Tracking Control Based on Model Predictive Control Using Laguerre Functions With Pole Optimization

Abstract

This paper focused on improving a model predictive control (MPC) using Laguerre functions. This study was conducted to achieve high performance while reducing the computational complexity of MPC for autonomous vehicle tracking control. Previous studies have used a conventional linear time-varying MPC (LTV-CMPC) for the linear time-varying (LTV) vehicle model. For LTV-CMPC, the computational complexity increases exponentially as a predictive horizon and control horizon increase. Real-time implementation of LTV-CMPC with long horizons was difficult due to limited computational resources. For reducing computational complexity, we proposed LTV-MPC using Laguerre functions (LTV-LMPC). Considering the vehicle system, LTV-LMPC used a non-augmented model and described the input rate as Laguerre functions. The proposed LTV-LMPC significantly reduced the number of optimization variables. The number of Laguerre functions and the Laguerre pole determined the performance of the LTV-LMPC. In this study, we derived and proved propositions for analyzing the performance change of LTV-LMPC according to the Laguerre pole. LTV-LMPC with pole optimization (LTV-OLMPC) was proposed based on these propositions. The performance of the proposed algorithm was verified by simulation. The LTV-OLMPC guarantees low computational complexity and high performance.