  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
ill-conditioned, 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.
