A Polynomial Approximation Algorithm for the Adaptive Control of High-Speed Train

The paper investigates the approximation of the complex additional resistance encountered during high-speed train operations and proposes the adaptive driving strategy of high-speed train which adopts polynomial approximation. By analyzing the forces acting on the train, the study employs a polynomial approximation method to adaptively adjust the polynomial variables, enabling real-time modeling and compensation of the unknown additional resistance. Simulation results show that this method effectively handles unknown additional resistance in complex operating environments, improving control accuracy and system stability. The velocity error and displacement error are reduced to the order of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${10}^{-3}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${10}^{-2}$</tex>.