Abstract Pursuit-Evasion is a game theoretic problem being studied since the 17th century. While optimal strategies are known for the case of a single-pursuer and single-evader system, the computational complexity makes a real time solution infeasible for collaborative pursuit. This talk introduces an output regulation technique based on a fluid version of the Newton-Raphson method for solving algebraic equations, and shows its efficacy through an application to the above problem. The proposed control law is based on a variable-gain integrator with online prediction of the evader’s trajectory. Lastly, we employ a deep neural network to approximate the evader’s future trajectory, based on the data gathered, which obviates the need for an a-priori knowledge of the evasion strategy used by the target.