Page 16 - Neural Network Modeling and Identification of Dynamical Systems

4 NEURAL NETWORK MODELING AND IDENTIFICATION OF DYNAMICAL SYSTEMS

of ANN models, it is proposed to use a com- lyze the kinds of adaptation, the basic types of
bined approach. It is based on ANN modeling, adaptive control schemes, and the role of mod-
due to the fact that only in this variant it is pos- els in the problem of adaptive control. The need
sible to get adaptive models. Theoretical knowl- for adaptability of the controlled object model
edge about the object of modeling, existing in is revealed, as well as the need for neural net-
the form of ODEs (these are, for example, tradi- work implementation of adaptive modeling and
tional models of aircraft motion), is introduced control algorithms.
in a special way into the ANN model of the com- Chapter 2 presents the neural network ap-
bined type (semiempirical ANN model). At the proach to modeling and control of dynamical
same time, a part of the ANN model is formed systems. The classes of ANN models for dy-
on the basis of the available theoretical knowl- namical systems and their structural organiza-
edge and does not require further adjustment tion are considered in this chapter, including
(training). Only those elements that contain un- static (feedforward) networks and dynamic (re-
certainties, such as the aerodynamic character- current) networks. The next significant problem
istics of the aircraft, are subject to adjustment that arises in the formation of ANN models of
and/or structural correction in the learning pro- dynamical systems is related to the algorithms
cess of the generated ANN model. of their learning. In the second chapter, algo-
The result of this approach is semiempirical rithms for learning dynamic ANN models are
ANN models, which allow us to solve prob- considered. The difficulties associated with such
lems inaccessible to traditional ANN methods. learning, as well as ways to overcome them, are
We can sharply reduce the dimensionality of analyzed. One of the fundamental requirements
the ANN model, which allows achieving the re- for the considered ANN models is giving them
quired accuracy using training sets that are in- the property of adaptability. Methods for satis-
sufficient in volume for traditional ANN mod- fying this requirement are considered, including
els. Besides, this approach provides the ability to the use of ANN models with interneurons and
identify the characteristics of the dynamical sys- subnets of interneurons, as well as the incremen-
tem, described by nonlinear functions of many tal formation of ANN models. One of the critical
variables (for example, the dimensionless coeffi- problems when generating ANN models, espe-
cients of aerodynamic forces and moments). cially dynamical system models, is an acquisi-
In subsequent chapters, we consider an im- tion of training sets. In the second chapter, the
plementation of this approach, as well as exam- specific features of processes needed to generate
ples of its application for simulating the motion training sets for the ANN modeling of dynami-
of an aircraft and identifying its aerodynamic cal systems are analyzed. We consider direct and
characteristics. indirect approaches to the generation of these
Chapter 1 is devoted to a statement of the training sets. Algorithms for generating a set of
modeling problem for controlled motion of non- test maneuvers and test excitation signals for the
linear dynamical systems. We consider the dynamical system required to obtain a represen-
classes of problems, which arise from the pro- tative set of training data are given.
cesses of development and operation of dynam- In Chapter 3, we deal with the neural network
ical systems (analysis, synthesis, and identifi- black box approach to solving modeling prob-
cation problems) and reveal the role of mathe- lems associated with dynamical systems. We
matical modeling and computer simulation in discuss state space representations and input-
solving these problems. The next set of ques- output representations for such systems. We at-
tions relates to the problem of the adaptability tempt to show that using ANN technology we
of dynamical systems. In this regard, we ana- can solve the problem of appropriate represen-