Lane change automation appears to be a fundamental problem of vehicle automated control, especially when the vehicle is driven at high speed. Selected relevant parts of the recent research project are reported in this paper, including literature review, the developed models and control systems, as well as crucial simulation results. In the project, two original models describing the dynamics of the controlled motion of the vehicle were used, verified during the road tests and in the laboratory environment. The first model - fully developed (multi-body, 3D, nonlinear) - was used in simulations as a virtual plant to be controlled. The second model - a simplified reference model of the lateral dynamics of the vehicle (single-body, 2D, linearized) - formed the basis for theoretical analysis, including the synthesis of the algorithm for automatic control. That algorithm was based on the optimal control theory. The algorithm includes the determination of time optimal reference profiles defining control input and vehicle response (the reference steering wheel angle of the "bang-bang" type). Implementation of the prescribed motion trajectory in the control system is made using Kalman regulators ensuring optimal trajectory following in the terms of the linear-quadratic problem. Presented in the paper exemplary simulation results demonstrate the effects of variations of the road surface, vehicle speed, and vehicle loading condition. The results show the complexity of the dynamic properties of the vehicle under study and confirm the benefits of the adopted solutions for vehicle automated control.