A guided rocket system performance is often evaluated by solving an optimal control problem which minimizes a pre-defined objective function, e.g. control effort, while satisfying required boundary conditions. However, rocket guidance has constrict “real-time” computational and duration restrictions, which the optimum solution methods do not satisfy. Therefore, there is need to efficiently obtain a solution close to the optimal solution without the accompanying computational burdens.
The current research presents a hybrid analytic and numerical approach for solving a required dynamic physics problem, while taking advantage of pre-defined optimal solution data. The chosen method, named Neighboring Extremal Path method, proposes a linearization of the nonlinear complex dynamic equations and optimality conditions around an optimal reference rocket trajectory, creating a linear “Two Point Boundary Value Problem” (TPBVP). The TPBVP resulting augmented neighboring control shall drive the rocket along a required path to the desired impact point. Both open loop (OL) and closed loop (CL) Neighboring analyses were conducted. The OL neighboring analysis was done with fixed final time and terminal impact point perturbations, using Indirect Shooting and Backwards Sweep approaches of solution. The CL neighboring optimum feedback law was tested in the presence of parameter uncertainties, using Backwards Sweep approach for fixed and unspecified terminal time.
The analysis showed the Neighboring Extremal method validity with perturbed rocket conditions (including wind) while reviewing a wide range of parameter uncertainties. Mostly, the analyses showed acceptable impact point errors, however, in order to fully fulfill the requirements, an unspecified final time closed loop neighboring control is necessary.