Sliding Mode Control of Uncertain Nonlinear Discrete Delayed Time System Using Chebyshev Neural Network

  • Parmendra Singh
  • Vishal GoyalEmail author
  • Vinay Kumar Deolia
  • Tripti Nath Sharma
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 553)


This paper investigates a Chebyshev Neural Network (CNN) sliding mode controller for stabilization of time-delayed version of system with uncertainty and nonlinearity. The nonlinearity in the system is unknown but bounded and has been approximated with the help of CNN. The input delay has been balanced and further converted into regular form and the original system is converted into a delayed free version with the help of Smith Predictor. Now, the predicted states of the system and “Gao’s reaching law” are used to derive the robust control law. Further, to prove the stability analysis Lyapunov–Krasovskii candidates has been chosen according to the proposed system. A numerical example is provided to illustrate the stability of the system in the presence of uncertainty, time delay and nonlinearity.


Chebyshev neural network Sliding mode control Smith predictor 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Parmendra Singh
    • 1
  • Vishal Goyal
    • 1
    Email author
  • Vinay Kumar Deolia
    • 1
  • Tripti Nath Sharma
    • 1
  1. 1.Department of Electronics and Communication EngineeringGLA UniversityMathuraIndia

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