A Nonlinear Finite-Time Robust Differential Game Guidance Law

Area of Science:

• Control Theory
• Robotics
• Artificial Intelligence

Background:

• Nonlinear zero-sum systems are challenging due to unknown dynamics and external disturbances.
• Traditional guidance laws struggle with real-time adaptation and uncertainty.
• Robust control is crucial for reliable system performance in dynamic environments.

Purpose of the Study:

• To develop a robust differential game guidance law for nonlinear zero-sum systems.
• To address unknown system dynamics and external disturbances effectively.
• To ensure system stability and accurate terminal cost satisfaction.

Main Methods:

• Transforming the problem into solving the nonlinear Hamilton-Jacobi-Isaacs equation.
• Utilizing a novel neural network identifier for approximating unknown nonlinear dynamics.
• Employing an online critic neural network for cost function estimation with time-varying activation functions.
• Developing an adaptive weight tuning law with additional terms for stability and terminal cost adherence.
• Applying Lyapunov stability analysis to prove uniform ultimate boundedness.

Main Results:

• The proposed guidance law effectively compensates for external disturbances.
• The neural network identifier accurately approximates unknown system dynamics online.
• The critic neural network successfully estimates the time-varying cost function.
• Simulation results demonstrate the effectiveness of the robust differential game guidance law for nonlinear interception.

Conclusions:

• The developed robust differential game guidance law enhances control performance in nonlinear systems.
• The adaptive neural network approach provides a robust solution for systems with uncertainties.
• The method ensures system stability and accurate interception, validated by simulations.