Tube model predictive control for a class of nonlinear discrete-time systems

Hashem Imani Marrani,Samane Fazeli,Hasan Hosseinzadeh,Hamid Malekizade,Yuanyuan Zou

doi:10.1080/23311916.2019.1629055

Abstract

This paper signifies a tube model predictive control for discrete time uncertain nonlinear systems in the presence of bounded disturbances. The problem of obtaining robustness against parametric un...

Highlights

Model predictive control (MPC) is one of the typical control methods for large-scale, constrained nonlinear systems in process industry (Qin & Badgwell, 2003)
A popular method for handling system uncertainties and disturbances is to develop Robust Model Predictive Control (RMPC) schemes which optimize over feasible state feedback control policies
One way is to rely on the inherent robustness properties of nominally stabilizing MPC algorithms, as it was done in the work by Grimm, Messina, Tuna, & Teel (2003); Limon, Alamo, & Camacho (2002a); Magni, De Nicolao, & Scattolini (1998); Scokaert, Rawlings, & Meadows (1997)

Summary

Introduction

Model predictive control (MPC) is one of the typical control methods for large-scale, constrained nonlinear systems in process industry (Qin & Badgwell, 2003). One way is to rely on the inherent robustness properties of nominally stabilizing MPC algorithms, as it was done in the work by Grimm, Messina, Tuna, & Teel (2003); Limon, Alamo, & Camacho (2002a); Magni, De Nicolao, & Scattolini (1998); Scokaert, Rawlings, & Meadows (1997) Another approach is to incorporate knowledge about the disturbances in the MPC problem formulation via open-loop worst case scenarios. The proposed tube MPC uses H1 control approach for solving an ancillary MPC problem, which serves to contain the trajectories of the actual system in a tube around the nominal trajectory This tube-based robust MPC algorithm can deal with bounded disturbances and uncertainties which provides a strong guarantee of robust stability. Control signal has two components: a nominal controller obtained from online optimization problem subject to nominal dynamics and ancillary controller which aims at steering the trajectories of the error system (13) to the origin, i.e. the trajectory of system (1) to the nominal trajectories

Nominal controller design

Ancillary controller design

Conclusion