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Adaptive Backstepping Control Design for Uncertain Non-smooth Strictfeedback Nonlinear Systems with Time-varying Delays

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  • Control Theory and Applications
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Abstract

This paper is concerned with the problem of adaptive neural tracking control for uncertain non-smooth nonlinear time-delay systems with a class of lower triangular form. Based on Filippov’s theory, the bounded stability and asymptotic stability are extended to the ones for the considered systems, which provides the theory foundation for the subsequent adaptive control design. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent system model, based on which, two types of controllers are designed by using adaptive neural network (NN) algorithm. The first designed controller can guarantee the system output to track a target signal with bounded error. In order to achieve asymptotic tracking performance, the other type of controller with proportional-integral(PI) compensator is then proposed. It is also noted that by exploring a novel Lyapunov-Krasovskii functional and designing proper controllers, the singularity problem frequently encountered in adaptive backstepping control methods developed for time-delay nonlinear systems with lower triangular form is avoided in our design approach. Finally, a numerical example is given to show the effectiveness of our proposed control schemes.

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Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Shuo Zhang & Wen-yue Cui

  2. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

    Fuad E. Alsaadi

Authors
  1. Shuo Zhang
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  2. Wen-yue Cui
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  3. Fuad E. Alsaadi
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Corresponding author

Correspondence to Shuo Zhang.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This work was partially supported by the National Natural Science Foundation of China (Grant No.61803071), China Postdoctoral Science Foundation (Grant No.2018M631786), and China State Key Laboratory of Robotics (Grant No.2017-O03).

Shuo Zhang received his Bachelor and Master Studies in Automation Department at Shanghai Jiaotong University. He got his Ph.D. degree in dynamic process modeling and optimization in the Chair of Process Dynamics and Operations at TU Berlin, Germany. He is currently a lecturer in the school of Control Science and Engineering at Dalian University of Technology. He is working in the research field of process simulation, operating strategies, kinetics modeling, and parameter estimation. He is skilled in adaptive algorithms and machine learning methods designed for nonlinear system modeling and identification.

Wen-yue Cui received his Bachelor Study in school of Mechanical engineering at Dalian University of Technology. He is a Master student in the school of Control Science and Engineering at Dalian University of Technology. He is working in the research of process simulation under complex operation conditions and MINLP optimization under uncertainty.

Fuad E. Alsaadi received his B.S. and M.Sc. degrees in electronic and communication from King AbdulAziz University, Jeddah, Saudi Arabia, in 1996 and 2002. He then received his Ph.D. degree in Optical Wireless Communication Systems from the University of Leeds, Leeds, UK, in 2011. Between 1996 and 2005, he worked in Jeddah as a communication instructor in the College of Electronics and Communication. He is currently an assistant professor of the Electrical and Computer Engineering Departement within the Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia. He has research interests in optical systems and networks, signal processing, Synchronization and Systems Design.

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Zhang, S., Cui, Wy. & Alsaadi, F.E. Adaptive Backstepping Control Design for Uncertain Non-smooth Strictfeedback Nonlinear Systems with Time-varying Delays. Int. J. Control Autom. Syst. 17, 2220–2233 (2019). https://doi.org/10.1007/s12555-019-0046-0

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  • DOI: https://doi.org/10.1007/s12555-019-0046-0

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