Online Parameter Estimation using Physics-Informed Deep Learning for Vehicle Stability Algorithms

Physics-informed deep learning is a popular trend in the modeling and control of dynamical systems. This paper presents a novel method for rapid online identification of vehicle cornering stiffness coefficient, a crucial parameter in vehicle stability control models and control algorithms. The new method enables designers to rapidly identify the vehicle front and rear cornering stiffness parameters so that the controller reference gains can be re-adjusted under varying road and vehicle conditions to improve the reference tracking performance of the control system during operation. The proposed method based on vehicle model-based deep learning is compared to other alternatives such as traditional neural network training and identification, and Pacejka model estimation with regression. Our initial findings show that, in comparison to these classical methods, high fidelity estimations can be done with much smaller data sets simple enough to be obtained from a lane-changing or vehicle overtake maneuver. In order to conduct experiments, and collect sensor data, a custom-built 1:8 scaled test vehicle platform is used real-time wireless networking capabilities. The proposed method is applicable to predict derived vehicle parameters such as the understeering coefficient so it can be used in parallel with conventional MIMO controllers. Our H∞ yaw rate regulation controller test results show that the reference gains updated with the proposed online estimation method improve the tracking performance in both simulations and vehicle experiments.

I. INTRODUCTION

Many modern automatic control applications require parameter identification of the plant model. These identified parameters can be used for the initial controller design, online adjustments and monitoring of the health of the system. Recent developments in data gathering and processing in embedded control systems enable combining modeling and control applications with learning techniques. However, due to the computational complexity, control-oriented neural networks are still difficult to implement in many applications [1]. Additionally, noisy sensor data also make complications to process collected data in a practicable way. To overcome this problem researchers gravitate to the physics-informed deep learning method [2]. There are numerous examples of modeling the plant with learning procedures to increase the fidelity of the control systems. In [3], in order to push the model predictive control’s (MPC) performance to the limits, the learning procedure for modeling is improved in a way that the prediction model ensures the best closed-loop performance. In [4], the performance of data-driven modeling and physical modeling approaches for vehicle lateral-longitudinal dynamics are compared. Results show that the data-driven model bests both linear and non-linear physical models. In [5], an online model-based reinforcement learning method is proposed to identify vehicle linear tire parameters to maximize maneuverability under variable road conditions such as unknown terrain.