Adaptive Super-Twisting Kernel Dynamic Programming: Energy Optimal and Robust Theory Application for Pursuit-Evasion Game System

This study focuses on the issues of energy optimal control and uncertain disturbance rejection in multi satellite pursuit-evasion zero-sum games involving non cooperative space targets. An Adaptive Super-Twisting Kernel Dynamic Programming (ASTKDP) method is proposed to realize fixed-time pursuit-evasion control of non-cooperative targets. The core innovation of this method resides in the integration of Kernel Adaptive Dynamic Programming (KADP) and Adaptive Super-Twisting Sliding Mode (ASTSM) within a finite-time domain. Specifically, KADP is incorporated to completely eliminate the manually designed feature processing procedure, thereby overcoming the feature selection bottleneck inherent in traditional neural network-based approximate dynamic programming methods. Meanwhile, ASTSM essentially suppresses sliding mode chattering and significantly mitigates the adverse effects of unknown bounded disturbances on the system. Performance validation results demonstrate that, in comparison with the Neural Network Adaptive Dynamic Programming (NNADP) method, the proposed ASTKDP reduces energy consumption in the x, y, and z directions by over 30%. Furthermore, under scenarios with uncertain disturbances, it can stably guarantee that the terminal relative distance satisfies the preset constraint requirements.