  In this paper, we present a game-theoretic feedback terminal guidance law for
an autonomous, unpowered hypersonic pursuit vehicle that seeks to intercept an
evading ground target whose motion is constrained in a one-dimensional space.
We formulate this problem as a pursuit-evasion game whose saddle point solution
is in general difficult to compute onboard the hypersonic vehicle due to its
highly nonlinear dynamics. To overcome this computational complexity, we
linearize the nonlinear hypersonic dynamics around a reference trajectory and
subsequently utilize feedback control design techniques from Linear Quadratic
Differential Games (LQDGs). In our proposed guidance algorithm, the hypersonic
vehicle computes its open-loop optimal state and input trajectories off-line
and prior to the commencement of the game. These trajectories are then used to
linearize the nonlinear equations of hypersonic motion. Subsequently, using
this linearized system model, we formulate an auxiliary two-player zero-sum
LQDG which is effective in the neighborhood of the given reference trajectory
and derive its feedback saddle point strategy that allows the hypersonic
vehicle to modify its trajectory online in response to the target's evasive
maneuvers. We provide numerical simulations to showcase the performance of our
proposed guidance law.
