Robust Model Predictive Control for Nonlinear Systems With Incremental Control Input Constraints

Abstract

This paper presents a robust model predictive control (RMPC) algorithm for nonlinear discrete-time systems subject to bounded disturbances and incremental control input constraints. To guarantee recursive feasibility, a terminal inequality constraint is integrated into the proposed RMPC algorithm. By employing constraint tightening techniques, we derive an upper bound on admissible disturbances that ensures the input-to-state stability (ISS) for the closed-loop system. The effectiveness of the proposed algorithm is validated through numerical simulations and practical experiments involving the control of a four-wheel mobile robot. The results demonstrate the capability of the proposed method to maintain system stability and optimize control performance in the presence of external disturbances. Note to Practitioners—In practical engineering, the prevalence of external perturbations and the necessity for incremental control input constraints significantly complicate the control system design process. Compared with traditional control methodologies, model predictive control (MPC) is better equipped to address disturbances and constraints, achieving enhanced control accuracy and safety. This paper introduces an enhanced RMPC method specifically designed to control a broad class of nonlinear systems in the presence of disturbances and input constraints. Additionally, we provide insights into the relationship between specific design parameters of the RMPC algorithm and the upper bounds of permissible disturbances, offering practical guidelines for implementation. The proposed method is validated through simulations and practical experiments with a four-wheeled mobile robot. The results confirm that the approach reliably maintains system stability while efficiently optimizing control inputs. Future work will focus on extending the algorithm to potential robotic systems and exploring alternative disturbance-handling methods, such as observer-based and set-membership approaches.