M.Sc Thesis

M.Sc StudentDavid Alkaher
SubjectCooperative Guidance for Duo Interceptors
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Shima Tal
Full Thesis textFull thesis text - English Version


Modern interceptors are commonly developed for one-on-one interception scenarios, with a goal of intercepting aerial, ground or marine vehicles. A disadvantage for the interceptor in maneuverability or guidance dynamics may result with a large miss distance and target evasion. Missile designers are faced with the dilemma between increasing the size of the warhead, and thus increase the radius of lethality, vs. increasing the interceptor's maneuverability over that of the typical target. When the target's evasion is possible, it is expected that using two interceptors might improve the homing performance; constituting a possible substitute to an 'expensive' single interceptor. However, merely multiplying the quantity of the interceptors may not satisfy this goal; thus, a cooperative guidance law should be developed to exploit the benefit of cooperation.  This thesis discusses the pursuit-evasion (PE) problem of two cooperating interceptors, acting as a team, against a single target. The goal of the intercepting team is to minimize a combination of the miss distance between the target and both of the interceptors; while that of the target is to maximize it. Both interceptors begin this PE problem simultaneously, though they do not necessarily terminate at the same time. All this under the assumptions of planar kinematic linearization, perfect information and a physical constraint on the control effort of the interceptors and target. An innovative method of modeling the two-team PE problem of two interceptors and a single target is achieved by rephrasing the equations of motion for two pursuit-evasion couplets and phrasing a linear quadratic differential game cooperative zero-sum cost function. A closed-loop solution is mathematically developed for any order of the players' linear dynamic responses, using the zero-effort-miss (ZEM) representation technique. Variations of cooperation strategies are derived with respect to the wise selection of the cost function parameters. A ZEM form closed-loop block-diagram is constructed and a unique adjoint model is derived for analyzing: the worst (with respect to each interceptor) 'bang-bang' target evasive maneuvers and the corresponding bounded miss. It is shown that the intercepting team's worst minimum distance of closest approach can be bounded. Sufficient conditions for a saddle-point solution, in which non-singularity of the navigation gains is guaranteed, are phrased as the bound on the sum of interceptor's penalty parameters. A tradeoff surface mapping-technique of 'best' solutions is introduced to provide a common basis for comparison between the resulting two-team strategy and the classic one-on-one strategy.