  In this paper, we study the convergence properties of an iterative algorithm
for fast nonlinear model predictive control of quasi-linear parameter-varying
systems without inequality constraints. Compared to previous works considering
this algorithm, we contribute conditions under which the iterations are
guaranteed to converge. Furthermore, we show that the algorithm converges to
suboptimal solutions and propose an optimality-preserving variant with
moderately increased computational complexity. Finally, we compare both
variants in terms of quality of solution and computational performance with a
state-of-the-art solver for nonlinear model predictive control in two
simulation benchmarks.
