Design and Comparison of Optimal Controllers Using Look-Ahead Error in Path Following Problem

Abstract

In this study, linear quadratic regulator (LQR) and linear matrix inequalities (LMI) based optimal controllers that guaranteed the stability of the vehicle are designed and performed in the double lane change problem. The simulation case is created according to a scenario frequently encountered in traffic. It is assumed that since the vehicle is positioned safely in the moving lane and the path following controllers provide double lane change maneuver to avoid the collision possibility. A nonlinear model of the vehicle is created and linearized to design the controller to provide automated steering. In the vehicle model, lateral and heading look-ahead errors are used as state variables and performance indexes are created to minimize them accordingly. While the LQR design is made for both linear time-invariant (LTI) and linear parameter-varying (LPV) models, LMI-based state and output feedback controllers are designed using the linear time-invariant model in a way that aims to minimize the H∞ norm of the system. In the simulation studies, the effect of minimizing the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and H∞ norms on the look-ahead error, as well as the advantages of the LPV model-based controller design compared to the LTI design, are examined.