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Adaptive dynamic programming-based hierarchical decision-making of non-affine systems.

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Summary

This study introduces an adaptive dynamic programming approach to solve complex multiplayer hierarchical decision-making problems in non-affine systems. The method transforms non-affine systems into an affine form, enabling optimal control strategies for all players.

Keywords:
Adaptive dynamic programmingMultiplayer Stackelberg gameNeural networksNon-affine systems

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Area of Science:

  • Control Theory
  • Artificial Intelligence
  • Systems Engineering

Background:

  • Multiplayer hierarchical decision-making presents challenges for non-affine systems.
  • Existing methods may require complex system transformations or initial control laws.

Purpose of the Study:

  • To develop an adaptive dynamic programming algorithm for solving multiplayer hierarchical decision-making problems in non-affine systems.
  • To transform non-affine systems into an equivalent affine form for simplified control.
  • To model the problem as a Stackelberg game for strategic decision-making.

Main Methods:

  • Constructing an affine augmented system using dynamic feedback and original system dynamics.
  • Modeling the problem as a Stackelberg game with a leader and followers.
  • Utilizing a single critic neural network (NN) to approximate value functions and derive optimal control strategies.
  • Employing Lyapunov theory to ensure system stability and NN weight convergence.
  • Introducing an additional term to the weight update law to eliminate the need for an initial admissible control law.

Main Results:

  • Successfully transformed non-affine multiplayer systems into a general affine form.
  • Developed an optimal control strategy for each player within the Stackelberg game framework.
  • Demonstrated uniform ultimate boundedness of system states and NN weight errors using Lyapunov theory.
  • Validated the algorithm's feasibility and effectiveness through simulation.

Conclusions:

  • The proposed adaptive dynamic programming method effectively solves multiplayer hierarchical decision-making for non-affine systems.
  • The transformation to an affine augmented system simplifies the control problem.
  • The use of a single critic NN and modified weight update law enhances the algorithm's practicality.