Tamaddoni, S., Taheri, S., and Ahmadian, M., "Robust Optimal Control of Vehicle Lateral Motion with Driver-in-the-Loop," SAE Technical Paper 2012-01-1903, 2012, doi:10.4271/2012-01-1903.
Dynamic “Game Theory” brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In previous studies, it was shown that vehicle stability can be represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the vehicle stability controller (VSC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the VSC command is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion. This study focus on the uncertainty in the inputs, and more specifically, the driver's steering input. A robust control strategy based on Integral Sliding Mode control is proposed to make the optimal controller robust to disturbances in the steering angles. The resultant robust optimal controller is evaluated in a lane change maneuver, and the optimal set of steering angle and corrective yaw moment as a part of vehicle stability control system is calculated. Simulation results show that the optimal control algorithm can robustly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability when the uncertainty in the driver's steering action is bounded.