  Model predictive control allows solving complex control tasks with control
and state constraints. However, an optimal control problem must be solved in
real-time to predict the future system behavior, which is hardly possible on
embedded hardware. To solve this problem, this paper proposes to compute a
sequence of one-step optimizations aided by pre-computed inner approximations
of reachable sets rather than solving the full-horizon optimal control problem
at once. This feature can be used to virtually predict the future system
behavior with a low computational footprint. Proofs for recursive feasibility
and for the sufficient conditions for asymptotic stability under mild
assumptions are given. The presented approach is demonstrated in simulation for
functional verification.
