  Reducing the computation time of model predictive control (MPC) is important,
especially for systems constrained by many state constraints. In this paper, we
propose a new online constraint removal framework for linear systems, for which
we coin the term constraint-adaptive MPC (ca-MPC). In so-called exact ca-MPC,
we adapt the imposed constraints by removing, at each time-step, a subset of
the state constraints in order to reduce the computational complexity of the
receding-horizon optimal control problem, while ensuring that the closed-loop
behavior is {\em identical} to that of the original MPC law. We also propose an
approximate ca-MPC scheme in which a further reduction of computation time can
be accomplished by a tradeoff with closed-loop performance, while still
preserving recursive feasibility, stability, and constraint satisfaction
properties. The online constraint removal exploits fast backward and forward
reachability computations combined with optimality properties.
