Nash equilibrium is a significant solution concept representing the optimal strategy in an uncooperative multiagent system. This study presents two deep reinforcement learning (DRL) algorithms for solving the Nash equilibrium of differential games. Both algorithms are built upon the distributed distributional deep deterministic policy gradient (D4PG) algorithm, which is a one-sided learning method. We modified it to a two-sided adversarial learning method. The first is D4PG for games (D4P2G), which directly applies an adversarial play framework based on the D4PG. A simultaneous policy gradient descent (SPGD) method is employed to optimize the policies of the players with conflicting objectives. The second is the distributional deep deterministic symplectic policy gradient (D4SPG) algorithm, which is our main contribution. More specifically, it newly designs a minimax learning framework that combines the critics of the two players and proposes a symplectic policy gradient adjustment method to find a better policy gradient. Simulations show that both algorithms converge to the Nash equilibrium in most cases, but D4SPG can learn the Nash equilibrium more accurately and efficiently, especially in Hamiltonian games. Moreover, it can handle games with complex dynamics, which is challenging for traditional methods.

To find superior guidance strategies for preventing possible interception threats from space debris, out-of-control satellites, etc., this paper investigates an orbital pursuit–evasion–defense game problem with three players called the pursuer, the evader, and the defender, respectively. In this game, the pursuer aims to intercept the evader, while the evader tries to escape the pursuer. A defender accompanying the evader can protect the evader by actively intercepting the pursuer. For such a game, a linear-quadratic duration-adaptive (LQDA) strategy is first proposed as a basic strategy for the three players. Later, an advanced pursuit strategy is designed for the pursuer to evade the defender when they are chasing the evader. Meanwhile, a cooperative evasion–defense strategy is proposed for the evader and the defender to build their cooperation. Simulations determined that the proposed LQDA strategy has higher interception accuracy than the classic LQ strategy. Meanwhile, the proposed two-sided pursuit strategy can improve the interception performance of the pursuer against a non-cooperative defender. But if the evader and defender employ the proposed cooperation strategy, the pursuer’s interception will be much more difficult.

The increasing population of objects in geostationary orbit has raised concerns about the potential risks posed by debris clouds resulting from fragmentation. The short-term evolution and associated hazards of debris generated by collisions in the geostationary region is investigated in this study. The initial distribution of two debris clouds is modeled using a single probability density function. The combined distribution of the evolved clouds is determined by solving boundary value problems. The risks associated with these debris clouds are evaluated by calculating the instantaneous impact rate and cumulative collision probability. The probability of collisions with millimeter-sized fragments may increase to 1% within 36 hours, while the probability of collisions with fragments 5 cm or larger is approximately $10^{-5}$. These findings underscore the vulnerability of the geostationary region to space traffic accidents.