Off-line RMPC Based on Tube Invariant Set for a Discrete-Time Uncertain System

A new off-line robust model predictive control(RMPC) method based on Tube invariant set is developed for a discrete-time linear uncertain system with input and state constraints.Firstly,an improved off-line model predictive control(MPC) algorithm with polytopic invariant sets is designed for a LTI(linear time invariant) system with input and state constraints,and then its stability is proved.Secondly,for the real uncertain system with bounded unknown disturbances,the Tube invariant set strategy is introduced;and then by designing the optimal control sequence and state trajectory for the corresponding nominal system,the control law for the real uncertain system,which is so-called off-line RMPC based on Tube invariant set,is presented to guarantee the real uncertain system processing robustly asymptotic stability and converging into the terminal disturbance invariant set.The simulation results prove the availability of the proposed method.