Feedback Strategies for Hypersonic Pursuit of a Ground Evader

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 along an axis. 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 difficulty, 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 accordance with the changes/dispersion to the target's position due to its evasive maneuvers. We provide numerical simulations to verify the performance of our proposed guidance law.