A New, General Neighboring Optimal Guidance for Aerospace Vehicles

This work describes and applies the recently introduced, general-purpose perturbative guidance termed variable-time-domain neighboring optimal guidance, which is capable of driving an aerospace vehicle along a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objective function (related to the flight time) along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of an iterative closed-loop guidance scheme. Original analytical developments, based on optimal control theory and adoption of a variable time domain, constitute the theoretical foundation for several original features. The real-time feedback guidance at hand is exempt from the main disadvantages of similar algorithms proposed in the past, such as the occurrence of singularities for the gain matrices. The variable-time-domain neighboring optimal guidance algorithm is applied to two typical aerospace maneuvers: (1) minimum-time climbing path of a Boeing 727 aircraft and (2) interception of fixed and moving targets. Perturbations arising from nonnominal propulsive thrust or atmospheric density and from errors in the initial conditions are included in the dynamical simulations. Extensive Monte Carlo tests are performed, and unequivocally prove the effectiveness and accuracy of the variable-time-domain neighboring optimal guidance algorithm.