  In this paper, we propose a parallel shooting algorithm for solving nonlinear
model predictive control problems using sequential quadratic programming. This
algorithm is built on a two-phase approach where we first test and assess
sequential convergence over many initial trajectories in parallel. However, if
none converge, the algorithm starts varying the Newton step size in parallel
instead. Through this parallel shooting approach, it is expected that the
number of iterations to converge to an optimal solution can be decreased.
Furthermore, the algorithm can be further expanded and accelerated by
implementing it on GPUs. We illustrate the effectiveness of the proposed
Parallel Shooting Sequential Quadratic Programming (PS-SQP) method in some
benchmark examples for nonlinear model predictive control. The developed PS-SQP
parallel solver converges faster on average and especially when significant
nonlinear behaviour is excited in the NMPC horizon.
