Differential-game for resource aware approximate optimal control of large-scale nonlinear systems with multiple...

Area of Science:

• Control Theory
• Artificial Intelligence
• Nonlinear Systems

Background:

• Large-scale nonlinear systems present challenges in optimizing performance and computational resource allocation.
• Cooperative control strategies are needed for N-player systems to enhance overall system efficiency.
• Reducing feedback execution frequency is crucial for managing computational load.

Purpose of the Study:

• To develop a unified framework for optimizing both system performance and computational resource usage in N-player nonlinear systems.
• To design cooperative control policies and adaptive sampling intervals for each player.
• To ensure stability and efficient resource utilization through an event-driven approach.

Main Methods:

• Formulation of an optimal control problem as a multi-player differential game.
• Numerical solution of the Hamilton-Jacobi (HJ) equation using event-driven approximate dynamic programming (E-ADP) and artificial neural networks (NNs).
• Employing critic neural networks for approximating the optimal value function with aperiodically available feedback.

Main Results:

• A novel NN control architecture for N-player systems is proposed.
• The approach successfully integrates system performance optimization with reduced feedback execution frequency.
• Stability and Zeno-free behavior of the event-driven sampling scheme are proven using Lyapunov methods.

Conclusions:

• The proposed differential-game based NN control architecture effectively addresses optimal control problems in large-scale nonlinear systems.
• The event-driven E-ADP method provides a robust framework for cooperative control and resource optimization.
• The study demonstrates practical stability and efficient sampling, validated by simulation results.