Two feedback control laws are employed for accurate trajectory following. One of them is the fixed-gain LQR, a classical method that has been used in many works and is also considered in comparison with our control formulations. Contrarily, a new time-varying optimal control law is used by solving the matrix DRE as a backward-time scheme. Finite-Time Linear-Quadratic Tracking (LQT) Finite-time LQT is an optimal control strategy that, rather than over an infinite time horizon, forces a linear system's output to track a prescribed reference curve in the forward direction over a finite period of time. In this way a tracking controller is formulated for an automobile (the ground vehicle) executing turning maneuvers, of which the step lane change-type may serve as an example ('constant radius, constant tangent’) with a front-wheel steering configuration. The analytical and numerical studies demonstrate that the proposed controllers are effective in enhancing the robustness of a classical LQR against model uncertainties and parameter variations. In this work, multiple trajectory options were explored by the controllers, and their simulated performances were systematically compared. The findings demonstrated that the LQT controller exhibited superior capability in following complex trajectories with higher accuracy and efficiency compared to LQR controllers. A critical discussion is also presented on the advantages and limitations associated with each control approach.