Robustness analysis on constrained model predictive control for nonholonomic vehicle regulation

A primary concern for nonlinear model predictive control (NMPC) strategies is the evaluation of their control performance, especially robustness. Many researchers show the existence of robustness as a byproduct of stability which is achieved by monotonicity of the cost function. However the design of a control architecture within the MPC frame and the analysis of its robustness to additive uncertainties are far from well solved together as a complete topic. The robust analysis is even more difficult when more than one control values from the optimal control sequence are applied to real systems. In this paper, a general stability condition is proposed to design a NMPC control strategy for a constrained discrete time system. Furthermore, a robustness analysis is also provided for the designed MPC control architecture. Under the proposed stability condition, an admissible invariant set for the nominal system and a terminal constraint set are defined for the MPC regulator. These compact sets make it possible to analyze the bound for additive uncertainties so that the closed-loop system is input-to-state stable with relation to additive uncertainties under this given bound.