Neural Networks Structured for Control 
Application to Aircraft Landing 
Charles Schley, Yves Chauvin, Van Henkle, Richard Golden 
Thomson-CSF, Inc., Palo Alto Research Operations 
630 Hansen Way, Suite 250 
Palo Alto, CA 94306 
Abstract 
We present a generic neural network architecture capable of con- 
trolling non-linear plants. The network is composed of dynamic, 
parallel, linear maps gated by non-linear switches. Using a recur- 
rent form of the back-propagation algorithm, control is achieved 
by optimizing the control gains and task-adapted switch parame- 
ters. A mean quadratic cost function computed across a nominal 
plant trajectory is minimized along with performance constraint 
penalties. The approach is demonstrated for a control task con- 
sisting of landing a commercial aircraft in difficult wind conditions. 
We show that the network yields excellent performance while re- 
maining within acceptable damping response constraints. 
1 INTRODUCTION 
This paper illustrates how a recurrent back-propagation neural network algorithm 
(Rumelhart, Hinton & Williams, 1986) may be exploited as a procedure for con- 
trolling complex systems. In particular, a simplified mathematical model of an 
aircraft landing in the presence of severe wind gusts was developed and simulated. 
A recurrent back-propagation neural network architecture was then designed to 
numerically estimate the parameters of an optimal non-linear control law for land- 
ing the aircraft. The performance of the network was then evaluated. 
1.1 A TYPICAL CONTROL SYSTEM 
A typical control system consists of a controller and a process to be controlled. The 
contro!ler's function is to accept task inputs along with process outputs and to de- 
termine control signals tailored to the response characteristics of the process. The 
415 
416 Schley, Chauvin, Henkle, Golden 
physical process to be controlled can be electro-mechanical, aerodynamic, etc. 
and generally has well defined behavior. It may be subjected to disturbances from 
its external environment. 
1.2 CONTROLLER DESIGN 
Many variations of both classical and modern methods to design control systems 
are described in the literature. Classical methods use linear approximations of the 
plant to be controlled and some loosely defined response specifications such as 
bandwidth (speed of response) and phase margin (degree of stability). Classical 
methods are widely used in practice, even for sophisticated control problems. 
Modern methods are more universal and generally assume that a performance in- 
dex for the process is specified. Controllers are then designed to optimize the 
performance index. Our approach relates more to modern methods. 
Narendra and Parthasarathy (1990) and others have noted that recurrent back- 
propagation networks can implement gradient descent algorithms that may be used 
to optimize the performance of a system. The essence of such methods is first to 
propagate performance errors back through the process and then back through the 
controller to give error signals for updating the controller parameters. Figure 1 
provides an overview of the interaction of a neural control law with a complex 
system and possible performance indices for evaluating various control laws. The 
functional components 
Control Disturbances needed to train the con- 
Task Neural Net 
Input . Control Process troller are shown within 
Signals the shaded box of Figure 
1. The objective per- 
formance measure con- 
tains factors that are writ- 
ten mathematically and 
usually represent terms 
such as weighted square 
error or other quantifiable 
measures. The perform- 
ance constraints are often 
more subjective in nature 
Figure 1: Neural Network Controller Design and can be formulated as 
reward or penalty functions on categories of performance (e.g., "good" or "bad"). 
2 A GENERIC NON-LINEAR CONTROL ARCHITECTURE 
Many complex systems are in fact non-linear or "multi-modal." That is, their 
behavior changes in fundamental ways as a function of their position in the state 
space. In practice, controllers are often designed for such systems by treating them 
as a collection of systems linearized about a "setpoint" in state space. A linear 
controller can then be determined separately for each of these system "modes." 
These observations suggest that a reasonable approach for controlling non-linear 
or "multi-modal" systems would be to design a "multi-modal" control law. 
2.1 THE SWITCHING PRINCIPLE 
The architecture of our proposed general non-linear control law for "multi-mod- 
al" plants is shown in Figure 2. Task inputs and process outputs are entered into 
Neural Networks Structured for Control Application to Aircraft Landing 417 
Task 
Inputs 
Process 
Outputs 
ht 
ht 
fin Switch 
Sigmoid( ) 
Multi 
Basic Controller Block 
,+ 
 
 
 
Repeat 
 
Figure 2: Neural Network Controller Architecture 
multiple basic controller 
blocks (shown within the 
shaded box of Figure 2). 
Each basic controller block 
first determines a weighted 
sum of the task inputs and 
process outputs (multipli- 
cation by weights W). 
Then, the degree to which 
the weighted sum passes 
through the block is modi- 
fied by means of a saturat- 
ing switch and multiplier. 
The input to the switch is 
itself another weighted sum 
of the task inputs and process outputs (multiplication by weights V). If the input to 
the saturating switch is large, its output is unity and the weighted sum (weighted by 
W) is passed through unchanged. At the other extreme, if the saturating switch has 
zero output, the weighted sum of task inputs and process outputs does not appear in 
the output. When these basic controller blocks are replicated and their outputs are 
added, control signals consist of weighted sums of the controller inputs that can be 
selected and/or blended by the saturating switches. The overall effect is a prototyp- 
ical feed-forward and feedback controller with selectable gains and multiple path- 
ways where the overall equivalent gains are a function of the task inputs and process 
outputs. The resulting architecture yields a sigrna-pi processing unit in the final 
controller (Rumelhart, Hinton & Williams, 1986). 
2.2 MODELLING DYNAMIC MAPPINGS 
Weights shown in Figure 2 may be constant and represent a static relationship be- 
tween input and control. However, further controller functionality is obtained by 
considering the weights V and W as dynamic mappings. For example, proportional 
plus integral plus derivative (PID) feedback may be used to ensure that process 
outputs follow task inputs with adequate steady-state error and transient damping. 
Thus, the weights can express parameters of various generally useful control func- 
tions. These functions, when combined with the switching principle, yield rich 
capabilities that can be adapted to the task at hand. 
3 AIRCRAFt LANDING 
The generic neural network architecture of Figure 2 and the associated neural net- 
work techniques were tested with a "real-world" application: automatic landing of 
an aircraft. Here, we describe the aircraft and environment model during landing. 
3.1 GLIDESLOPE AND FLARE 
During aircraft landing, the final two phases of a landing trajectory consist of a 
"glideslope" phase and a "flare" phase. Figure 3 shows these two phases. Flare 
occurs at about 45 feet. Glideslope is characterized by a linear downward slope; 
flare by an exponential shaped curve. When the aircraft begins flare, its response 
characteristics are changed to make it more sensitive to the pilot's actions, making 
the process "multi-modal" or non-linear over the whole trajectory. 
418 Schley, Chauvin, Henkle, Golden 
Altitude: h 
At Flare Initiation 
Altitude: h = h.! 
Altitude Rate: /t = h! 
Speed: V = Vf 
At Touchdown: 
Altitude: 
Altitude Rate: 
Position: 
Pitch Angle: 
0 < min  h TD ' hmax 
Xmin - XTD  Xmax 
Omin  OTD  Omax 
begin flare 
Glideslope Angle: 
Pitch angle is measured between the 
x axis and the aircraft velocity vector. 
touchdown point 
XTD -max 
position x Glideslope Predicted Xm 
Intercept Point 
Figure 3: Glideslope and Flare Geometry 
3.2 STATE EQUATIONS 
Linearized equations of motion were used for the aircraft during each phase. They 
are adequate during the short period of time spent during glideslope and flare. A 
pitch stability augmentation system and an auto-throttle were added to the aircraft 
state equations to damp the bare airframe oscillatory behavior and provide speed 
control. The function of the autoland controller is to transform information about 
desired and actual trajectories into the aircraft pitch command. This is input to the 
pitch stability augmentation system to develop the aircraft elevator angle that in 
turn controls the aircraft's actual pitch angle. Simplifications retain the overall 
quality of system response (i.e., high frequency dynamics were neglected). 
3.3 WIND MODEL 
The environment influences the process through wind disturbances represented by 
constant velocity and turbulence components. The magnitude of the constant ve- 
locity component is a function of altitude (wind shear). Turbulence is a stochastic 
process whose mean and variance are functions of altitude. For the horizontal and 
vertical wind turbulence velocities, the so-called Dryden spectra for spatial turbu- 
lence distribution are assumed. These are amenable to simulation and show rea- 
sonable agreement with measured data (Neuman & Foster, 1970). The generation 
of turbulence is effected by applying Gaussian white noise to coloring filters. 
4 NEURAL NETWORK LEARNING IMPLEMENTATION 
As previously noted, modern control theory suggests that a performance index for 
evaluating control laws should first be constructed, and then the control law should 
be computed to optimize the performance index. Generally, numerical methods 
are used for estimating the parameters of a control law. Neural network algorithms 
can actually be seen as constituting such numerical methods (Narendra and Partha- 
sarathy, 1990; Bryson and Ho, 1969; Le Cun, 1989). We present here an imple- 
mentation of a neural network algorithm to address the aircraft landing problem. 
Neural Networks Structured for Control Application to Aircraft Landing 419 
4.1 DIFFERENCE EQUATIONS 
The state of the aircraft (including stability augmentation and autothrottle) can be 
represented by a vector X, containing variables representing speed, angie of attack, 
pitch rate, pitch angle, altitude rate and altitude. The difference equations de- 
scribing the dynamics of the controlled plant can be written as shown in equation- 1. 
X,+ t -- A,X, + B,U, + CD, + N (1) 
The matrix A represents the plant dynamics and B represents the aircraft response 
to the control U. D is the desired state and N is the additive noise computed from 
the wind model. The switching controller can be written as in equation 2 below. 
Referring to Figure 2, the weight matrix V in the sigmoidal switch links actual alti- 
tude to each switch unit. The weight matrix W in the linear controller links altitude 
error, altitude rate error and altitude integral error to each linear unit output. 
Ut -- Pt T Lt where Pt = Sigrnoidal switch and Lt = Linear controller (2) 
Figure 4 shows a recurrent network implementation of the entire system. Actual 
and desired states at time t+l are fed back to the input layers. Thus, with recurrent 
JE jp connections between out- 
put and input, the network 
Xt+' -  Dt+  generates entire trajectories 
         '  and is seen as a recurrent 
\ ............. ///':':"":":': /'l/l/ back-propagation network 
(Rumelhart, Hinton & Wil- 
l iiiiiiil i i.i.,(/ ["':::t'!il K,  / llama, 1986; Jordan & Ja- 
-: cobs, 1990). The network 
iliiii!ii x/ n .K/, is trained using the back- 
\ ! propagation algorithm with 
given wind distributions. 
For the controller, we 
chose initially two basic 
PID controller blocks (see 
Figure 2) to represent gli- 
deslope and flare. The task 
of the network is then to 
eeeeeeee eee learn the state dependent 
Xt Dt PID controller gains that 
Figure 4: Recurrent Neural Network Architecture optimize the cost function. 
4.2 PERFORMANCE INDEX OPTIMIZATION 
The basic performance measure selected for this problem was the squared trajecto- 
ry error accumulated over the duration of the landing. Trajectory error corre- 
sponds to a weighted combination of altitude and altitude rate errors. 
Since minimizing only the trajectory error can lead to undesirable responses (e.g., 
oscillatory aircraft motions), we include relative stability constraints in the perform- 
ance index. Aircraft transient responses depend on the value of a damping factor. 
An analysis was performed by probing the plant with a range of values for controller 
weight parameters. The data was used to train a "damping judge" net to categorize 
"good" and "bad" damping. This net was used to construct a penalty function on 
"bad" damping. As seen in Figure 4, additional units were added for this purpose. 
420 Schley, Chauvin, Henkle, Golden 
The main optimization problem is now stated. Given an initial state, minimize the 
expected value over the environmental disturbances of performance index J. 
J = JE + Jv r = Trajectory Error + 
JE = Z an[ hcmat- ht ]2 + 
t=l 
T 
 . 
t=l 
Performance Constraint Penalty 
ai[ hcmat - ht ]2 We used an = a; = 1 
(3) 
Note that when it -  ie, there ts 
no penalty. Otherwtse, it is quadratic. 
5 SIMULATION EXPERIMENTS 
We now describe our simulations. First, we introduce our training procedure. We 
then present statistical results of flight simulations for a variety of wind conditions. 
5.1 TRAINING PROCEDURE 
Networks were initialized in various ways and trained with a random wind distribu- 
tion where the constant sheared speed varied from 10 ft/sec tailwind to 40 ft/sec 
headwind (a strong wind). Several learning strategies were used to change the way 
the network was exposed to various response characteristics of the plant. The exact 
form of the resulting V switch weights varied, but not the equivalent gain schedules. 
5.2 STATISTICAL RESULTS 
After training, the performance of the network controller was tested for different 
wind conditions. Table 1 shows means and standard deviations of performance 
variables computed over 1000 landings for five different wind conditions. Shown 
Table 1: Landing Statistics (standard deviations in parenthesis). 
Overall i Glide Slope Fixre Touchdown 
P,rformance Mean Squared Error Moan Squared Error Performance 
Wind J/'T T J: h, J: h, J: hit J: h!t Zro Ova hrr) 
It=-10 1.34 21.6 13.500 4.230 8.50 2.67 1030 0.0473 -2.15 
(0 56) (0.047) (9.8) (2.6) (1.4) (1.2) (111 (0.0039) (0.052) 
H=0 0.27 22.2 0,603 0,209 3,31 1 86 1080 -0.0400 ~1.98 
0.00) (0.000) (0.0) (0.0) 0.0) (0 0) (0) (0.0000) (0.000) 
H=10 0.96 23.0 12.500 4,390 3,17 2.01 1160 -0.1260 -1.79 
(0.53) (0.052) (9.2) (2.6) (2.2) (1.1) (12) (0.0046) (0.040) 
It=20 3,56 23.8 54.000 18,500 8,65 3.43 1230 -0,2170 -1.64 
(2.10) (0.100) (38.0) (11.0) (8.2) (2.7) (24) (0.0100) (0.061) 
It=30 8.03 24.6 130.000 43.200 19.20 5.73 1310 -0.3110 -1.50 
(4 70) (0.160) (91.0) (25.0) (19.0) (4 7) (39) (0.0170) (0.076) 
H=40 13.40 25,5 219 000 76 200 37 00 9 24 1400 -0.4030 -1.39 
,T 80) (0.220) (150.0/ (16.0) 36.0) q.O) (54) (0.02301 (0.083) 
are values for overall performance (quadratic cost J per time step, landing time T), 
trajectory performance (quadratic cost J on altitude and altitude rate), and landing 
performance (touchdown position, pitch angle, altitude rate). 
Neural Networks Structured for Control Application to Aircraft Landing 421 
5.3 CONTROL LAWS OBTAINED BY LEARNING 
By examining network weights, equation 2 yields the gains of an equivalent control- 
ler over the entire trajectory (gain schedules). These gain schedules represent 
optimality with respect to a given performance index. Results show that the switch 
builds a smooth transition between glideslope and flare and provides the network 
controller with a non-linear distributed control law for the whole trajectory. 
6 DISCUSSION 
The architecture we propose integrates a priori knowledge of real plants within the 
structure of the neural network. The knowledge of the physics of the system and its 
representation in the network are part of the solution. Such a priori knowledge 
structures are not only useful for finding control solutions, but also allow interpreta- 
tions of network dynamics in term of standard control theory. By observing the 
weights learned by the network, we can compute gain schedules and understand 
how the network controls the plant. 
The augmented architecture also allows us to control damping. In general, inte- 
grating optimal control performance indices with constraints on plant response 
characteristics is not an easy task. The neural network approach and back-propa- 
gation learning represent an interesting and elegant solution to this problem. Other 
constraints on states or response characteristics can also be implemented with simi- 
lar architectures. In the present case, the control gains are obtained to minimize 
the objective performance index while the plant remains within a desired stability 
region. The effect of this approach provides good damping and control gain sched- 
ules that make the plant robust to disturbances. 
Acknowledgements 
This research was supported by the Boeing High Technology Center. Particular 
thanks are extended to Gerald Cohen of Boeing. We would also like to thank Anil 
Phatak for his decisive help and Yoshiro Miyata for the use of his XNet simulator. 
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