Near-Optimal Control for Nonzero-Sum Differential Games of Continuous-Time Nonlinear Systems Using Single-Network ADP

Area of Science:

• Control Theory
• Game Theory
• Artificial Intelligence

Background:

• Nonzero-sum differential games present complex control challenges for nonlinear systems.
• Traditional adaptive dynamic programming (ADP) often requires dual networks (actor-critic) and initial stabilizing policies.

Purpose of the Study:

• To develop a near-optimal control scheme for continuous-time nonlinear systems facing nonzero-sum differential games.
• To simplify ADP by using a single critic network per player.
• To ensure system stability and convergence to Nash equilibrium without requiring initial stabilizing controls.

Main Methods:

• Utilizing a single-network adaptive dynamic programming (ADP) architecture.
• Developing novel weight tuning laws for critic neural networks.
• Applying Lyapunov theory to prove uniform ultimate boundedness of the closed-loop system.

Main Results:

• The proposed control scheme effectively reaches the Nash equilibrium for nonzero-sum differential games.
• The novel tuning laws guarantee system stability.
• The method demonstrates effectiveness in simulations without needing initial stabilizing control policies.

Conclusions:

• The single-network ADP approach offers an efficient and stable solution for controlling nonlinear systems in differential games.
• This method simplifies ADP implementation while ensuring robust performance and stability.
• The findings contribute to advancements in intelligent control for complex dynamic systems.