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Adaptive neural network control for uncertain dual switching nonlinear systems.

Qianqian Mu1,2, Fei Long3, Lipo Mo4

  • 1College of Big Data and Information Engineering, Guizhou University, Guiyang, 550025, Guizhou, China. xtqqian@163.com.

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This study introduces a novel adaptive controller for dual switching systems with uncertainties. The new method ensures global asymptotic stability almost surely and exponential stability almost surely for nonlinear error systems.

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Adaptive Control Theory

Background:

  • Dual switching systems combine deterministic and stochastic elements, presenting unique control challenges.
  • Research on uncertain dual switching systems is limited due to their inherent complexity.
  • Markov jump systems are commonly used to model stochastic subsystems.

Purpose of the Study:

  • To develop an adaptive neural network controller for uncertain dual switching systems.
  • To investigate the global asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of these systems.
  • To minimize tracking errors in dual switching nonlinear error systems.

Main Methods:

  • Radial Basis Function (RBF) neural networks were employed to model uncertain subsystems.
  • A neural network adaptive controller was designed using energy attenuation theory and Lyapunov functions.
  • The approximation error of uncertain functions was controlled to be below 0.05.

Main Results:

  • The designed adaptive controller and switching rules effectively stabilized the dual switching nonlinear error system.
  • The approximation error for uncertain functions was successfully bounded.
  • The error system demonstrated a good convergence rate and significantly reduced tracking errors.

Conclusions:

  • The proposed RBF neural network-based adaptive control strategy is effective for uncertain dual switching systems.
  • The controller ensures desirable stability properties (GAS a.s. and ES a.s.).
  • The approach significantly improves tracking performance compared to the original uncertain system.