Tracking control of disturbed crowd dynamic system using unit sliding mode control and feedback linearization

  • Wei QinEmail author
  • Baotong Cui
  • Xuyang Lou
Original paper


Based on the conservation law of mass, a distributed parameter system is constructed to describe the disturbed crowd dynamics. To deal with the non-directionality of crowd movement, the free flow speed is considered as a control variable, and the actuation system will guide pedestrians to change their speed and moving direction. Unit sliding mode control is used to eliminate disturbances and stabilize the crowd dynamic system to a reference density. Since the sliding mode control may cause chattering phenomenon, a second-order unit sliding mode controller is designed for the crowd dynamic system. Conditions for stability of the crowd dynamic system with the controllers are established. Finally, numerical examples illustrate the effectiveness of the proposed method.


Disturbed crowd dynamic system Distributed parameter system Tracking control Sliding mode control Feedback linearization 



This research is supported by National Natural Science Foundation of China (Grant No. 61807016), China Postdoctoral Science Foundation (2018M642160) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX17_1460)

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things EngineeringJiangnan UniversityWuxiPeople’s Republic of China

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