LAUSR

In this article, the adaptive tracking control problem is investigated for a multibody high-speed train dynamic model in the presence of unknown parameters, which is an open adaptive control problem. A four-car train unit model with input signals acting on the second and third cars and output signals being the speeds of the first and third cars is chosen as a benchmark model, in which the aerodynamic resistance force is also considered. To handle the nonlinear term, the feedback linearization method is employed to decompose the system into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is a Lyapunov stable and is also partially input-to-state stable under the condition that the speed error between the first and third cars is exponentially convergent (to be ensured by a nominal controller) or belongs to the $L^{1}$ signal space (to be achieved by a properly designed adaptive controller). The system configuration leads to a relative degree 1 subsystem and a relative degree 2 subsystem, for which different feedback linearization-based adaptive controllers and their nominal versions are developed to ensure the needed stabilization condition, the desired closed-loop system signal boundedness, and asymptotic output speed tracking. Detailed closed-loop system stability and tracking performance analysis are given for the new control schemes. Simulation results from a realistic train dynamic model are presented to verify the desired adaptive control system performance.