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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.

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.