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Adaptive discrete-time neural prescribed performance control: A safe control approach.

Zhonghua Wu1, Bo Huang1, Xiangwei Bu2

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Neural Networks : the Official Journal of the International Neural Network Society
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Summary

This study introduces a novel adaptive switching control for discrete-time nonlinear systems, overcoming input saturation and initial condition limitations in prescribed performance control (PPC). The new method ensures stability and finite-time convergence, even with arbitrary initial values.

Keywords:
Adaptive backstepping controlDiscrete-timeInput saturationNeural networksPrescribed performance control

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Discrete-Time Systems

Background:

  • Existing prescribed performance control (PPC) primarily addresses continuous-time systems.
  • Challenges include input saturation and initial condition limitations in discrete-time nonlinear systems.
  • Singular problems arise in PPC when input saturation is present.

Purpose of the Study:

  • To develop a novel adaptive switching control strategy for discrete-time nonlinear systems.
  • To address input saturation and initial condition limitations within the PPC framework.
  • To release initial condition constraints under PPC.

Main Methods:

  • Devised a new discrete-time global finite-time performance function (DTGFTPF) to ensure performance boundaries are insensitive to initial values.
  • Constructed a discrete-time adaptive finite-time prescribed performance controller (DTAFPPC) for finite-time tracking error convergence.
  • Developed a discrete-time adaptive backstepping controller (DTABC) to handle input saturation and prevent instability.
  • Integrated current error values into controllers and adaptive update laws to overcome non-causal issues in backstepping.

Main Results:

  • The DTGFTPF ensures performance boundaries are independent of arbitrary initial system values.
  • The DTAFPPC guarantees tracking errors converge within finite time and predefined bounds.
  • The DTABC maintains system stability during input saturation, allowing temporary excursions beyond performance bounds.
  • Lyapunov analysis and simulations confirm the closed-loop system's stability.

Conclusions:

  • The proposed adaptive switching control strategy effectively handles discrete-time nonlinear systems with input saturation and initial condition variations.
  • The controller ensures finite-time prescribed performance and overall system stability.
  • The approach relaxes limitations of existing PPC methods for discrete-time systems.