To address the limitation that existing control strategies for multi-train system can only achieve asymptotic stability under the disturbance, and that the tracking errors remain relatively large, this paper proposes a novel distributed cooperative control scheme based on the finite-time prescribed performance method. The scheme enables trains to achieve a consensus on displacement and speed on a finite-time framework, while ensuring that the tracking errors of trains can converge to the prescribed region with the user-defined different thresholds within finite time. The main technical features of the proposed approach lie in that, a novel finite-time prescribed performance function with multilevel threshold is devised to constrain the convergence boundary and settling time for the tracking errors, while an innovative fixed-time disturbance observer is constructed to estimate the unknown compound disturbance. By utilizing the Lyapunov theory, the practical finite-time stability of the closed-loop system is analyzed, and the feasibility and effectiveness of the proposed controller are verified via numerical simulations. Compared with the existing works, the advantages of the control approach are that it can flexibly adjust the tracking errors boundary constraints of the multi-train system during different cooperative control stages, thereby reducing the transient and the steady-state errors, as well as improving estimation accuracy and response speed to compound disturbance.

The repetitiveness prerequisite of iterative learning control has always been the main obstacle to promoting its practical applications. In this article, a novel adaptive iterative learning reliable control scheme is proposed for the nonrepetitive systems with multiple iteration-varying parametric uncertainties, where actuator faults and state delays are considered simultaneously. During the design of the controller, the class- $k_{\infty } $ function is leveraged to dispose of the unmodeled lumps of systems through neural networks, and the transformation of control signals is established to compensate for the negative impact of the inefficient actuator. The technical features of our approach lie in an innovative parametric estimation mechanism that integrates the hyperbolic tangent function and an auxiliary sequence is presented to accommodate the nonrepetitive uncertainties, thus achieving the zero-error convergence of output. As the main merits, the proposed control scheme is promising to manifest better performance and practicality than the existing methods, owing to the weak assumptions on the system dynamics, the little prior knowledge of parametric uncertainties, and the strong learning ability of the controller.

The periodic operation pattern of high-speed train (HST) grants the immense potential for iterative learning control (ILC) approach regulating the displacement and velocity, but the non-repetitive uncertainties caused by carrying loads, random disturbances, etc., may weaken the capability of controller. Further, the typical operating situations of rail transit, e.g., station entrance/exit, slowdown sections, can compress the safety margin of HST, increasing the difficulty of precise tracking. In this paper, an adaptive ILC scheme is proposed for HST subject to the safety constraints, where the unknown iteration-varying parameters and the modeling inaccuracies are handled deliberately. Our technical route could be divided into two phases. The transformation mechanism of tracking errors, that can convert the control problem of constrained systems into an unconstrained form, is first established to guarantee that HST is always located within the safety zone. On this basis, the iterative learning controller is devised through integrating the hyperbolic tangent function and iteration-related sequence, where the neural network is leveraged to approximate the unmodeled lumps. The main innovative features lie in that, the iteration-dependent terms of control system are evolved into the parametric compensation components of controller and the iterative convergence parts, while the nested structure of control law is built to accommodate the iteration-variation of loads. As a result, the proposed approach can theoretically achieve the zero-error tracking of HST in the presence of the non-repetitive uncertainties and safety constraints, which indicates the better performance and practicability than the existing ones.

A novel iterative learning control (ILC) strategy is developed for displacement and velocity tracking control of high-speed trains (HSTs) across all operational phases. In practical operations, HSTs encounter complex nonlinear uncertainties, such as variations in coupler forces and aerodynamic resistance, which are more appropriately characterized by norm-bounded models rather than traditional Lipschitz continuous disturbances. To capture these effects accurately, a multi-particle dynamic model of HSTs with norm-bounded uncertainties is formulated, considering the coupler dynamics, mechanical resistance, and aerodynamic resistance acting upon different carriages. Based on this model, a robust ILC scheme, together with an associated parameter updating law, is designed to ensure precise tracking control despite the presence of nonlinear uncertainties. Furthermore, the classical resetting condition in conventional ILC frameworks is replaced by a practical alignment condition that better reflects the continuous operation characteristics of HSTs. A composite energy function (CEF) is constructed to rigorously prove the convergence of control errors. Real-time hardware-in-the-loop (HIL) simulations are conducted to validate the effectiveness of the proposed method. The proposed strategy achieves effective tracking control and stability across traction, cruising, coasting, and full braking stages.

In this article, an adaptive iterative learning control scheme is presented for a class of nonlinear parametric strict-feedback systems with unknown state delays, aiming to achieve the point-wise tracking of desired trajectory in a finite interval. The appropriate Lyapunov-Krasovskii functions are established to compensate the influence of time-delay uncertainties on the control systems. As the main features, the proposed approach integrates the command filter into the backstepping procedure to avoid the differential explosion problem that may occur with the increase of system order, and introduces the hyperbolic tangent functions into the learning controller to handle the singularity problem thus maintaining the continuity of input signal. The results of theoretical analysis and numerical simulation demonstrate that the tracking errors at the entire period will converge to a compact set along the iteration axis. Compared with the existing works, the proposed control scheme is promising to manifest the better performance and practicability owing to the learning mechanism, the dynamic model, as well as the implementation of controller.

In this article, a novel iterative learning control scheme is proposed for high-speed trains, aiming to track the desired reference displacement and velocity, where the Krasovskii function is constructed to compensate for the negative influence of unknown time-varying speed delays. The main feature of the proposed approach is that the hyperbolic tangent function and the command filter are integrated into the learning controller to overcome the singularity problem that may occur during the control process and relax the requirement for the derivability of the desired velocity. The stability of control system is strictly proved through establishing the composite energy function, and the effectiveness is confirmed via numerical simulations. Compared with the existing works, the merits of the proposed control scheme lie in that more general nonlinear uncertainties are imposed on the dynamic model of train instead of the Lipschitz condition, and the reference acceleration assigned by the railway department is not required.Note to Practitioners—High-speed train always runs periodically on the same railway, e.g., the same tunnels, slopes, and bridges, according to the scheduling plans developed by the railway department. Due to the repetitive operation pattern, the iterative learning control has the prospect of becoming an inherent method for devising the tracking controller of trains. Nevertheless, the unknown speed delays, which are inevitable due to the damping effect of wheel rails, couplers, and so on as well as the disturbance of external environments, may degrade the performance of control system and even cause instability in severe cases. As a result, this article exploits a compensation method to eliminate the effects of unknown delay under the iterative learning control framework, thus guaranteeing the safety of train operation and the comfort of passengers. To enhance the practicability, the hyperbolic tangent function is introduced to keep the continuity of control signal, and the command filter is synthesized to reduce the complexity of controller implementation. Although the stability analysis and numerical simulations have confirmed the feasibility and effectiveness of the proposed scheme, it is still expected to be verified by experiments in the future.

The precise operation control of high-speed trains is pivotal to maintain the safety and efficiency of trains, while the inevitable state delays will seriously attenuate the performance of control system. In this paper, an adaptive iterative learning control (ILC) approach for high-speed trains is presented in the presence of the nonlinearly parameterized uncertainties and multiple unknown state delays, aiming to drive that the displacements and velocities of trains can track the desired reference trajectories. To describe the operational dynamics of trains more realistically, the multi-particle model of trains involving multiple time-varying delays is established by analyzing the aerodynamic resistance, mechanical resistance, and coupler force acting on different cars. The proposed adaptive ILC scheme fully leverages various techniques, e.g., the hyperbolic tangent function, the parameter separation, to cope with the inherent nonlinearities, uncertainties and couplings of system. Specially, to eliminate the negative influence of unknown delays, an appropriate Krasovskii function is integrated into the Lyapunov criterion to devise the learning controller and check the stability of control systems. The novelties of our work lie in that the refinement model and periodical characteristic are simultaneously utilized to improve the practicability and performance of control scheme for the high-speed trains with multiple state delays.

The precise tracking control of high-speed train is an essential prerequisite to ensure the safety and comfort of the train. In this paper, an adaptive iterative learning control (ILC) scheme for the velocity and displacement tracking of high-speed train is proposed to handle the unknown time-varying parameters and lumped uncertainties. The composite energy function (CEF) method is used to analyze the stability of closed-loop system. Since the train usually runs on the same railway periodically, such as the same tunnels, slopes, bridges, etc., ILC is an inherent method for designing the tracking controller that is able to improve the operation performance of train iteratively. To the best of our knowledge, it is the first time that the multi-agent framework and ILC methodology are considered simultaneously in a single train, which can better reveal the coupled characteristic of adjacent cars and impose the repetitive operation pattern of train. The results of numerical simulations show that the tracking performance of the train toward the reference trajectory is significantly improved along with the increase of the number of operations.