Adaptive Backstepping Dynamic Surface Control Design of a Class of Uncertain Non-lower Triangular Nonlinear Systems

  • Gang SunEmail author
  • Mingxin Wang
  • Sheng Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11555)


An adaptive backstepping control method is developed for a class of uncertain non-lower triangular nonlinear systems by combining techniques of neural network online approximation and dynamic surface control. In the design, adaptive backstepping technique is employed to establish virtual control laws and actual control law recursively. The unknown functions contained in control laws are replaced by neural network online approximators. And dynamic surface control technique is used to eliminate the problem of circular structure of the controller. The results of stability analysis show that all the closed-loop system signals are guaranteed to be uniformly ultimately bounded, and the steady-state tracking error can be made to converge to an arbitrarily small neighborhood of zero by choosing control parameters appropriately. The effectiveness of the proposed approach is demonstrated via a numerical simulation example.


Adaptive backstepping Dynamic surface control (DSC) Neural network (NN) Uncertain non-lower triangular nonlinear systems 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical Science and Energy EngineeringHunan Institute of TechnologyHengyangPeople’s Republic of China
  2. 2.School of Information EngineeringJiangxi University of Science and TechnologyGanzhouPeople’s Republic of China

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