This project establishes a control-theoretic generative capability for trajectory generation in drone kinetic interception scenarios. By reformulating diffusion-based generative models as dynamical systems with Lyapunov stability properties, which is called Lyapunov Energy Matching (LEM), the effort embeds trajectory generation within a zero-sum pursuit-evasion framework and trains generators through adversarial reinforcement learning as strategic agents. The resulting methods aim to produce safe, dynamically feasible, and near-optimal interception trajectories against intelligent and maneuvering threats. Expected outcomes include new theory linking generative modeling, differential games, control theory, and reinforcement learning along with executable trajectory-generation algorithms that strengthen national security capabilities in autonomous interception and online trajectory generation and execution.

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