Stability analysis and motion control of autonomous vehicles under nonlinear disturbances on low-friction surfaces

This study focuses on the motion control problem of autonomous vehicles operating on low-friction surfaces under nonlinear disturbances. Under such conditions, the vehicle system is highly prone to instability. Thus, stability analysis and control study need to be carried out. Based on Lyapunov stability theory and incorporating tangent direction difference information, a predictive dynamic stability envelope region is constructed, which, for the first time, reveals relationship among vehicle instability risk, velocity, road adhesion coefficient, and curvature. This predictive region provides a theoretical foundation for proactive controller intervention to prevent vehicle instability. To mitigate the effects of unknown nonlinear disturbances, an adaptive disturbance-rejection controller is developed within the nonlinear model predictive control framework. Specifically, a Random Projection Neural Network-based error estimator is employed, whose weights are continuously updated by the designed adaptive weight update law, enabling real-time compensation of uncertainties in the control loop. Owing to the designed adaptive update law, the proposed estimator effectively reduces the adverse impact of model uncertainties while ensuring closed-loop stability, thereby improving trajectory tracking performance. To further ensure real-time requirement, a numerical solution algorithm is proposed, which integrates the continuation method with the Nelder–Mead method. This approach enhances computational efficiency by reducing the dimensionality of the optimization variables. Finally, the proposed controller is validated through both simulations and experiments. The results demonstrate that the controller can maintain vehicle stability and decrease tracking errors while satisfying the real-time requirements.