Tamaddoni, S., Taheri, S., and Ahmadian, M., "Linear Quadratic Game Theory Approach to Optimal Preview Control of Vehicle Lateral Motion," SAE Int. J. Passeng. Cars – Mech. Syst. 4(1):740-748, 2011, doi:10.4271/2011-01-0963.
Vehicle stability is maintained by proper interactions between the driver and vehicle stability control system. While driver describes the desired target path by commanding steering angle and acceleration/deceleration rates, vehicle stability controller tends to stabilize higher dynamics of the vehicle by correcting longitudinal, lateral, and roll accelerations. In this paper, a finite-horizon optimal solution to vehicle stability control is introduced in the presence of driver's dynamical decision making structure. The proposed concept is inspired by Nash strategy for exactly known systems with more than two players, in which driver, commanding steering wheel angle, and vehicle stability controller, applying compensated yaw moment through differential braking strategy, are defined as the dynamic players of the 2-player differential linear quadratic game. The optimal preview feedback gains are obtained, and the resulting controllers are evaluated by the nonlinear vehicle model of CarSim7 for the standard lane change maneuver.