This document describes the development of a neurofuzzy control system for guiding air-to-air missiles. The system uses two neural network controllers to control the longitudinal and lateral motions separately. A fuzzy logic controller then blends the outputs of the neural networks to obtain the overall control action. The fuzzy controller has a 25 rule base to handle uncertainties from cross-coupling between the motions. Simulation results showed the neurofuzzy hybrid system performed better than using just neural networks or fuzzy systems alone for control.

1. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
DEVELOPMENT OF A NEUROFUZZY CONTROL SYSTEM FOR THE
GUIDANCE OF AIR TO AIR MISSILE
Hosny, A.M.*, Zeyada, Y.F.** and Hassan, G.A.***
*Research Student,
**
Assistant Professor, ***Professor, Mechanical Design and Production Department
Faculty of Engineering, Cairo University, Giza 12316, Egypt.
E-Mail AHMEDMOMTAZHOSNY@YAHOO.COM &YZEYADA@YAHOO.COM & GAHASSAN99@HOTMAIL.COM
ABSTRACT
In recent years, there has been an increasing interest in the fusion of neural networks and fuzzy logic
specially in missile control problems. A technique for the preliminary design of a control system is
presented using a neurofuzzy approach for a highly nonlinear MIMO 5_DOF AIM 9R model. The model
reflects cross coupling effects between the longitudinal and lateral motions. Two neural network
controllers are used for the low level control of each motion separately. The control effort of these
networks is then blended by a fuzzy logic controller to obtain the overall control action.The fuzzy
controller which is a Mamdani type inference system has 25 rule base designed to cope with model
uncertainties specially in cross coupling between lateral and longitudinal motions. A computer simulation
is performed to compare between various control techniques. The result showed the effectiveness of the
hybrid system compared to other control strategies where fuzzy systems or neural networks are used
separately.
KEYWORDS
Fuzzy logic controller (FLC), neural network controller (NNC), air intercept missile (AIM).
1. INTRODUCTION
Recently, neurofuzzy modeling techniques have been successfully applied to modeling complex systems,
where traditional approaches hardly can reach satisfactory results due to lack of sufficient domain
knowledge. Much research has been done on applications of neural networks (NNs) for identification and
control of dynamic systems [1]. According to their structures, the NNs can be mainly classified as
feedforward neural networks and recurrent neural networks [2]. It is well known that a feedforward neural
network is capable of approximating any continuous functions closely. However, the feedforward neural
network is a static mapping. Without the aid of tapped delays the feedforward neural network is unable to
represent a dynamic mapping. Although much research has used the feedfoward neural network with
tapped delays to deal with dynamical problem, the feedforward neural network requires a large number of
neurons to represent a dynamic response in the time domain. Moreover, the weight updates of the
feedforward neural network do not utilize the internal information of the neural network and the function
approximation is sensitive to the training data. On the other hand, recurrent neural network (RNNs) [2]
have superior capabilities than the feedforward neural networks, such as dynamic and ability to store
information for later use. Since recurrent neuron has an internal feedback loop, the RNN is a dynamic
mapping and demonstrates good control performance in the presence of uncertainties, which is usually
composed of unpredictable plant parameter variations, external force disturbance, unmodeled and
nonlinear dynamics, in practical application of air to air missile.
In recent years, the concept of incorporating fuzzy logic into a neural network has been grown into a
popular research topic. In contrast to the pure neural network or fuzzy system, the fuzzy neural network
(FNN) possesses both their advantages. It combines the capability of fuzzy reasoning in handling
uncertain information and the capability of artificial neural networks in learning from processes [1],[2]. In
missiles controlling branch it is needed to minimize the output performance errors until fulfilling the

2. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
required specifications such as the minimum locking time and the maximum fuse distance. Nowadays
there are different types of missiles using different types of control strategy. Some of them use reference
frame unit as they controlled by a remote base or an aircraft. Consequently controlling such missiles by
reference angles  ,, with respect to fixed frame. Other type of control strategy doesn’t use reference
frame unit (fire and forget types) such as all heatseeking, active radar missiles. In this paper, both types of
control strategy are discussed. A technique for the preliminary design of a control system is presented
using neurofuzzy systems for a diverse data range of a highly nonlinear MIMO 5_DOF model (AIM 9R
air to air missile). This system is composed of 3_body axes velocities and rotating in both pitch and yaw
direction only as the rolling motion is prevented due to gyroscopic stabilizers (anti roll system) attached
at the rear fins. The model has cross coupling effects between the longitudinal and lateral motions due to
the coupled equations of motion. MIMO model was divided into two separated SISO models taking into
consideration the nonlinear cross coupling effects, then generating the neural network controller for each
separated SISO model, blending the output performance using a 25 rule base Mamdani type fuzzy logic
controller. A Mamdani fuzzy logic controller can deal with the system uncertainty due to cross coupling
effect and affecting gust in the whole system when instantaneously applying both inputs to the model.
The main goal is to fulfill certain specifications within its limited ranges such as proximity fuse distance
and the target locking time during the whole mission of the missile consequently keeping the error
between actual and desired performance according these tolerances. The first obvious error is due to the
AOA (angle of attack of the missile) and SSA (side slipping angle), resulting in error in the desired
trajectory itself as the (camera) detector is attached to the body frontal area of the missile that is inclined
to the actual body velocity vector. A second error is due to the error between the desired and actual
trajectory of the missile and this is actually due to the whole system performance (AIM_9R dynamic
model and controllers). To minimize the second error over different regimes of flight, a hierarchical
design of multi NN controllers using a TSK [4] fuzzy fusion system classifier is recommended which
compute the weight of each controller according to the flight regime parameters such as (altitude,
velocity, required track rate [target_seeker distance]). Fortunately both types of performance errors are
damping each other to some extent, this will lead to minimize the net output error of the actual
performance. The model was established and simulated through (MATLAB-SIMULINK ), and the final
performance was examined using FLC (fuzzy logic controllers) with and without NNC (neural network
controllers).
2.SYSTEM EQUATIONS
The kinematical and dynamical equations of motion of the air-to-air missile can be written briefly as
following [3]:
Force equations:
0.5  .v
2
.Cx.S - mg sin = m(U

+ QW – RV ) (1)
0.5  .v
2
.Cl.S + mg cos sin = m(V

+ RU – PW ) (2)
0.5  .v
2
.Cl.S + mg cos cos  = m(W

+ PV - QU ) (3)
Moment equations:
0.5  .v
2
.Cm.S.L=BQ

(4)
0.5  .v
2
.Cm.S.L= C R

(5)
Missile orientations:
















=









 



seccossecsin
tancostansin
sincos






R
Q
(6)

3. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
Flight path calculations:.
















dt
dz
dt
dy
dt
dx
=
















coscoscossinsin
cossinsinsincoscoscossinsinsinsincos
sinsincossincossincoscossinsincoscos










W
V
U
(7)
2.1. Cross Coupling Effect Representation
As mentioned before the model has a considerable cross coupling effect between its longitudinal and
lateral motion. The cross coupling effect on the pitch motion is shown in Fig. 1 for rudder input
deflection of frequency.2 (rad/s) in yaw direction. Figure 2 shows the cross coupling effect (delta)
expressed by the standard deviation quantity versus the rudder input deflection frequency. It is obvious
that the cross coupling effect is maximum at rudder input frequency of .1(rad/s).
Fig. 1 Cross coupling effect (yaw pitch)
Fig. 2 Standard deviation of cross coupling effect (yaw pitch)
2.2. Gust Effect Representation
To determine the gust effect the whole system should be examined without gust effect and then with
gust effect as shown in Fig. 3. This is done by applying a Dryden gust through the pitch angular velocity
q and angle of attack  . It is obvious from Fig. 3 that the pitch motion is affected when the system is
subjected to Dryden gust with difference (delta).

4. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
. Fig. 3 Gust effect (pitch motion)
3. Control with NN Inverse Models
Conceptually, the most fundamental neural network based controllers are probably those using the
‘’inverse’’ of the process as the controller as shown in Fig. 4. The simplest concept is called direct
inverse control.
The principle of this is that if the process can be described by:
y(t+1)= g(y(t), ….., y(t-n+1), u(t), …,u(t-m))
A network is trained as the inverse of the process:
u(t)=g-1(y(t+1),y(t), ..., y(t-n+1),u(t-1),u(t-m))
The inverse model is subsequently applied as the controller for the process by inserting the desired
output, the reference r(t+1), instead of the output y(t+1). Figure 5 shows the output performance in
accordance with reference input. As shown in Fig. 5 the output performance is verifying the desired
output.
Fig. 4 Control by direct inverse control

5. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
Fig. 5 Control by direct inverse control at steady state flight
4. APPLYING FUZZY INFERENCE SYSTEM FOR CONTROL
The above inference technique can be very useful in missile control system [4], [5]. A standard control
system would utilize a numerical input and produce numerical output and so should a fuzzy controller.
The knowledge base contains the set of inference rules chosen to achieve the control objectives and the
parameters of the fuzzy systems used to define the data manipulation in the fuzzification, inference
engine, and defuzzyification processes. The input to the fuzzification process is the measured or estimated
variable that appears in the antecedent part of the if_then rule. This input variable has associated linguistic
values to describe it. Each linguistic value is defined by a membership function, parameterized by data
from the knowledge base. In the inference engine the decision–making logic is conducted, inferring
control laws from the input variables through fuzzy implication. The final step is the defuzzification
process as shown in Fig. 6, where a crisp control command is determined based on the inferred fuzzy
control law.
Rule Derivation
The knowledge of the relationship between inputs and outputs of fuzzy controllers are expressed as a
collection of if-then rules to form what so called the rule-base of the fuzzy controller. Four methods,
possibly used in combination, are mainly used to generate the rule-base of a fuzzy controller.
1-Expert experience and control engineering judgment
In this approach the knowledge and experience of the designer are used to manually construct the rule-
base of the controller.
2-Observation of an operator’s control action
Many practical control tasks are difficult to describe by an explicit mathematical model. However, they
are successfully performed by skilled human operators.
3-Fuzzy model of the plant
A fuzzy model of the plant can be thought of as a linguistic description of the dynamic characteristics of
plant using fuzzy logic and inference. A set of subsequent fuzzy control rules can be designed based on
the fuzzy model of the plant to be controlled.
4-Learning approaches
Motivated by the need of a systematic method to generate and modify fuzzy rule-bases, much research is
being conducted on developing learning approaches. This technique began with the self-organizing
controllers that consist of two levels of fuzzy rule bases. The first rule base is the standard control fuzzy
rule base. The second level contains a fuzzy rule base consisting of meta-rules, which attempt to assess
the performance of the closed loop control system and subsequently used to modify the standard rule
base. Learning approaches based on evaluation theory, such as genetic algorithms, may have a promising
potential towards the derivation of fuzzy rule bases.

6. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
Fig. 6 Error, error rate and control signal
4.1. Comparison between the Neural Network and Fuzzy Logic Controllers
It is significant from Fig. 7 that the output performance of the Fuzzy Logic Controller is better than the
Neural Network Controller output performance.
Fig. 7 Comparison between Fuzzy logic controller and NN controller
4.2. Comparison between Different Fuzzy Logic Controllers
Figure 8 shows Fuzzy Logic Controllers with different normalized and denormalized factors.
Consequently the dynamic performance of FLC can be modified by changing these factors according to
the flight regime of the missile.
Fig. 8 Effect of normalized and denormalized factors

7. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
4.3. The Effect of using Neural Network in the First Time Period
It is obvious from Fig. 9 that using a Neural Network Controller with Fuzzy Logic Controller in the first
5_seconds is better than using Fuzzy Logic Controller only as the ISE of the combined controllers in the
first 5_seconds is lower than the ISE of the FLC only.
Fig. 9 Effect of using NNC for the first 5 seconds
5. DISCUSSIONS
The main goal is to control an air-to-air missile (AIM9R) [6] to follow the desired trajectory according to
the actual missile track rate with the minimum error between desired and actual trajectories, to verify the
proximity fuse distance between the missile and the target to achieve the required impact against the
target. This control system is exposed to a significant uncertainty due to cross coupling effect between
inputs and due to the gust affecting the missile actual performance. The following steps describe how to
apply the neurofuzzy controller to air-to-air missiles:
1.Deal with the (MIMO) model as 2(SISO) models.
2.Train neural network controllers for each model separately using applied kits.
3. Apply (25 rule MAMDANI fuzzy logic controllers) to both NN controller models after connecting
them to the actual (MIMO) model. As FLC will enhance the output performance in case of existing gust
or cross coupling effect as it is the best way to deal with large uncertainty without having instability in the
dynamic system.
4.Simulation and result as shown in Fig. 10.
5-To present the target and seeker flight actual paths it is required to calculate the A/C [6] orientation
angles then integrate the flight path equation (7) through MATLAB_SIMULINK editor to get the A/C
trajectory. Consequently the missile trajectory has to be calculated from the intensity and the position of
the target on the plane focal array at the dome of the missile. Both A/C and missile trajectories are shown
in Fig. 11 where the triggering point was verified.
Fig. 10 AIM 9 model with 2 separate controllers

8. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004
Fig. 11 Actual trajectories for target and missile in meter
6. CONCLUSION
It is noticed that the performance using both FLC and NNC in the first 5_seconds time interval of the
mission is better than the performance using FLC only. As the FLC output signal is increasing slowly in
the first time period to reach the desired trajectory according to the control signal increment value. But for
the rest of the mission it is recommended to use FLC only rather than with NNC, as using NNC may
loose some stability against the uncertainty even when used with FLC on the contrary when using FLC
only. The FLC is robust enough to cope with the whole system against the existing uncertainty (cross
coupling effect and gust). Consequently, it is recommended to use both types of controllers NNC, FLC in
the first 5_seconds then using FLC only for the rest of mission. The TSK [4] Fusion Fuzzy System
Classifier will enhance the output performance using multi NN controllers for different regimes mainly in
the first 5_seconds time interval. Finally, the simulation gives the recommended triggering specifications
required for such missile which are the minimum locking time for triggering it should not exceed 0.065
seconds and the maximum proximity fuse distance should not be less than 3 meters [7] at triggering point
as shown in Fig. 11. These tolerances are according to the dynamic model data of AIM 9 missile used in
the simulation.
REFERENCES
1. K. S. Narendra and K. Parthasarathy, ‘’Identification and control of dynamical systems using neural
networks, ‘’IEEE Trans. Neural Networks, vol. 1, pp.4-27, 1990.
2. C. C. Ku and K. Y. Lee ,”Diagonal recurrent neural networks for dynamic systems control, ” IEEE
Trans. Neural Networks, vol. 6, pp.44-156, 1995.
3. B. Etkin, “Dynamics of flight,” pp.4-103, 1990
4. T. Takagi and M. Sugeno, ‘’Fuzzy identification of systems and its applications to modeling and
control,’’ IEEE Tans, Syst., Man, Cybern., vol. 15, pp. 116-132, 1985.
5. P. K. Menon and V. R., “Blended homing guidance law using fuzzy logic,” Optimal Synthesis Inc.,
1998
6. http://www.sci.fi/~fta/aim9.html
7. L. Tsao and C. Lin,’’A new optimal guidance law for short-range homing missiles,’’ Department of
System Engineering, Taiwan, R.O.C., 2000
NOMENCLATURE
B, C = moment of inertia about (y, z) axes
Cm , Cx, Cl = aerodynamic moment coefficient, drag coefficient, lift coefficient
m, S, v, L = missile mass, equivalent surface area, absolute velocity of the missile, reference length
Q, P, R = angular velocities around missile body axis
U, W ,V = velocity components with respect to missile body axis
X, Y, Z = coordinates of mass center of missile and target relative to fixed axes
 ,  ,  = missile orientations around fixed frame of reference
 = air density
ABBREVIATIONS
A/C = aircraft
FLC = fuzzy logic controller
NNC = neural network controller
TSK = Takagi Sugeno Kang

9. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004

10. MDP-8 Cairo University Conference on Mechanical Design and Production Cairo,
Egypt, January 4-6, 2004