Robust Laguerre‐based model predictive control for trajectory tracking of a mobile robot using an linear matrix inequality (LMI)‐based approach

Abstract

Abstract This paper studies the trajectory tracking of a constrained mobile robot under slippery conditions. The goal is to propose a controller for real‐time operations of time‐varying dynamics with insignificant execution time. Therefore, a Laguerre‐based model predictive control (LMPC) is designed, and robustness is provided with an linear matrix inequality (LMI)‐feedback controller. Moreover, a recursive least square (RLS) algorithm with a forgetting factor is utilized to identify the required parameters of the LMI‐based controller. LMPC and LMI‐based controller stability is achieved with suboptimal theory and Lyapunov function, respectively. This algorithm separates the nominal system and introduces new dynamics containing uncertainties. Furthermore, LMPC is removed from the online calculation, which dramatically reduces computation burden and time; consequently, online computation is dedicated to determining the LMI feedback. Simulations are provided to compare the proposed robust controller to its not robust counterpart. Finally, it is demonstrated that this controller diminishes the execution time considerably, making it incomparable to previous robust MPC strategies.