Page 141 - Neural Network Modeling and Identification of Dynamical Systems

CHAPTER
4

Neural Network Black Box Modeling of

Nonlinear Dynamical Systems: Aircraft

Controlled Motion

m
4.1 ANN MODEL OF AIRCRAFT ϕ : R → R as some ANN model with any pre-
n
MOTION BASED ON A defined accuracy. 1
MULTILAYER NEURAL The ANN model design problem for the non-
linear controlled dynamical system is treated
NETWORK
further as a problem of a neural network ap-
proximation of the initial mathematical model
As we noted in Chapter 1, many adaptive
of the aircraft motion, defined in one way or
control schemes require the presence of a con- another, more often in the form of a system of
trolled object model. To obtain such a model, differential equations. A structural diagram of
one needs to solve the classical problem of dy- the neural network identification process for the
namical systems identification [1]. As experience controlled system that corresponds to this prob-
shows, one of the most effective approaches to lem is presented in Fig. 4.1.
solving this problem for nonlinear systems is The error signal ε that directs the learning of
based on the use of ANNs [2–4]. Neural net- the ANN model is taken to be the squared dif-
work modeling allows us to build reasonably ference between the outputs of the controlled
object y p and the neural network model y m for
accurate and computationally efficient mod-
the control signal u. The trained ANN model im-
els.
plements a recurrent relation that allows us to
y
compute the value of the output at time instant
4.1.1 The General Structure of the t i+1 given the values of y and u at some previous
ANN Model of Aircraft Motion time instants.
Based on a Multilayer Neural We use the Nonlinear Auto-Regressive net-
Network work with eXternal inputs (NARX) as a model
of a dynamical system because it conforms to
An ANN is an algorithmically universal math- the nature of the considered problem of flight
ematical model [5–7]. This fact is the basis of
the computational efficiency of ANN models. It 1 That is, any nonlinear mapping of the n-dimensional input
allows us to represent any nonlinear mapping vector to the m-dimensional output vector.

Neural Network Modeling and Identification of Dynamical Systems
https://doi.org/10.1016/B978-0-12-815254-6.00014-9 131 Copyright © 2019 Elsevier Inc. All rights reserved.