Model predictive control of systems with actuator amplitude and rate saturation

We develop a continuous-time model predictive control design procedure for single-input single-output linear systems with actuator amplitude and rate saturation. This design methodology formulates the actuator amplitude and rate saturation problem as an equivalent amplitude saturation problem with system dynamics augmented by rate dynamics. It is shown that the MPC laws have closed-form analytical solution in the limit that the prediction horizon is small. The stability analysis is performed using a Lyapunov function framework which results in a subset of domain of attraction for guaranteed closed-loop stability in the event of actuator amplitude and rate saturation. A numerical example is presented for illustrating the proposed control design methodology