A Nonlinear Optimal Guidance Law with Terminal Impact Angle Constraint

Abstract

State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design methods for nonlinear controllers. A nonlinear optimal guidance law with impact angle constraint is derived for planar engagements to attack stationary targets. The guidance problem is formulated as an infinite horizon nonlinear regulator problem whose equilibrium state is zero. It is solved by SDRE technique and the state weight matrix is chosen as a function of time-to-go. Performance of the guidance law is tested numerically with different initial firing conditions for a realistic GPS/INS guided artillery rocket model with low available lateral acceleration. A reasonable launch angle is helpful to reduce the control effort, and it is acquired by trajectory optimization using genetic algorithm. Results show negligible errors for miss-distance and the desired impact angle. The proposed guidance law is a choice for the guided artillery rocket.

Keywords:

• Guidance Law
• Genetic Algorithm
• State-dependent Riccati Equation
• Impact Angle Constraint
• Trajectory Optimization