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Summary

This study introduces an artificial neural network (ANN) controller for finite-horizon optimization problems with system uncertainties. The ANN controller ensures practical stability and effectively handles perturbations, offering a robust sub-optimal solution.

Keywords:
Approximate dynamic-programmingArtificial neural networksBellman functionHamilton–Jacobi–Bellman equationSub-optimal controller

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Area of Science:

  • Control Systems Engineering
  • Artificial Intelligence
  • Optimization Theory

Background:

  • Finite-horizon optimization problems are crucial for control systems.
  • Systems often face uncertainties, including modeling errors and external perturbations.
  • Existing methods may struggle with complex dynamics and uncertainties.

Purpose of the Study:

  • To design an artificial neural network (ANN) based sub-optimal controller.
  • To address finite-horizon optimization for systems with uncertainties.
  • To develop an adaptive control law for the ANN weights.

Main Methods:

  • Utilized dynamic neural programming for an approximate solution.
  • Employed an ANN to approximate the Value function and HJB equation solution.
  • Applied Lyapunov stability theory to confirm system stability.

Main Results:

  • Developed an explicit adaptive law for ANN weights.
  • Demonstrated practical stability of the equilibrium point.
  • Simulations confirmed the controller's effectiveness in handling perturbations.

Conclusions:

  • The ANN-based controller provides a viable sub-optimal solution for uncertain systems.
  • The approach ensures practical stability and robustness against disturbances.
  • The method offers an effective way to approximate solutions to HJB equations.