Tube-Based Robust MPC for Two-Timescale Systems Using Reduced-Order Models

A tube-based robust Model Predictive Control (MPC) formulation is presented for systems with slow and fast timescale dynamics. The controller uses a reduced-order model that approximates the slow timescale dynamics and is implemented with a relatively large time step size. By analyzing the error between the full- and reduced-order models, the MPC optimization problem is proven to be recursively feasible and to produce closed-loop trajectories that satisfy state and input constraints. By relating bounds on all model errors to bounds on the change of the input in time, input change bounds are included as decision variables in the MPC problem to achieve a time-varying balance between fast transients with large model error and steady-state operation with zero model error. Zonotopes are used to make the approach practical and a numerical example demonstrates the benefits of optimizing time-varying input change bounds as part of the MPC formulation.