Robust Model Predictive Control with Temporally-Uncertain Disturbance Preview Information

A Model Predictive Control (MPC) formulation is presented for systems with time-varying disturbances corresponding to an unknown but bounded time-shift of known nominal disturbance trajectories. Specifically, at each time step the true system disturbance is assumed to lie within a bounded time window of the known nominal disturbance trajectory. Through a time-varying constraint tightening approach, the MPC formulation is designed to be robust to a combination of the time-shifted nominal disturbance and a more conventional bounded unknown additive disturbance. Assuming finite-time system operation, a shrinking horizon formulation is presented for when the controller always predicts to the end of the operation, and a receding horizon formulation is presented to enable the use of a shorter prediction horizon. Constraint satisfaction is guaranteed in the receding horizon formulation through the use of wayset-based terminal constraints, which are computed offline using constrained zonotopes to achieve computational efficiency and scalability. Numerical results demonstrate the robustness and low degree of conservatism of the approach along with the computational benefits of a receding horizon formulation using waysets.