Preconditioned continuation model predictive control

    •  Knyazev, A.; Fujii, Y.; Malyshev, A., "Preconditioned Continuation Model Predictive Control", SIAM Conference on Control and Its Applications, DOI: 10.1137/1.9781611974072.15, ISBN: 978-1-61197-407-2, July 2015, pp. 101-108.
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      • @inproceedings{Knyazev2015jul,
      • author = {Knyazev, A. and Fujii, Y. and Malyshev, A.},
      • title = {Preconditioned Continuation Model Predictive Control},
      • booktitle = {SIAM Conference on Control and Its Applications},
      • year = 2015,
      • pages = {101--108},
      • month = jul,
      • doi = {10.1137/1.9781611974072.15},
      • isbn = {978-1-61197-407-2},
      • url = {}
      • }
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Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses the GMRES iterative algorithm to solve a forward difference approximation Ax = b of the Continuation NMPC (CNMPC) equations on every time step. The coefficient matrix A of the linear system is often illconditioned, resulting in poor GMRES convergence, slowing down the on-line computation of the control by CNMPC, and reducing control quality. We adopt CNMPC for challenging minimum-time problems, and improve performance by introducing efficient preconditioning, utilizing parallel computing, and substituting MINRES for GMRES.