Robust Laguerre based model predictive control for trajectory tracking of LTV systems

In this paper, the trajectory tracking of a nonholonomic and linear time-varying (LTV) mobile robot is studied. The slippery surface condition is a source of uncertainty for this constrained mobile robot and is modeled as a bounded additive disturbance. The primary objective is to design a robust model predictive control based on Laguerre functions utilizing the tubes' theory. The system's time-varying dynamic results in generating time-varying tubes and increasing the operation time. To tackle this challenge, some offline calculations are performed to guarantee the control algorithm's real-time operation, ensuring satisfactory performance and stability. Two controllers were designed. In the first case, the designing inputs changed through the execution time, while the other controller was just designed for the specifically chosen dynamic. Illustrative simulations are presented to show the applicability of the proposed method.