Optimal Time-to-Entry Pursuit-Evasion Games Under Sun-Angle Constraints with Non-Smooth Terminal Regions

Recent advancements in satellite optical reconnaissance have elevated the sun angle to a critical factor in orbital pursuit-evasion games. The stringent imaging constraints imposed by sun angle and relative distance induce non-smoothness in the terminal region of such differential games, significantly complicating equilibrium-solution derivation. To address this challenge, we formulated a novel differential game model where the pursuer minimizes the time-to-entry into the evader’s effective imaging region. We first constructed a sequence of low-dimensional manifolds that collectively cover the terminal region, solving the differential game with this sequence to yield the Nash equilibrium. Subsequently, we approximated the terminal region using a smooth manifold of identical dimensions, enabling a computationally efficient approximate solution. Both methodologies demonstrate broad applicability to orbital differential games featuring non-smooth terminal regions. Simulation results confirm that the approximation error becomes pronounced only under extreme initial sun angles, though this error remains acceptable for practical space reconnaissance applications.