I-Steps Closed-Loop Sets for Constrained Linear Systems Under Model Predictive Control

The understanding of invariant set theory is essential in the design of controllers for constrained systems. This paper presents some concepts related with the invariant set theory and Set-Based Model Predictive Control (set-based MPC). Precisely, introduces a new class of sets from where the closed-loop system reaches a target set before a pre-established number of steps. These novel concepts are based on several results presented in a former work [1]. The main results are exposed in a theoretical context, however several simulation examples show its potential and properties.