Koopman operator theory is a kind of data-driven modeling approach that accurately captures the nonlinearities of mechatronic systems such as vehicles against physics-based methods. However, the infinite-dimensional Koopman operator is impossible to implement in real-world applications. To approximate the infinite-dimensional Koopman operator through collection dataset rather than manual trial and error, we adopt deep neural networks (DNNs) to extract basis functions by offline training and map the nonlinearities of vehicle planar dynamics into a linear form in the lifted space. Besides, the effects of the dimensions of basis functions on the model accuracy are explored. Furthermore, the extended state observer (ESO) is introduced to online estimate the total disturbance in the lifted space and compensate for the modeling errors and residuals of the learned deep Koopman (DK) operator while also improving its generalization. Then, the proposed model is applied to predict vehicle states within prediction horizons and later formulates the constrained finite-time optimization problem of model predictive control (MPC), i.e., ESO-DKMPC. In terms of the trajectory tracking of autonomous vehicles, the ESO-DKMPC generates the wheel steering angle to govern lateral motions based on the decoupling control structure. The various conditions under the double-lane change scenarios are built on the CarSim/Simulink co-simulation platform, and extensive comparisons are conducted with the linear MPC (LMPC) and nonlinear MPC (NMPC) informed by the physics-based model. The results indicate that the proposed ESO-DKMPC has better tracking performance and moderate efficacy both within linear and nonlinear regions.

Featuring the fast response and flexibility in control allocation, an electric vehicle with in-wheel motors is a good platform for implementing advanced vehicle dynamics control. Among many active safety functions of an in-wheel motor driven vehicle (IMDV), lateral stability control is a key technology, which can be realized through torque vectoring. To further advance the lateral stabilization performance of the IMDV, in this article a novel data-driven nonlinear model predictive control (NMPC) is proposed based the recurrent high-order neural network (RHONN) modelling method. First, the new RHONN model is developed to represent vehicle’s nonlinear dynamic behaviors. Different from the conventional physics-based modelling method, the RHONN model forms high-order polynomials by neuron states to feature nonlinear dynamics. Based on the RHONN model, the steady-state responses of vehicle’s yaw rate and sideslip angle are iteratively optimized and set as the control objectives for low-level controller, aiming to improve the system robustness. Besides, a nonlinear model predictive controller is designed based on the RHONN, which is expected to improve the prediction accuracy during the receding horizon control. Further, a constrained optimization problem is formulated to derive the required yaw moment for vehicle lateral dynamics stabilization. Finally, the performance of the developed RHONN-based nonlinear MPC is validated on an IMDV in the CarSim/Simulink simulation environment. The validation results show that the developed approach outperforms the conventional method, and further improves the stable margin of the system. It is able to enhance the lateral stabilization performance of the IMDV under various driving scenarios, demonstrating the feasibility and effectiveness of the proposed approach.

High-performance path tracking is a key technology for autonomous vehicles. Feedforward-feedback control architectures are suitable for accurate path tracking with adequate margins of stability. For system modelling in the feedforward component, the learning-based method has been proven to be a promising approach owing to its model-free framework. However, the offline-learned data model trained with collection data is confined by its feature space, resulting in insufficient generalization. As a solution, in this study, we introduce an online learning network – the recurrent high-order neural network (RHONN) – to characterize vehicle behaviors. The RHONN is used to feature vehicle behaviors in a timely manner with a high fidelity and flexible form. The equilibrium at the preview point on the desired path is found based on the online-identified RHONN model, and its induced steering angle is taken as the feedforward command. For the feedback steering controller, the preview point position-based control law incorporating the steady vehicle sideslip angle is adopted to enhance the stability performance. Finally, in the CarSim/Simulink environment, the performance of the designed RHONN-informed feedforward and feedback controller is validated in two typical scenarios – double-lane change and single-turn. The validation results reveal that the proposed approach offers better tracking accuracy in linear and nonlinear regions than other techniques. More notably, the average execution time (3.55 ms) is less than the sampling frequency of the controller (50 ms), which further confirms the applicability and efficiency of the proposed approach.

Intelligent connected vehicles can perform better decision making and path planning tasks when they obtain the accurate motion state of preceding vehicles. In this article, an event-triggered estimation scheme considering the effects of packet loss and unknown vehicle inertia parameters is proposed for predicting the motion state of the preceding vehicle in vehicle-to-everything communications. First, an event-triggered communication mechanism is employed instead of the traditional periodic wireless communication rules to enable intermittent transmission of preceding vehicle sensor data to the host vehicle. Further based on the obtained sensor data, an event-triggered cubature Kalman filter (ETCKF) is designed for the host vehicle to estimate the motion state of the preceding vehicle. To further improve the robustness of the algorithm against perturbation of model parameters, a strong tracking algorithm is utilized to optimize the ETCKF to form a strong tracking ETCKF (STETCKF). Finally, the experimental results demonstrate that the estimation accuracy of the STETCKF under the communication rate of 7.08% and model parameters perturbation can be comparable to that of the cubature Kalman filter with 100% communication rate.

Modeling of nonlinear behaviors with physical-based models poses challenges. However, Koopman operator maps the original nonlinear system into an infinite-dimensional linear space to achieve global linearization of the nonlinear system through input and output data, which derives an absolute equivalent linear representation of the original state space. Due to the impossibility of implementing the infinite-dimensional Koopman operator, finite-dimensional kernel functions are selected as an approximation. Given its flexible structure and high accuracy, deep learning is initially employed to extract kernel functions from data and acquire a linear evolution dynamic of the autonomous vehicle in the lifted space. Additionally, the control barrier function (CBF) converts the state constraints to the constraints on the input to render safety property. Then, in terms of the lateral stability of the in-wheel motor driven vehicle, the CBF conditions are incorporated with the learned deep Koopman model. Because of the linear fashion of the deep Koopman model, the quadratic programming problem is formulated to generate the applied driving torque with minimal perturbation to the original driving torque as a safety command governor. In the end, to validate the fidelity of the deep Koopman model compared to other mainstream approaches and demonstrate the lateral improvement achieved by the proposed safety command governor, data collection and safety testing scenarios are conducted on a hardware-in-the-loop platform.