Title: Extended linear quadratic regulator control and its application in trajectory following control of autonomous vehicles

Authors: Jianwei Wu; Lin Chen; Yang Zhou; Beibei Sun

Addresses: School of Mechanical Engineering, Southeast University, Nanjing 211189, China; School of Mechanical and Electrical Engineering, Guilin University of Electronic and Technology, Guilin 541004, China ' School of Mechanical Engineering, Southeast University, Nanjing 211189, China ' School of Mechanical Engineering, Southeast University, Nanjing 211189, China ' School of Mechanical Engineering, Southeast University, Nanjing 211189, China

Abstract: Due to the limitation that the linear quadratic regulator (LQR) method cannot consider the weight of input rate, we propose an extended linear quadratic regulator (ELQR) method, and further extend the application of the LQR. Considering that the standard Riccati equation cannot be obtained after adding the weight term of input rate in the quadratic performance index, it cannot be solved by the traditional matrix algebra equation method. Therefore, an optimisation model is constructed, and is solved by the genetic algorithm. A simulation example from the trajectory following control for autonomous vehicles, which need to consider the limitations on the angular velocity of front steering to ensure safe driving, is given to illustrate the effectiveness of the ELQR in this paper. The results show that both the LQR and ELQR can achieve the expected control effects. Compared with the LQR, the ELQR considering the weight of input rate has obvious advantages, which avoids exceeding the limitations on the angular velocity of front steering and thus improves safety and comfort of driving.

Keywords: extended linear quadratic regulator; ELQR; linear quadratic regulator; LQR; weight of input rate; genetic algorithm; algebraic Riccati equation.

DOI: 10.1504/IJMIC.2023.130127

International Journal of Modelling, Identification and Control, 2023 Vol.42 No.3, pp.241 - 250

Received: 12 Dec 2021
Received in revised form: 02 Apr 2022
Accepted: 29 Apr 2022
Published online: 05 Apr 2023 *

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