  In this paper, a time-optimal feedback solution to the game of two cars, for
the case where the pursuer is faster and more agile than the evader, is
presented. The concept of continuous subsets of the reachable set is introduced
to characterize the time-optimal pursuit-evasion game under feedback
strategies. Using these subsets it is shown that, if initially the pursuer is
distant enough from the evader, then the feedback saddle point strategies for
both the pursuer and the evader are coincident with one of the common tangents
from the minimum radius turning circles of the pursuer to the minimum radius
turning circles of the evader. Using geometry, four feasible tangents are
identified and the feedback min-max strategy for the pursuer and the max-min
strategy for the evader are derived by solving a $2 \times 2$ matrix game at
each instant. Insignificant computational effort is involved in evaluating the
pursuer and evader inputs using the proposed feedback control law and hence it
is suitable for real-time implementation. The proposed law is validated further
by comparing the resulting trajectories with those obtained by solving the
differential game using numerical techniques.
