. M. Gerdts: Gradient evaluation in DAE optimal control problems by sensitivity equations and adjoint equations, PAMM, Vol. 5 (1), p. 43--46, 2005
  66. M. Gerdts: Parameter Optimization in Mechanical Multibody Systems and Linearized Runge-Kutta Methods, in 'Progress in Industrial Mathematics at ECMI 2002' (A. Buikis; R. Ciegis, A.D. Flitt (Eds.)), Vol. 5 of 'Mathematics in Industry', pp. 121-126, Springer, 2004
  67. M. Gerdts: A Moving Horizon Technique for the Simulation of Automobile Test-Drives, Zeitschrift für Angewandte Mathematik und Mechanik 83 (3), pp. 147-162, 2003
  68. M. Gerdts: Direct Shooting Method for the Numerical Solution of Higher Index DAE Optimal Control Problems, Journal of Optimization Theory and Applications Vol. 117, No. 2, pp. 267-294, 2003
  69. M. Gerdts: Optimal Control and Real-Time Optimization of Mechanical Multi-Body Systems, Zeitschrift für Angewandte Mathematik und Mechanik 83 (10), pp. 705-719, 2003
  70. H. J. Pesch, M. Gerdts: Simulation of Test-drives of Automobiles at Driving Limit, in 'Mathematics-Key Technology for the Future' (W. Jäger, H.-J. Krebs (Eds.)), Springer, 2003
  71. C. Büskens, M. Gerdts: Emergency Landing of a Hypersonic Flight System: A Corrector Iteration Method for admissible Real--Time Optimal Control Approximations, Proceedings of the Workshop “Optimal Control” in Greifswald, Sonderforschungsbereich 255: Transatmosphärische Flugsysteme, Hieronymus München, 2003, pp. 51-60, ISBN 3-89791-316-X
  72. M. Gerdts, C. Büskens: Consistent Initialization of Sensitivity Matrices for a Class of Parametric DAE Systems, BIT Numerical Mathematics 42:4, pp. 796-813, 2002
  73. M. Gerdts: Numerical Treatment of Optimal Control Problems with Differential-Algebraic Equations and Applications to Virtual Test-drives, in 'Progress in Industrial Mathematics at ECMI 2000' (M. Anile, V. Capasso, A. Greco (Eds.)), Vol. 1 of 'Mathematics in Industry', pp. 549-553, Springer, 2002
  74. M. Gerdts: Numerische Methoden optimaler Steuerprozesse mit differential-algebraischen Gleichungssystemen höheren Indexes und ihre Anwendungen in der Kraftfahrzeugsimulation und Mechanik, Bayreuther Mathematische Schriften 61, Bayreuth, 2001.
  75. M. Gerdts, C. Büskens: Computation of Consistent Initial Values for Optimal Control Problems with DAE Systems of Higher Index, Zeitschrift für Angewandte Mathematik und Mechanik 81 (2001) S2, pp. 249-250
  76. C. Büskens, M. Gerdts: Real-time Optimization of DAE Systems , in 'Online Optimization of Large Scale Systems' (M. Grötschel, S.O. Krumke, J. Rambau (Eds.)), pp. 117-128, Springer, 2001
  77. C. Büskens, M. Gerdts: Numerical Solution of Optimal Control Problems with DAE Systems of Higher Index, Proceedings of the Workshop “Optimalsteuerungsprobleme in der Luft- und Raumfahrt” in Greifswald, Sonde rforschungsbereich 255: Transatmosphärische Flugsysteme, Hieronymus München, 2000, pp. 27-38, ISBN 3-89791-147-7
  78. M. Gerdts, M. H. Breitner, R. Lachner, J. Gottlieb: Synthese optimaler Kollisionsvermeidungsalgorithmen gegen Geisterfahrer mit neuronalen Netzen, Mathematik Bericht 96/10, Institut für Mathematik, TU Clausthal, 1996

     

 


Technical Reports


  1. M. Gerdts, J. Sternberg: Stable Memory-Efficient Nonsmooth Newton Method for Control-State Constrained Optimal Control Problems, Technical Report, Department of Mathematics, University of Hamburg, 2010.
  2. T. Nikolayzik, C. Büskens, M. Gerdts: Nonlinear Large-Scale Optimization with WORHP, 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, 13-15 September 2010, Fort Worth, Texas, AIAA 2010-9136.
  3. G. Ortega et al.: STA, The Space Trajectory Analysis Project, European Space Agency (ESA), paper presented at Fourth International Conference on Astrodynamics Tools and Techniques, Madrid, Spain, 2010.
  4. M. Gerdts, M. Kocvara: Current trends in nonlinear programming, Project report: Sparse NLP Solver in Aerospace Applications, funded by ESA, University of Birmingham, 2008.
  5. M. Gerdts, B. Frank, V. Niendorf: QP Solver Documentation, Sparse NLP Solver Project, funded by BMBF 50JR0689, TIB Hannover, 2007.
  6. M. Gerdts, M. Kunkel: A Nonsmooth Newton's Method for Discretized Optimal Control Problems with State and Control Constraints , Hamburger Beiträge zur Angewandten Mathematik, Nr. 2007-03, University of Hamburg, 2007
  7. M. Gerdts: Parameter Identification in Higher Index DAE Systems, Technical Report, Department of Mathematics, University of Hamburg, 2005
  8. M. Gerdts: Local minimum principle for optimal control problems subject to index one differential-algebraic equations , Technical Report, Department of Mathematics, University of Hamburg, 2005