Cooperative Optimal Guidance Law with Simultaneous Attack and Impact Angle Constraint Using Linear Pseudospectral Model Predictive Control

Abstract

This paper aims at developing a nonlinear cooperative optimal guidance law for multiple missiles to simultaneously attack a maneuvering target with relative impact angle constraint. The guidance law is based on the recently developed linear pseudospectral model predictive control (LPMPC), in which the nonlinear dynamics is linearized around the nominal state and then discretized at the support points. This procedure converts the nonlinear optimal control problem with undetermined terminal time to a quadratic programming problem, the optimizing variables of which are the control variations at the support points and terminal time. Then, the optimal improvement can be successfully derived by iteratively solving the resulting problem in an analytical manner. In the implementation, the initial guess is provided by an optimal guidance law with constraint on one-to-one impact angle. The accuracy, optimality, and efficiently of the proposed guidance law is investigated by a nonlinear two-dimensional intercept simulation. It is also shown that the consistency of impact time is can also be ensured in comparison with typical cooperative guidance law only imposing the impact angle.