Near-Optimal Guidance with Impact Angle and Velocity Constraints Using Sequential Convex Programming

Pei Pei,Jiang Wang

doi:10.1155/2019/2065730

Abstract

This paper proposes a near-optimal air-to-ground missile guidance law with impact angle and impact velocity constraints based on sequential convex programming. A realistic aerodynamic model is introduced into the problem formulation, such that traditional optimization theory cannot obtain an analytical solution to the optimization problem under state constraints. The original problem is considered as an optimization problem, and the angle of attack is replaced with the angle of attack rate as a new control variable to reconstruct the problem and simplify the solving process. Next, the independent variable is changed in the differential equations to linearize and discretize the problem such that the reconstructed problem can be solved using sequential convex programming. The results obtained by numerical simulations confirmed that the proposed algorithm is valid and faster than the general-purpose nonlinear optimal control problem solver. Finally, it was verified that different impact angles and impact velocities were achieved.

Highlights

In modern warfare, the objectives of the guidance law are limited to zero miss distance interception and include target interception at a certain impact angle and impact velocity. e impact angle constraint in a terminal interception engagement is critical for a homing missile attacking modern warships, tanks, and ballistic missiles
By adding the angle of attack rate dynamics expressed in equation (9) to equation (4) and changing the independent variable, the augmented equations of the dynamic and kinematic equations can be reformed as follows: x′ f(x) + B(x)u, (11)
With the original dynamic and kinematic equations in equation (4) replaced by the augmented dynamics and new independent variable, Problem 1 can be reformulated into a new optimization-control problem, as follows: Problem 2

Summary

Introduction

The objectives of the guidance law are limited to zero miss distance interception and include target interception at a certain impact angle and impact velocity. e impact angle constraint in a terminal interception engagement is critical for a homing missile attacking modern warships, tanks, and ballistic missiles. Optimal control theory has been implemented to solve optimal guidance law problems under an impact angle constraint [13,14,15,16,17,18], but a limit has not been set on the terminal velocity owing to the complicated form of the aerodynamic coefficients. The realistic form of aerodynamic coefficients is introduced to precisely control the impact angle and impact velocity. To overcome the inherent shortcoming of traditional optimization theory, whereby the analytical solution to the realistic velocity control problem cannot be obtained, the sequential convex programming algorithm is proposed to handle the time-varying nonlinear optimization problem.

Problem Formulation

Convexification and SCP Method

Numerical Simulations