IEEE - Aerospace and Electronic Systems - April 2023 - 34

Neural Network-Based Controller for Terminal Guidance Applied in Short-Range Rockets
are placed inside the stability region. Stability is guaranteed
inside rocket flight envelope, for the time and Mach
numbers variation described in Table 1 and Figure 2,
respectively, according to the poles' locations obtained, as
it can be shown in Figure 5, (see [4] for more information).
Following that, ML techniques based on NNs are
used to find the values of the controller output d from the
ndem and the measurements n, c, and _c outside of the linearization
points and to give a self-programming
mechanism.
Figure 4.
Closed-loop feedback scheme.
NEURALNETWORK
d is calculated using NNs outside of the linearization
points. By using the computed values at the linearization
sites as inputs and outputs of a self-learning mechanism,
the goal is to achieve high accuracy in its determination
process.
Both classic and modern GNC applications have
Figure 5.
Location of closed-loop poles and zeros.
!
Yp
!
Yp ¼
DpðM; tÞ¼
¼ CpðM; tÞXp
!
2
4
x
c
c_
2
4
3
5
d1
3
5
þDpðM; tÞ Up
!
CpðM; tÞ¼
c1j ¼ VðMÞ
g
2
4
c11 c12 c13
01 0
00 1
g
b1:
3
5
a1j for j ¼½1; 2; 3
d1 ¼ VðMÞ
(10)
CLOSED-LOOPFEEDBACKSYSTEM
Three poles may be discovered by analyzing the system in
(6). A modern theory-based closed-loop controller is presented,
which is to be used to obtain the inputs and outputs
of the system for the training of a NN-based controller.
Figure 4 shows the scheme of the closed-loop controller,
in which ndem is the desired load factor and n is the measured
load factor.
The values of the controller gain matrix (K) at the linearization
points are determined using robust pole placement
techniques, on where controlled flight system poles
34
already incorporated ML approaches (see [9] and [24]).
The capacity of NN to learn flight dynamics equations is
its primary advantage over alternative approximations.
This feature allows flight prediction without knowing the
physics of the application [9]. As a result, the K determination
procedure can be replicated outside of the preset
operational locations. It should be mentioned that the use
of NNs to solve nonlinear equations is successful, even
when there is uncertainty [9].
To predict the values of canard deflection (d), several
NNs are used. Three distinct techniques have been given
to demonstrate the applicability of the proposed methodology,
which is based on NNs and contemporary control theory,
as shown in Table 3. For each of the techniques, a
hyperparametric study (see [9]), on where the key factor
has been finding a break-even between the time used during
the training process and the correlation between
expected results, avoiding overfitting, has been used to
determine the number, shape of neurons, and the quantity
of training and validation data. Finally, parameters, such
as the maximum number of epochs, the gradient decay
factor, the validation frequency, and the initial learn rate
have been set to 1000, 0.9, 10, and 0.005, respectively,
Table 3.
Input and Target Values For Neural Network
Inputs
ndem
n
Target
c cd_
0.700 0.7668 0.0291 -0.5542 0.0856
1.011 0.906 -0.711 0.006 -0.0724
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IEEE A&E SYSTEMS MAGAZINE
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APRIL 2023
IEEE - Aerospace and Electronic Systems - April 2023

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