Low-thrust strategies in orbital pursuit-evasion games with rendezvous constraints: A PINNs-Based approach

The focus of this work is to enhance the efficiency and ensure the analytical satisfaction of boundary constraints in the context of orbital pursuit-evasion games with rendezvous constraints. The proposed approach integrates Physics-Informed Neural Networks (PINNs) with the Theory of Functional Connections (TFC) to solve a set of ordinary differential equations (ODEs) derived from differential games theory. In this approach, PINNs are initially utilized as a surrogate model for the solution to the ODEs. Subsequently, the TFC guarantees the analytical satisfaction of the boundary conditions by constructing a functional representation of the PINNs, where the constraint expressions in orbital pursuit-evasion games are derived for the first time. Through employing radial basis functions as activation functions, the issues including vanishing gradients and parameter initialization are mitigated in the network training. Moreover, an improved training algorithm is introduced to increase the accuracy, which incorporates an adaptive mechanism for optimizing the distribution of training points. The simulation results validate the efficiency and accuracy of the method, and additional parameters analyses provide novel and insightful conclusions for such problems.