Optimal Impact Angle Guidance for Exoatmospheric Interception Utilizing Gravitational Effect

Abstract

This paper aims to develop a new optimal intercept angle guidance law for exoatmospheric interception by utilizing gravity. A finite-time optimal regulation problem is formulated by considering the instantaneous zero-effort-miss and the intercept angle error as the system states. The analytical guidance command is then derived based on Schwarz's inequality approach and Lagrange multiplier concept. Capturability analysis using instantaneous linear time-invariant system concept is also presented to provide better insights of the proposed guidance law. Theoretical analysis reveals that the proposed optimal guidance law encompasses previously suggested optimal impact angle constrained guidance laws. Numerical simulations with some comparisons clearly demonstrate the effectiveness of the proposed guidance law.