An optimal mid-course guidance law for fixed-interval propulsive maneuvers

In this paper we develop an optimal midcourse strategy for guiding an interceptor. We assume that the target is outside of the sensible atmosphere and is not maneuvering throughout the engagement and the thrust vector controlled interceptor has a fixed maneuvering time that ends well before the actual intercept. The existence of an unguided phase before the target intercept distinguishes our work from other formulations found in the literature. We also extend the optimal solution to a family of guidance laws that guarantee perfect intercept for the fixed-interval maneuvering problems. N this paper we concentrate on the problem of guiding a missile to intercept a nonmaneuvering target moving at high velocities outside the atmosphere. The important distinguishing constraint that we impose on this problem is that the thrust vector controlled interceptor has a fixed maneuvering time that ends well before the actual intercept. Therefore, there is a period of time before the intercept that the missile is not maneuvering at all and is coasting ballistically toward the target. This scenario is representativ e of a midcourse strategy during which the missile is guided so as to assure a proper collision course to the target before the depletion of the propulsive subsystem that provides the missile maneuvering capability. Following propulsion depletion, the missile coasts ballistically to the target intercept region where a small kill vehicle (KKV) is released to achieve target impact with minimum steering effort. Here, we ignore the kill vehicle and concentrate our effort on developing the guidance law for the propelled stage that delivers the KKV to its intercept region. It turns out that the optimal guidance law for a simplified (but realistic) formulation of our problem has a closed-form solution that is an intricate modification of the proportional navigation (PN) guidance law. We will analyze the many interesting properties of this guidance law and will illustrate its performance using a computer simulation of the engagement scenario. Note that many modern formulations of PN found in the literature1'2 do not include a coasting phase before the impact, and the guidance law developed in this paper differs drastically from PN in this regard, and this is the main contribution of our article. II. Optimal Guidance Law