Constructive Approximate Nash Equilibrium for In-Orbit Target Enclosing with Collision Avoidance and Full-state Constraint via Nonzero-Sum Differential Games

Bosong Wei, Xiaokui Yue, Zhiwei Hao, Zongcheng Liu

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for target enclosing task with all constraints above, by integrating the collision threat and maneuver boundaries into a novel nonlinear cost functional, the studied target enclosing problem is described as a nonlinear nonzero-sum differential game. Further, to avoid iterative calculations caused by traditional nonlinear-game-solving methods, an approximate solution which can be constructed directly is designed. Then the approximate Nash equilibrium strategies can be educed by the constructive approximate solution for the proposed nonzero-sum game. Analysis shows that the proposed control strategies can asymptotically approach the exact one and can ensure a zero-error tracking of the enclosing configuration. Simulation results illustrate lower time costs and better enclosing accuracy while the collision avoidance and maneuver amplitude constraints are satisfied simultaneously.

Original languageEnglish
Article number2441008
JournalGuidance, Navigation and Control
Volume4
Issue number3
DOIs
StatePublished - 31 Aug 2024

Keywords

  • Approximate Nash equilibrium
  • asymptotic stability
  • differential game
  • invariant manifold
  • target enclosing

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