A New Optimal Guidance Law with Impact Time and Angle Constraints Based on Sequential Convex Programming

Pei Pei,Jiang Wang,Xiao Chen

doi:10.1155/2021/6618351

Pei Pei, Jiang Wang + Show 1 more

Open Access

https://doi.org/10.1155/2021/6618351

Copy DOI

Abstract

This paper proposed an optimal time-varying proportional navigation guidance law based on sequential convex programming. The guidance law can achieve the desired impact angle and impact time with look angle and lateral acceleration constraints. By treating the multiconstraints’ guidance problem as an optimization problem and changing the independent variable to linearize the problem and constraints, the original nonlinear and nonconvex problem is transformed into a series of convex optimization problem so that it can be quickly solved by sequential convex programming. Numerical simulations compared to nonlinear programming and traditional analytical guidance law demonstrate the effectiveness and efficiency of the proposed algorithm. Finally, the proposed guidance law is verified to satisfy different impact time periods and impact angle constraints.

Highlights

In modern warfare, the aims of guidance law are limited to zero miss distance interception and required to intercept the target with a certain impact time and impact angle
Nonsingular terminal sliding-mode guidance law is employed to intercept the virtual target with a specific impact angle; the proportional navigation guidance law is used to get the desired impact angle. e impact time and the virtual target position are designed by an optimization routine. e optimization process is too complicated to use onboard
To transform Problem O into the sequential second-order cone convex programming (SOCP) problem, the kinematic equations must be discretized as linear equations, and the integrated performance index must be discretized for numerical integration; all nonconvex constraints must transform into convex constraints

Summary

Introduction

The aims of guidance law are limited to zero miss distance interception and required to intercept the target with a certain impact time and impact angle. Optimal control theory has been implemented to solve optimal guidance law under impact time and angle constraints [1,2,3]. Chen [11] proposed a two-stage impact time constraint guidance law with field-of-view constraint; the impact angle is out of control. Kim and Kim [12] proposed a Mathematical Problems in Engineering guidance law based on the backstepping method to control impact time with reduced seeker field-of-view constraint. Liu [26] has used convex programming to derive a time-varying PN guidance law for impact angle constraint. (3) e sequential convex programming is proposed to calculate the optimal time-varying PN guidance law with impact time and impact angle constraints. The numericalsolution process must be reliable and converges fast. ese requirements motivate us to solve the optimization problem using the sequential second-order cone convex programming (SOCP) algorithm [31]

Numerical Solution by Sequential SOCP

Numerical Simulation

Conclusion