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A Nonlinear Finite-Time Robust Differential Game Guidance Law.

Axing Xi¹, Yuanli Cai¹

¹School of Automation Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China.

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|September 9, 2022

Summary

This summary is machine-generated.

This study introduces a robust guidance law for nonlinear systems facing unknown dynamics and disturbances. The novel approach ensures system stability and accurate interception using adaptive neural networks and differential game theory.

Keywords:

differential game guidance law neuro-dynamic programming nonlinear system

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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.