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In this paper, we present a game-theoretic feedback terminal guidance law foran autonomous, unpowered hypersonic pursuit vehicle that seeks to intercept anevading ground target whose motion is constrained in a one-dimensional space.We formulate this problem as a pursuit-evasion game whose saddle point solutionis in general difficult to compute onboard the hypersonic vehicle due to itshighly nonlinear dynamics. To overcome this computational complexity, welinearize the nonlinear hypersonic dynamics around a reference trajectory andsubsequently utilize feedback control design techniques from Linear QuadraticDifferential Games (LQDGs). In our proposed guidance algorithm, the hypersonicvehicle computes its open-loop optimal state and input trajectories off-lineand prior to the commencement of the game. These trajectories are then used tolinearize the nonlinear equations of hypersonic motion. Subsequently, usingthis linearized system model, we formulate an auxiliary two-player zero-sumLQDG which is effective in the neighborhood of the given reference trajectoryand derive its feedback saddle point strategy that allows the hypersonicvehicle to modify its trajectory online in response to the target's evasivemaneuvers. We provide numerical simulations to showcase the performance of ourproposed guidance law.

Feedback Strategies for Hypersonic Pursuit of a Ground Evader