A new command shaping guidance law using Lagrange multiplier

This article presents a new command shaping guidance law by change of Lagrange multiplier (LM), called CSGL-LM. The Schwarz inequality approach is used to solve the optimal guidance problems considering both terminal constraints on interception and impact angle control. LM is introduced to combine two terminal constraints into a single equation. The main idea of this paper is to use LM as a design parameter for shaping the guidance command as well as controlling the terminal constraints. The guidance command of CSGL-LM is given a unified functional form of the time-to-go, the state variables, and LM. Therefore, through an appropriate choice of LM, we can achieve various shapes of the guidance commands for the interception case, as well as the impact angle control case. As illustrative examples, this paper also shows that a class of previous guidance laws is just one of particular solutions of CSGL-LM. Numerical simulations are performed to validate the properties of CSGL-LM, compared with the conventional guidance law.