Chassis control systems play a significant role in achieving the desired vehicle performance and stability during various severe maneuvers. A probabilistic estimation approach by hybridization of optimal robust control and a damped least-square backpropagation based neural networks (NN) is proposed to design a control system for dealing with unknown nonlinear dynamics of a passenger car. To this end, a four-wheel active steering (4WAS) model is employed and a multilayer perceptron (ML) feed-forward backpropagation neural network (FFBPNN) model is developed as an approximator. The optimal robust control is employed to regulate the yaw rate and side-slip angle of the vehicle to follow the desired vehicle response. The developed FFBPNN model is trained to distinguish the nonlinear dynamics of the vehicle and the corresponding optimal feedback gain during a wide range of operating conditions via the state variables. The robustness of the controller is evaluated using Lyapunov stability method. The performance of the proposed controller is analyzed considering the open-loop and closed-loop responses of the nonlinear vehicle model and a sliding mode controller to track the desired yaw rate and side-slip angle responses. The results obtained during severe maneuvers suggest that the proposed control method can substantially enhance the handling and stability performances of the vehicle.