Nonlinear Contractive Model Predictive Control via Polytopic Robust Controllable Sets

A general framework for computing polytopic robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed polytopic robust controllable sets is introduced in this paper. The resulting one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solvers of set inversion and constrained minimax optimization via interval analysis are applied to compute robust controllable sets and one-step control inputs in a reliable way. The computed robust controllable sets are unions of boxes and polytope geometry is applied to approximate a union of boxes innerly by one polytope.