Application of contraction theory provides a platform to analyze the exponential stability of nonlinear system. To effective compensate the time-varying parametric uncertainties exist in the longitudinal dynamics of the train, this paper proposes a contraction based saturated adaptive robust control for automatic train operation, which is subject to input limit of actuator. With consideration of actuator saturation, a recently developed robust modification is used to saturate the control input in each step, while the global stability is preserved. The resulting saturated adaptive robust control renders the transformed error enter the predefined region, furthermore, inside the predefined region, the contracting behaviour of closed-loop dynamics is regain and the tracking error exponentially converge to a residual set subsequently. The results of comparative experiments under different control strategies also verify the effectiveness of the proposed saturated adaptive robust control.


Automatic train operation Actuator saturation Contraction theory Adaptive robust control 


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.BeijingChina

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