  This paper is concerned with the computing efficiency of model predictive
control (MPC) problems for dynamical systems with both rate and amplitude
constraints on the inputs. Instead of augmenting the decision variables of the
underlying finite-horizon optimal control problem to accommodate the input rate
constraints, we propose to solve this problem using the fast gradient method
(FGM), where the projection step is solved using Dykstra's algorithm. We show
that, relative to the Alternating Direction of Method Multipliers (ADMM), this
approach greatly reduces the computation time while halving the memory usage.
Our algorithm is implemented in C and its performance demonstrated using
several examples.
