Habilitation

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

Submitted

  1. M. Gerdts: A nonsmooth Newton's method for control-state constrained optimal control problems, Proceedings 5th Vienna Symposium on Mathematical Modelling, (I. Troch; F. Breitenecker (Eds.)), ARGESIM Report No. 30, Vienna, 2006, ISBN 3-901608-30-3

  2. 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, Proceedings 5th Vienna Symposium on Mathematical Modelling, (I. Troch; F. Breitenecker (Eds.)), ARGESIM Report No. 30, Vienna, 2006, ISBN 3-901608-30-3

  3. M. Gerdts: Global Convergence of a Nonsmooth Newton's Method for Control-State Constrained Optimal Control Problems

  4. 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

  5. M. Gerdts, S. Karrenberg, B. Müller-Beßler, G. Stock: Generating Optimal Trajectories for an Automatically Driving Car

Publications

  1. 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

  2. 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

  3. 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, to appear 2006

  4. 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

  5. C. Büskens, M. Gerdts: Differentiability of Consistency Functions for DAE Systems, Journal of Optimization Theory and Applications, 125 (1), pp. 37-61, 2005

  6. 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

  7. 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

  8. M. Gerdts: Gradient evaluation in DAE optimal control problems by sensitivity equations and adjoint equations, PAMM, Vol. 5 (1), p. 43--46, 2005

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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.

  18. 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

  19. 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

  20. 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

  21. 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: Parameter Identification in Higher Index DAE Systems, Technical Report, Department of Mathematics, University of Hamburg, 2005

  2. 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