This study focuses on cooperative tracking of multiple high speed trains, an effective way to accommodate rising passenger demand now that train to train communication is mature. A novel distributed adaptive model predictive control algorithm built on multi-point mass model is proposed. Firstly, the cooperative tracking task is recast with individual cars as the smallest nodes, yielding a distributed model predictive control strategy in which each car acts as a control agent. Subsequently, an adaptive weighting matrix is introduced to adjust the weights of multiple control input variables during the rolling optimization of model predictive control, thereby improving control accuracy and reducing tracking error. Furthermore, to accelerate computation, an adaptive prediction horizon scheme is presented that shortens or lengthens the horizon in real time according to the current tracking error. Finally, simulations with three high speed trains demonstrate that the proposed multi-point mass distributed adaptive model predictive control approach is both feasible and stable, highlighting its potential for enhancing cooperative tracking performance of multiple high-speed trains.

A high-speed train (HST) is a physically interconnected underactuated system consisting of both motor cars and trailer cars. During operation, all cars experience varying degrees of aerodynamic resistance, which imparts nonlinear characteristics to each car, posing significant challenges for controller design and stability analysis. Investigating the distributed tracking control problem for underactuated HSTs, where aerodynamic resistance acts on every car, remains a long-standing open problem. The challenge is further compounded when actuator faults are involved. Additionally, accurately obtaining the system parameters for a HST is difficult. To address these challenges, we propose a distributed tracking control approach that does not rely on system parameters, where each motor car uses only its own information, as well as that of the cars in front and behind. In this paper, a new Lyapunov function is innovatively established by incorporating elastic potential energy and relative kinetic energy into its construction. Based on this function, it is rigorously proved that the closed-loop tracking error system remains stable as long as at least one motor car exists, and that the velocity-tracking errors of the motor cars are guaranteed to asymptotically converge to zero. Furthermore, an innovative algorithm is proposed, which effectively reduces the cumulative position-tracking error by adjusting the desired trajectory. Compared with the existing results, the proposed method does not depend on any system parameters, and the resulting closed-loop tracking error system is guaranteed to be stable. Finally, we provide simulations on two HSTs to verify our theoretical results.

This paper presents a novel data-based adaptive control strategy based on feedback linearization to address the asymptotic tracking control problem of position and speed for underactuated high-speed train (HST). The proposed strategy accounts for basic resistances, in-train forces, multiple unknown disturbances, and unknown system parameters. The key contributions of this paper are threefold. First, the proposed strategy eliminates the reliance on exact model parameters by incorporating adaptive mechanism, which is a significant advancement over traditional feedback linearization method. Second, by combining Lyapunov stability theory with a novel output redefinition approach, the stability of the zero dynamics system for underdriven HST is rigorously demonstrated. Third, an improved equivalent control law is introduced, which not only suppresses unknown disturbances automatically but also mitigates severe chattering phenomenon. Simulation on a HST with 2 motor cars and 6 trailer cars is provided for verifying the theoretical results. Simulation results show that the proposed strategy achieves asymptotic tracking of the locomotive to the desired position and speed trajectories as well as ensures the uniformly ultimately bounded stability of the internal dynamics of all trailers.Note to Practitioners—The underactuated high-speed train (HST) system, as a practical engineering system, is characterized by multi-input multi-output, multivariable coupling, and nonlinearity. During the operation of an underactuated HST, the system is inevitably affected by basic resistances, in-train forces, multiple unknown disturbances, and time-varying system parameters. This paper aims to achieve high-precision tracking of the position and speed of underactuated HST under accounting for these factors. The proposed data-based control scheme enhances practicality by applying the feedback linearization combined with adaptive mechanism to deal with the nonlinearity of the underactuated HST. To address the challenges posed by the complex operating environments of HST, adaptive control is introduced. Additionally, an adaptive sliding mode control method is employed to enhance the robustness and fast convergence of the proposed control scheme, while effectively mitigating severe chattering. The simulation results show that the HST can achieve high-precision tracking of the desired position and speed curves in the presence of unknown system parameters and disturbances.

This paper investigates decentralized tracking control problem for a single high-speed train (HST) with unknown aerodynamic resistance, motor faults and disturbances. First, a multiple point-mass model of the HST system, which reflects in-train coupling force between adjacent cars, is derived. It is assumed that the first car of the HST is a motor car, i.e. the car is capable of traction and braking. Next, under the conditions that the bias faults and the disturbances are norm-bounded, a computationally inexpensive decentralized adaptive control method with backstepping technique is developed. Utilizing the information garnered from the adaptive mechanism, the detrimental effects stemming from the aerodynamic resistance and the motor faults can be comprehensively eradicated in the motor cars. Furthermore, a linear matrix inequality technique is introduced to address the in-train coupling forces for ensuring the tracking stability of the trailer cars. It is shown that the resulting closed-loop system is not only stable, but also that the position tracking error and velocity tracking error of the motor cars can asymptotically converge to zero. Compared with the existing results, a computationally inexpensive decentralized adaptive asymptotic tracking control approach is proposed, which requires only one parameter to be updated online adaptively per motor car. Finally, simulation on a HST with 2 motor cars and 6 trailer cars is provided for verifying the theoretical results.

Coupler systems are critical to the secure operation of the high-speed train. For this reason, this paper investigates the tracking control problem for the train under coupler displacement constraints. Firstly, by considering the security constraints and multiple disturbances, a multiple point-mass model of the train containing coupler displacements is established. Then, a disturbance observer is introduced to eliminate the adverse effects of complex disturbances on train operation, thereby improving the train’s anti-disturbance capability. With the help of Lyapunov stability analysis, a new upper bound of observer estimation error is developed. Next, an input compensation signal is designed to address the issues of the coupler constraints and the low control accuracy based on disturbance observer. The state deviations of the train system caused by the disturbances can be almost completely compensated by the input compensation controller. Finally, a sufficient condition is provided to ensure that the coupler constraints are not violated throughout the entire train operation. Even if the couplers are stretched or compressed under the initial condition, the compensation signal could still ensure that the couplers work safely. Simulation experiments confirm that the designed compound controller can ensure the coupler always satisfies the constraint condition and effectively suppresses external disturbances, achieving safe and high-precision tracking control of the train.