Stackelberg orbital pursuit-evasion game with model uncertainty and input saturation via ADP-based algorithm

In practical on-orbit servicing missions, spacecraft are inevitably subject to model uncertainty and actuator input saturation, which can result in non-optimal or even infeasible controls. Motivated by these challenges, this paper investigates a Stackelberg orbital pursuit-evasion game (OPEG) under such practical constraints. The OPEG is first formulated as a Stackelberg differential game to explicitly characterize the hierarchical leader-follower interaction between the pursuer and the evader. By incorporating the follower’s optimal response into the leader’s performance index through a Lagrange multiplier, the original hierarchical game is equivalently reformulated into Hamilton-Jacobi-Isaacs (HJI) equations. To avoid the computational intractability associated with directly solving the HJI equations, an adaptive dynamic programming-based approach is developed to approximate the Stackelberg equilibrium controls. In the presence of model uncertainty, a neural-network-based identifier is designed to estimate the model uncertainty, while actuator input saturation is explicitly handled via a smooth saturation function. Moreover, an experience replay technique is incorporated into the learning process to alleviate the persistent excitation requirement. A Lyapunov-based stability analysis is conducted to rigorously establish the convergence and boundedness properties of the proposed algorithm. Numerical simulations are finally presented to demonstrate the effectiveness of the proposed algorithm in the constrained Stackelberg OPEG scenario.