Continuous-time Nonlinear Robust MPC for Offset-free Tracking of Piece-wise Constant Setpoints with Unknown Disturbance

• Published in: International journal of control, automation, and systems Vol. 20; no. 4; pp. 1063 - 1075
• Main Authors: Zamani, Abbas, Bolandi, Hossein
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.04.2022; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Continuous time systems; Control; Controllers; Cost function; Engineering; Feasibility; Liapunov functions; Mechatronics; Nonlinear systems; Optimization; Predictive control; Regular Papers; Robotics; Robust control; Satellite attitude control; Terminal constraints; Tracking control; Tracking errors; 제어계측공학; recursive feasibility; Continuous-time MPC; nonlinear systems; robust control
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-021-0121-1

This paper develops a novel robust tracking predictive controller for continuous-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbance. The sudden changes in a setpoint and/or existence of disturbance may lead to feasibility and stability issues if a stabilizing terminal constraint-based predictive controller is used. The robust tracking MPC presented in this paper extends the artificial reference-based nonlinear MPC for continuous-time systems and disturbance rejection. Closed-loop input-to-state stability and recursive feasibility of the optimization problem are guaranteed by tightening the terminal region, input constraint, and appropriate terminal cost function. An explicit formula that specifies the bound of sampling time interval is also introduced. We show that the proposed controller can reach an offset-free tracking if the disturbance is slowly time varying. However, in the case of non-slowly varying disturbance, a specific bound on tracking error will be guaranteed using an appropriate disturbance observation error based Lyapunov function. The satellite attitude control system simulation results are provided to show the efficiency of the proposed controller.