Data-Driven Steering Controller Tracks Autonomous Vehicle Paths Within Certified Error Funnels

Researchers have formulated an off-policy reinforcement learning approach that calculates optimal lateral steering control for autonomous vehicles without requiring prior knowledge of the underlying vehicle dynamics. Published in Scientific Reports, the investigation focuses on lateral path tracking when the vehicle’s governing state-space matrices are entirely unknown to the control designer. Rather than relying on standard identification models or complex neural architectures, the system determines an infinite-horizon linear-quadratic optimal steering gain directly from recorded operational measurements. At the same time, the research introduces explicit mathematical certificates that bound tracking deviations and prevent vehicles from wandering outside specified safety envelopes.

The learning mechanism extracts the control law from a single batch of measured vehicle state and steering data using an off-policy policy iteration scheme. This computational structure eliminates several traditional engineering hurdles, as it operates successfully without requiring explicit system matrices, numerical calculations of state derivatives, or the training of function-approximation networks.

A fundamental theoretical contribution of the study demonstrates how this purely data-driven optimization relates to classical control theory. The authors established a formal mathematical proof showing that, under an explicit rank condition verified in the symmetric quadratic basis, the data-driven iteration coincides exactly with Kleinman’s classical model-based policy iteration. This equivalence confirms that the algorithm preserves the reliable convergence properties of model-based methods while depending strictly on collected input-output trajectories rather than pre-identified physical parameters.

To address safety, the investigators developed a prescribed-performance certificate specifically adapted to linear control structures. While traditional prescribed-performance control often relies on nonlinear barrier transformations to constrain vehicle coordinates within designated funnels, the controller deployed in this architecture remains a fixed linear feedback gain. Consequently, the researchers avoided claiming that barrier transformations enforce the tracking envelopes, choosing instead to derive an explicit sufficient per-channel exponential upper bound directly from the modal decomposition of the closed-loop dynamical system.

This analytical performance certificate establishes precise sufficient conditions that directly connect the geometric funnel parameters to the decay margin of the closed loop and the disruptive influence of unmatched road-curvature disturbances. Alongside the lateral error envelope, the theoretical derivation provides an accompanying mathematical bound governing the vehicle’s steering angle, ensuring that trajectory constraints are balanced against realistic limits on actuator demand during automated steering execution.

The control algorithm and its certification framework were tested in detailed computer simulations involving two standard vehicle maneuvers: a thirty-kilometer-per-hour S-turn and an eighty-kilometer-per-hour highway lane change. The numerical results confirmed that the data-derived gain converged within two to six percent of the theoretical model-based Riccati gain. Furthermore, the relative performance gap in nominal linear-quadratic cost remained within three times ten to the negative sixth power, with all lateral error trajectories staying strictly inside the certified performance funnels throughout both maneuvers.

Alongside these positive results, the researchers documented several significant limitations and trade-offs of the methodology. Because the certificate is nominal, a Monte Carlo evaluation introducing variations of plus or minus twenty percent in vehicle speed and plus or minus thirty percent in tire cornering stiffness revealed coverage across two hundred out of two hundred trials in one scenario and one hundred ninety-eight out of two hundred trials in the other. Additionally, the direct data learner proved markedly more sensitive to measurement noise than conventional system identification combined with a Riccati solver, while substantial initial tracking errors saturated the steering actuator, requiring controller retuning at the expense of a wider certified performance funnel.

Subject of Research: Data-driven optimal path tracking control for autonomous vehicles

Article Title: Data-driven LQ-optimal path tracking with prescribed-performance certificates for autonomous vehicles

Article References: Lu, M., Sun, Y., & Wu, M. (2026). Data-driven LQ-optimal path tracking with prescribed-performance certificates for autonomous vehicles. Scientific Reports. https://doi.org/10.1038/s41598-026-75250-4

Image Credits: AI Generated

DOI: 10.1038/s41598-026-75250-4

Keywords: path tracking, autonomous vehicles, linear-quadratic control, policy iteration, prescribed-performance certificates, off-policy learning, Kleinman iteration, least-squares optimization, modal decomposition, Riccati equation, lane change maneuver, S-turn trajectory, road-curvature disturbance, steering actuator saturation, Monte Carlo simulation, cornering stiffness