Non-smooth missiles guidance: Interceptor-defender scenario with uncertainties

Here the dynamic scenario with two participants (an interceptor interpreted as an anti-missile and a defender treated as an anti-anti-missile) is considered. The first one (an interceptor) is intended to reach a capture zone, associated with a given nominal trajectory of a missile which is assumed to be non-maneuvered. But in the same time it should maintain a large enough distance from the second player (a defender) whose individual aim is to protect the nominal plant (a missile). The second participant realizes its behavior in such a way that its position would be as close as possible to an interceptor and far enough from a missile which it protects. Individual cost functions related with non-smooth feedback control strategies for each participant are introduced. The gain parameters of the non-smooth feedbacks are selected in an “optimal manner” providing the biggest rate of convergence to the desired regime. The effective zones in the state space, where the designed control decreases the cost functions, are obtained. Illustrative numerical simulations confirm the workability of the suggested approach.