A three-dimension terminal guidance method based on adaptive PN law and convex optimization

Abstract

A three-dimension guidance method is proposed for the multi-constrained optimal terminal guidance problem. First, an adaptive proportion navigation (PN) guidance law is designed to obtain a nominal trajectory of the guidance task, and the guidance logic is designed to allocate the guidance commands. Then, the guidance problem is linearized as a linear time-varying quadratic convex optimal problem based on the nominal trajectory, and the discretization is done to convert the infinite-dimensional optimization problem to a finite-dimensional one. Finally, the linearized quadratic convex optimal problem can be solved by a convex optimization method with deterministic convergence properties, and the optimal guidance command is obtained. Simulation results show that the proposed method can satisfy the terminal state constraints and control constraints, and reduce the control consumption significantly.