We consider a planar pursuit-evasion problem in which a Dubins pursuer seeks to capture a slower first-order point-mass evader that can change its heading instantaneously. First, we propose a turn-rate feedback law with a single tunable gain and derive an explicit admissible gain interval that guarantees finite-time capture against any admissible evader strategy while satisfying the turn-rate constraint. Next, we obtain an explicit capture-time bound and characterize the turning authority required for the gain interval to be non-empty. Finally, we show that the dependence on the evader's speed bound can be removed by deriving a speed ceiling, computable solely from the pursuer's parameters, below which the guarantees hold at the maximum allowable gain. Numerical simulations illustrate the effectiveness of the proposed approach.
