Closed-form guidance law for velocity maximization with impact angle constraint

doi:10.23919/JSEE.2024.000078

Abstract

Abstract:

Final velocity and impact angle are critical to missile guidance. Computationally efficient guidance law with comprehensive consideration of the two performance merits is challenging yet remains less addressed. Therefore, this paper seeks to solve a type of optimal control problem that maximizes final velocity subject to equality point constraint of impact angle constraint. It is proved that the crude problem of maximizing final velocity is equivalent to minimizing a quadratic-form cost of curvature. The closed-form guidance law is henceforth derived using optimal control theory. The derived analytical guidance law coincides with the widely-used optimal guidance law with impact angle constraint (OGL-IAC) with a set of navigation parameters of two and six. On this basis, the optimal emission angle is determined to further increase the final velocity. The derived optimal value depends solely on the initial line-of-sight angle and impact angle constraint, and thus practical for real-world applications. The proposed guidance law is validated by numerical simulation. The results show that the OGL-IAC is superior to the benchmark guidance laws both in terms of final velocity and missing distance.

Key words: missile, guidance law, proportional-navigation guidance, impact angle

Jiahui ZHANG, Qiuqiu WEN. Closed-form guidance law for velocity maximization with impact angle constraint[J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1295-1303.

Figures/Tables 8

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Parameter	Value
Initial position $({x_0},{y_0})/ {\text{m}}$	$(0,2\;000)$
Initial velocity ${V_0}/\left( {{\text{m}}/{\text{s}}} \right)$	$500$
Initial angle ${\gamma _0}/\left( ^\circ \right)$	$0$
Final position $({x_f},{y_f})/{\text{m}} $	$(10\;000,0)$
Final impact angle ${\gamma _f}/\left( ^\circ \right)$	$ - 60$

Parameter	Value
Parasite drag parameter ${k_0}$	$0.9 \times {10^{ - 5}}$
Induced drag parameter ${k_1}$	$1.2 \times {10^3}$

Gain		Miss distance/m	Impact angle/(°)	Final velocity/(m/s)
N_p	N_q	Miss distance/m	Impact angle/(°)	Final velocity/(m/s)
6	2	0.015	−60.001	350.34
6	1	0.083	−59.768	285.29
5	2	0.064	−59.989	305.08
7	2	0.020	−59.993	323.02
6	3	0.028	−59.996	299.14

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