Robust MPC for perturbed nonholonomic vehicle

Abstract

This paper considers the robust model predictive control (RMPC) synthesis for the simultaneous tracking and regulation problem (STRP) of nonholonomic vehicle, which is perturbed by bounded disturbance. Considering the bounded disturbance, a robust positively invariant (RPI) set with a designed admissible controller is first given for the perturbed nonholonomic vehicle, which contributes to the foundation of the RMPC synthesis. Then by extending the “tube-based” approach to the nonholonomic, nonlinear and continuous-time case, we employ the developed RPI set for determining the robust tubes and terminal state region, and construct the optimal control problem. Following the contributed properties of the developed RPI set and extended “tube-based” approach, a robust MPC algorithm is finally proposed with the guarantees of recursive feasibility and robustly exponential convergence, i.e., robustly exponential stability of tracking and regulation errors.