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Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown

Wenrui Shi1, Mingzhe Hou1, Mingrui Hao2

  • 1Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China.

ISA Transactions
|April 25, 2021
PubMed
Summary

This study introduces a new controller for strict-feedback nonlinear systems with unknown control direction. The controller effectively handles uncertainties and disturbances, achieving asymptotic tracking performance.

Keywords:
Adaptive robust controlAsymptotic tracking controlDynamic surface controlFuzzy logic systemsNussbaum gain technique

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Artificial Intelligence

Background:

  • Strict-feedback nonlinear systems (SFNSs) present challenges due to unknown control directions and uncertainties.
  • Traditional control methods struggle with 'differential explosion' and unknown system parameters.
  • External disturbances further complicate control design for SFNSs.

Purpose of the Study:

  • To develop an asymptotic tracking controller for SFNSs with unknown control direction.
  • To address unknown nonlinear uncertainties and external disturbances simultaneously.
  • To overcome the 'differential explosion' issue inherent in adaptive control design.

Main Methods:

  • Integration of Dynamic Surface Control (DSC) with nonlinear filters to prevent 'differential explosion'.
  • Application of Nussbaum Gain Technique (NGT) to resolve the unknown control direction problem.
  • Utilization of Fuzzy Logic Systems (FLSs) for adaptive control of unknown nonlinearities without prior assumptions.

Main Results:

  • The proposed controller successfully obviates 'differential explosion' using DSC.
  • FLSs effectively manage system uncertainties and approximation errors.
  • The NGT ensures robust performance despite unknown control directions, achieving asymptotic tracking.
  • Validation through simulations on a second-order system and a Norrbin model.

Conclusions:

  • The combined DSC, NGT, and FLS approach provides a unified solution for complex SFNS control problems.
  • This method effectively tackles unknown control direction, 'differential explosion', and system uncertainties.
  • The proposed controller demonstrates feasibility and effectiveness for achieving asymptotic tracking in challenging nonlinear systems.