Deep Koopman Operator-Based Linear Quadratic Regulator for Quadrotor Pursuit-Evasion Game

This paper proposes a deep Koopman operatorbased output regulation framework to address the pursuitevasion (PE) game problem of quadrotors with strongly nonlinear dynamics. First, for the nonlinear quadrotor dynamics, a deep neural network is trained to lift the physical states into a high-dimensional latent linear space. Then, an output matrix is introduced to map the lifted states to task-relevant outputs. Next, a discrete-time linear quadratic regulator (LQR) with an output-weighted quadratic cost is formulated to yield a Riccati-based controller for efficient regulation. In contrast to existing Koopman-based control schemes, the proposed approach improves the modeling fidelity for nonlinear flight dynamics. Finally, simulation demonstrates that the proposed controller outperforms the baseline controller and also provides a principled and computationally efficient alternative to purely reinforcement learning (RL)-based policies.