Finite-time convergence results in robust model predictive control

Abstract

Robust asymptotic stability (asymptotic attractivity and ϵ-δ stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite-time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite-time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set-based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite-time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.