Distributed Finite-Time Prescribed Performance Cooperative Control of Multi-Train System Under Compound Disturbance

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.