Closed-form optimal cooperative guidance law against random step maneuver

Abstract

Based on the optimal control theory, the present study proposes a novel approach to derive a cooperative guidance law for two pursuers with an arbitrary-order linear dynamics against one zero-lag evader with random step maneuver. This approach is intended to minimize the mean value of the resultant control effort taken over a set of possible evader maneuvers which is modeled as a step function, the parameters of which are unknown. Since the resultant control effort is the minimum effort among the pursuers, we encounter the nonlinear “min” function in the performance index. By introducing binary parameters, it is changed to a linear function including binary parameters and continuous variables. After the optimal control problem is solved, the optimal binary parameters are determined through an integer programming approach. Then, the closed-form optimal cooperative guidance law (OCGL) is derived in feedback form. The analytical and numerical results, obtained for the engagement of two missiles against a maneuvering target, show that OCGL is superior to the noncooperative guidance laws such as proportional navigation (PN) and optimal guidance law (OGL), even if the real model, used in evaluations, differs from the model used in the derivation of the guidance law. The performance of the proposed guidance law has been evaluated for higher order dynamics at the presence of acceleration saturation.