Event-Triggered Robust Adaptive Dynamic Programming for Multiplayer Stackelberg-Nash Games of Uncertain Nonlinear...

Area of Science:

• Control Theory
• Game Theory
• Machine Learning

Background:

• Multiplayer Stackelberg-Nash games (MSNGs) involve hierarchical decision-making under uncertainty.
• Controlling uncertain nonlinear systems presents significant challenges in dynamic environments.

Purpose of the Study:

• Develop an event-triggered robust adaptive dynamic programming (ETRADP) algorithm.
• Solve MSNGs for uncertain nonlinear continuous-time systems efficiently.

Main Methods:

• Designed value functions to transform robust control into optimal regulation.
• Employed an online policy iteration algorithm for Hamilton-Jacobi equations.
• Integrated an event-triggered mechanism to reduce computational and communication burdens.
• Utilized critic neural networks for approximate optimal control policies.

Main Results:

• Achieved Stackelberg-Nash equilibrium for MSNGs.
• Demonstrated system stability using Lyapunov's direct method (uniform ultimate boundedness).
• Validated the ETRADP scheme's effectiveness through numerical simulations.

Conclusions:

• The ETRADP algorithm effectively solves MSNGs for uncertain nonlinear systems.
• The event-triggered mechanism enhances efficiency without compromising stability.
• This method provides a robust and computationally feasible approach to complex game theory problems.