1
Missile guidance law design based on free-time convergent error
dynamics
LIU Yuanhe
1, 2
, XIE Nianhao
1, 2
, LI Kebo
1, 2
, LIANG Yangang
1, 2
1.College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410072, China
2. Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions, Changsha 410072, China
Abstract: The design of guidance law can be
considered a kind of finite-time error-tracking
problem. A unified free-time convergent guidance law
design approach based on the error dynamics and the
free-time convergence method is proposed in this
paper. Firstly, the desired free-time convergent error
dynamics approach is proposed, and its convergent
time can be set freely, which is independent of the
initial states and the guidance parameters. Then, the
illustrative guidance laws considering the leading
angle constraint, impact angle constraint, and impact
time constraint are derived based on the proposed
free-time convergent error dynamics respectively. The
connection and distinction between the proposed and
the existing guidance laws are analyzed theoretically.
Finally, the performance of the proposed guidance
laws is verified by simulation comparison.
Keywords:guidance design; free-time convergence;
error dynamics approach; impact angle constraint;
impact time constraint.
DOI: 10.21629/JSEE.XXXX.XX.XX
1. Introduction
Modern warfare puts forward higher
performance requirements and more terminal
constraints for tactical missile guidance, which
results in the emergence of advanced guidance
laws, such as impact angle control guidance
(IACG) law and impact time control guidance
(ITCG) law. IACG was first proposed by Kim et
al.[1] in 1973 and ITCG first appears in 2006 to
solve the salvo attack of the anti-ship missile[2].
The mainstream method of IACG and ITCG
include improved biased proportional navigation
guidance (BPNG) laws[3]-[6], optimal guidance
(OG) laws based on various optimal
theories[7]-[9], and nonlinear guidance laws
based on various modern nonlinear control
theories[10]-[13].
*Corresponding author.
Essentially, the guidance law design for an
aerodynamically controlled missile is a kind of
finite-time error-tracking problem. If the
convergence time is too short, the acceleration
command, generated by the designed guidance
law, may exceed the saturation of the missile
actuator, leading to the degradation of guidance
performance in application. On the contrary, if
the convergence time is too long, there is a risk
that the tracking error cannot converge to 0 in
the desired time. Therefore, the key to missile
guidance design is to make the tracking error
converge to 0 in a limited time without
generating too largeguidance command. That is,
it is necessary to find an appropriate finite-time
reaching law.
Some finite-time convergence (FnTC) theories
are investigated to find the better reaching law
referring to the guidance problem. The FnTC
theory was first proposed in[14], whose upper
bound of convergence time depends on the
initial system states, which need different
guidance parameters in different scenarios.
Theauthors in [15] proposed an FnTC control
approach, where the convergence time can be
preset regardless of the initial states and control
parameters. While its preset time-varying
function is too complex. As an improvement of
FnTC, the fixed-time convergence (FxTC)
theory is developed in [16], whose upper bound
of convergence time is independent of the initial
system states. However, the actual convergence
time cannot be obtained and there are too many
control parameters with unclear physical
meanings. To further enhance the constraint on
the convergence time, the concept of free-time
convergence (FeTC) was proposed in [17],
which could be considered as a further
development of the FnTC and FxTC. The
convergence time is not only independent of the
