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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. 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, 2011, DOI: 10.1080/02331934.2011.568619
  2. 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.
  3. 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
  4. 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.
  5. 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 .
  6. 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.
  7. 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
  8. 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.
  9. 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.
  10. 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.
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. C. Büskens, M. Gerdts: Differentiability of Consistency Functions for DAE Systems, Journal of Optimization Theory and Applications, 125 (1), pp. 37-61, 2005
  20. 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
  21. 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
  22. M. Gerdts: Gradient evaluation in DAE optimal control problems by sensitivity equations and adjoint equations, PAMM, Vol. 5 (1), p. 43--46, 2005
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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.
  32. 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
  33. 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
  34. 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
  35. 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