Longitudinal modeling and velocity control of autonomous electric vehicles with energy optimization using non-linear autoregressive model with exogenous inputs (NLARX) system identification method

• A novel NLARX longitudinal vehicle modeling strategy trained and tested with high-fidelity simulation data derived from the MATLAB vehicle dynamics blockset under the Urban Dynamometer Driving Schedule (UDDS) drive cycle was presented. • The structured regressor form of NLARX is combined with the flexibility of a wavelet based non-linear function, providing the efficient modelization of high order longitudinal dynamics with moderate data requirements. • A systematic benchmarking study against two competing modeling paradigms: a third-order transfer function and a LSTM network, using standardized fit percentage and root mean squared error (RMSE) metrics for quantitative comparison were carried out. • A PID based velocity tracking controller, optimized using the continuous oscillation technique, is also designed and implemented to verify closed loop behavior under differing road conditions. • The proposed model is rigorously tested through independent training and validation splits, with residual analysis performed to verify accuracy and robustness, establishing its potential for real-time autonomous vehicle control. Precise modeling and control of vehicle longitudinal dynamics are critical to guaranteeing the safety, efficiency, and real time performance of autonomous electrical driving systems. This paper suggests a non-linear autoregressive model with exogenous inputs (NLARX) for longitudinal velocity estimation. MATLAB vehicle dynamics blockset was used to generate high fidelity simulation data for three degrees of freedom dual track configuration of the Urban Dynamometer Driving Schedule (UDDS) drive cycle. The suggested framework combines five input states, i.e., tyre forces and steering commands, and three output states, thus allowing detailed capture of dynamic interaction. Validation results demonstrate a substantial improvement in predictive accuracy compared with a long short term memory (LSTM) network and a third order transfer function model indicate superior accuracy of the NLARX model with highest fit percentage and lowest root mean square error (RMSE). For longitudinal velocity, the NLARX model achieved a fit of 99.01% with an RMSE of 0.0552 m/s, compared to 78.29% (0.1967 m/s) for LSTM and 69.30% (0.5820 m/s) for the transfer function model. Averaged over all three outputs, the NLARX attained 98.54% fit with an average RMSE of 0.0333, significantly outperforming LSTM ( 80.49%, 0.2114 ) and the transfer-function model (67.54%, 1.5170 m/s). Frequency domain analysis further confirmed smooth gain and phase characteristics of the NLARX model, indicating superior bandwidth suitability and dynamic consistency. A PID velocity tracking controller, optimized through the continuous oscillation method, was applied and tested for various road grade conditions, showing negligible overshoot, zero steady state error, and robust tracking performance. Frequency domain analysis also provided further evidence of model stability and bandwidth suitability for real time implementation. The suggested NLARX based approach thus bring forth a twofold benefit such that it offers enhanced tracking performance and energy efficient operation, which is of utmost concern to electric power and energy networks.