In the linear-quadratic pursuit-evasion game, the pursuer (interceptor) wishes to minimize the terminal miss whereas the evader (target) wishes to maximize it. Therefore, the optimal interceptor strategy is derived against the anticipated worst possible target strategy. If the interceptor has a lag, the current approach is to include this lag directly in the system dynamics which are known to both players. In this problem formulation, the optimal cost could easily go to infinity which means that the target will win the game. This is expected because the target has knowledge about interceptor's lag. To ensure the existence of an interceptor strategy, the weighting on the terminal miss has to be chosen small enough so that the optimal cost will remain finite. However, this manipulation prevents the target from maximizing the terminal miss and effectively constrains the target strategy. Therefore, the interceptor strategy is derived against the "worst-case" target strategy that is not really the worst case. In this paper, it is shown that this interceptor strategy performs poorly in realistic situations where the target tries to maximize the terminal miss. Instead, two new interceptor strategies are derived against target strategies that are determined without knowledge about interceptor's lag. These two optimal interceptor strategies improve the game-theoretic guidance law for homing missiles by correctly taking into account the autopilot lag.

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Application of a second-order sliding mode observer, which is based on the nonlinear dynamic sliding manifold, as a nonlinear uncertain system estimator in the homing (terminal guidance) loop with augmented proportional navigation guidance is demonstrated. It is shown that sliding mode observers have an advantage over traditional Kalman filters in the homing loop upon target maneuvering at a short time-to-go.

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