Nonlinear Dynamics

, Volume 93, Issue 3, pp 1201–1217 | Cite as

A constraint-following control for uncertain mechanical systems: given force coupled with constraint force

  • Ruiying Zhao
  • Ye-Hwa Chen
  • Shengjie Jiao
  • Xiyong Ma
Original Paper


A novel constraint-following control for uncertain mechanical systems is proposed. In mechanical systems, certain given forces may arise due to the constraint forces, which means the given forces are coupled with the constraint forces. By using the second-order form of the constraints, the given forces are decoupled explicitly. The uncertainty of the mechanical system is time-varying and bounded. But its bound is unknown. A series of adaptive parameters are invoked to estimate the bound information of the uncertainty in virtue of state feedback. Based on the estimated bound information, a robust control is designed to render the mechanical system an approximate constraint-following. The system performance under the control is guaranteed as uniform boundedness and uniform ultimate boundedness.


Mechanical system Constraint-following Robust control Given force Constraint force 



Ruiying Zhao is supported by the National Natural Science Foundation of China (Grant No. 51605038) and Natural Science Basic Research Plan in Shaanxi Province of China (No. 2017JQ5034). Shengjie Jiao is supported by the National Science and Technology Pillar Program (No. 2015BAF07B08).


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Engineering Laboratory for Highway Maintenance EquipmentChang’an UniversityXi’anPeople’s Republic of China
  2. 2.The George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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