Full-state autopilot-guidance design under a linear quadratic differential game formulation

Full-state single-loop and full-state two-loop autopilot-guidance architectures are derived under a linear quadratic differential game formulation. In the full-state single-loop case, the guidance command is injected directly to the actuator, whereas in the full-state two-loop case, it is the input to the autopilot loop. To prevent impractical end-game scenarios, where the states diverge to unacceptable values, a cost function that includes appropriate running cost terms on some of the states is proposed. The conditions for obtaining an equivalence relation between the full-state single-loop and full-state two-loop architectures are derived under a linear quadratic differential game formulation and the proposed cost function. Under such a formulation, the two full-state architectures are identical if and only if the number of guidance commands matches the number of available controllers. The guidance laws performance is illustrated using an interceptor missile having forward and aft controls in linear and nonlinear settings, while considering two types of evasion strategies. The first strategy is a linear controller based on the linear quadratic differential game solution. The second strategy is a “bang-bang” controller based on the optimal evasion solution. It is shown that the linear evasion strategy may not be suitable to represent a realistic evading strategy. In addition, the conditions for the existence of a saddle point solution are analyzed for the two full-state guidance laws.