  This paper deals with the development and analysis of novel time-optimal
point-to-point model predictive control concepts for nonlinear systems. Recent
approaches in the literature apply a time transformation, however, which do not
maintain recursive feasibility for piecewise constant control parameterization.
The key idea in this paper is to introduce uniform grids with variable
discretization. A shrinking-horizon grid adaptation scheme ensures convergence
to a specific region around the target state and recursive feasibility. The
size of the region is configurable by design parameters. This facilitates the
systematic dual-mode design for quasi-time-optimal control to restore
asymptotic stability and establish a smooth stabilization. Two nonlinear
program formulations with different sparsity patterns are introduced to realize
and implement the underlying optimal control problem. For a class of numerical
integration schemes, even nominal asymptotic stability and true time-optimality
are achieved without dual-mode. A comparative analysis as well as experimental
results demonstrate the effectiveness of the proposed techniques.
