Tube-based MPC for Two-Timescale Discrete-Time Nonlinear Processes with Robust Control Contraction Metrics*

A computationally efficient model predictive control scheme is proposed for constrained nonlinear processes with inherent slow and fast dynamics. Specifically, the nonlinear process is approximated by a surrogate model, whose slow state is sampled with a larger time interval than the fast one. This reduces optimization variables and, on the other hand, introduces prediction errors and henceforth may induce constraint violation without further treatments. To mitigate these issues, we tighten constraints by leveraging Robust Control Contraction Metrics. Furthermore, a back-up strategy is employed to ensure feasibility over time. The numerical efficiency of this proposed scheme is illustrated with a crops growth process, e.g., in indoor farming.