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This study investigates the problem of vehicle exploitation in the mountainous and wooded regions of the Russian Federation. Considering how critical rollover accidents are in the logging industry, it is vital to ensure safe and stable driving. This study aims to develop a model of electric power steering (EPS) control using a quasi-continuous sliding-mode controller in MATLAB/Simulink. Experiments were carried out under the following conditions: maximum slope angle, 30°; maximum steering angle, 30°; maximum driving speed, 7 m/s. The dynamic characteristics of the suspension and EPS systems were optimized using the receding horizon optimization technique. The theoretical and experimental results suggest that the model reaches its critical state of stability (−0.2) at a speed range of 0–7 m/s with a steering angle of 25°. After optimization, critical stability (0.3) occurs at the driving speed of 7 m/s when the steering angle is 30°. The paper discussed the possibility of installing the EPS control system into vehicles that operate in mountainous wooded areas.