  This paper proposes a parallelizable algorithm for linear-quadratic model
predictive control (MPC) problems with state and input constraints. The
algorithm itself is based on a parallel MPC scheme that has originally been
designed for systems with input constraints. In this context, one contribution
of this paper is the construction of time-varying yet separable constraint
margins ensuring recursive feasibility and asymptotic stability of sub-optimal
parallel MPC in a general setting, which also includes state constraints.
Moreover, it is shown how to tradeoff online run-time guarantees versus the
conservatism that is introduced by the tightened state constraints. The
corresponding performance of the proposed method as well as the cost of the
recursive feasibility guarantees is analyzed in the context of controlling a
large-scale mechatronic system. This is illustrated by numerical experiments
for a large-scale control system with more than 100 states and 60 control
inputs leading to run-times in the millisecond range.
