Fast numerical methods for mixed-integer nonlinear model-predictive control. The author develops and investigates efficient numerical methods for nonlinear mixed-integer optimal control and model-predictive control problems. His thesis presents a lot of novel results and tools in a number of areas. New algorithms based on Bock’s direct multiple shooting method consist of convexification and relaxation techniques and a real-time iteration scheme. A proof of local contractivity under reasonable assumptions is given. The obtained nonlinear programs are treated as mathematical programs with vanishing constraints. The author develops and describes new tools for solving the arising nonconvex quadratic subproblems such as a new parametric active set method based on strong stationarity, a block structured factorization, and new matrix update techniques for this factorization. All developed algorithms are implemented in two software packages MuShROOM and qpHPSC and their efficiency is demonstrated on several applications, especially on a real-time predictive cruise control problem.

References in zbMATH (referenced in 15 articles )

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  1. Göttlich, Simone; Hante, Falk M.; Potschka, Andreas; Schewe, Lars: Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints (2021)
  2. Liu, Zhe; Li, Shurong: A quantum computing based numerical method for solving mixed-integer optimal control problems (2021)
  3. Liu, Zhe; Li, Shurong; Zhao, Kai: Extended multi-interval Legendre-Gauss-Radau pseudospectral method for mixed-integer optimal control problem in engineering (2021)
  4. Sager, Sebastian; Zeile, Clemens: On mixed-integer optimal control with constrained total variation of the integer control (2021)
  5. Thinh, V. D.; Chuong, T. D.; Anh, N. L. H.: Second order variational analysis of disjunctive constraint sets and its applications to optimization problems (2021)
  6. Zeile, Clemens; Robuschi, Nicolò; Sager, Sebastian: Mixed-integer optimal control under minimum dwell time constraints (2021)
  7. Jäkle, Christian; Volkwein, Stefan: POD-based mixed-integer optimal control of evolution systems (2020)
  8. Kirches, C.; Lenders, F.; Manns, P.: Approximation properties and tight bounds for constrained mixed-integer optimal control (2020)
  9. Andersson, Joel A. E.; Gillis, Joris; Horn, Greg; Rawlings, James B.; Diehl, Moritz: CasADi: a software framework for nonlinear optimization and optimal control (2019)
  10. Jung, Michael N.; Kirches, Christian; Sager, Sebastian; Sass, Susanne: Computational approaches for mixed integer optimal control problems with indicator constraints (2018)
  11. Herceg, M.; Jones, C. N.; Morari, M.: Dominant speed factors of active set methods for fast MPC (2015)
  12. Palagachev, Konstantin; Gerdts, Matthias: Mathematical programs with blocks of vanishing constraints arising in discretized mixed-integer optimal control problems (2015)
  13. Schwickart, T.; Voos, H.; Hadji-Minaglou, J.-R.; Darouach, M.; Rosich, A.: Design and simulation of a real-time implementable energy-efficient model-predictive cruise controller for electric vehicles (2015)
  14. Kirches, Christian; Leyffer, Sven: TACO: a toolkit for AMPL control optimization (2013)
  15. Kirches, Christian: Fast numerical methods for mixed-integer nonlinear model-predictive control (2011)