## 6 Conclusions  
In this study, we developed and validated an innovative active guidance control algorithm for IRW vehicles, leveraging the advantages of the MARL algorithm. We constructed a nonlinear dynamic model of a two-a-wide prototype IRW vehicle utilizing SIMPACK MBS software and established a feedback control loop based on the MARL. Within this framework, each independently rotating wheelset is assigned an independent decision-making agent to achieve local control, enabling distributed control strategies through collaboration with all other agents. We modeled the control of IRW vehicles as cooperative Markov games. We propose the PER-MADDPG algorithm based on CTDE, in which the MADDPG allows each agent to optimize its behavior strategy based on the global state through centralized training, and the PER mechanism is used to improve sample efficiency by sorting experiences stored in a SumTree structure according to their TD error. We also designed a reward function and corresponding observation and action spaces to guide the MARL model toward enhancing the running stability and curve-negotiation ability of IRWs. Our  
Figure 11: Test results for the scaled IRW vehicle. (**a**) Lateral displacement of the wheelsets, (**b**) Yaw angle of the wheelsets, (**c**) Control torque of the PMSMs. proposed algorithm demonstrates convergence efficiency and higher final performance during reinforcement training, achieving a stable MARL learning process and surpassing the existing DRL and MARL algorithms. In MBS simulations, the PER-MADDPG algorithm improved the straight-line centering and curve-negotiation capabilities of IRWs while reducing wheel-rail wear compared to the classical model-based control strategy. Furthermore, we constructed a 1:5 scale vehicle based on Iwnicki's similarity laws to test the controller in actual operation and deployed our proposed method on a GPU-based development board for real-time inference. The results of the experiments showed that our method significantly reduced the lateral displacement and yaw angle of the IRWs, with control outputs simultaneously meeting design requirements and avoiding flange-rail collisions, confirming its effectiveness. For the first time, we emphasize the ability of the MARL-based algorithm to adaptively learn railway vehicle dynamics, enhancing the overall steering performance through collaborative interactions among multiple IRW controllers and overcoming challenges in traditional controller designs that consider the nonlinear characteristics of vehicle models and homogenized treatment of IRWs. In addition, the proposed method eliminates the need to observe the entire vehicle's dynamic state, reducing the observation dimensions and communication cost to accelerate the control response speed in practical applications. Nevertheless, our study has several limitations that deserve further investigation. While we established various typical operational scenarios to train MARL agents for IRW guidance control, real-world applications involve additional complexities, such as varying wear levels on wheel tread profiles, deviations in suspension parameters, and track irregularities that could impact controller performance. Further investigations may focus on encompassing a more extensive range of operational scenarios in the learning environment and incorporating advanced machine learning strategies such as domain randomization [28], meta-learning [29], and cross-modal large models [30; 31; 32] to enhance controller robustness. Additionally, this research has focused mainly on lateral dynamic stability; however, an integrated approach that includes MARL with longitudinal characteristics from traction and braking systems is vital for comprehensive control optimization. In the future, we will extend our method to more widely used railway vehicle configurations with two bogies and four wheelsets or other wheelset types, such as the actuated solid-axle wheelset (ASW), instead of confining it to single-bogie vehicles primarily used in urban terms.