Page 15 - Neural Network Modeling and Identification of Dynamical Systems

NEURAL NETWORK MODELING AND IDENTIFICATION OF DYNAMICAL SYSTEMS 3
When implementing the above functions, As experience shows, the modeling tool that
both in the process of design and in the sub- is most appropriate for this situation is the con-
sequent operation of various types of aircraft, cept of an artificial neural network (ANN). Such
a significant place is occupied by the analysis an approach can be considered as an alterna-
of the behavior of dynamical systems, the syn- tive to traditional methods of dynamical sys-
thesis of control algorithms for them, and the tem modeling, which provides, i.a., the possibil-
identification of their unknown or inaccurately ity of obtaining adaptive models. At the same
known characteristics. A crucial role in solving time, traditional neural network dynamical sys-
the problems of these three classes belongs to tem models, in particular, the models of the
mathematical and computer models of dynami- NARX and NARMAX classes, which are most
cal systems. often used for the simulation of controlled dy-
The traditional classes of mathematical mod- namical systems, are purely empirical (“black
els for engineering systems are ordinary dif- box”–type) models, i.e., based solely on exper-
ferential equations (ODEs) (for systems with imental data on the behavior of an object. How-
lumped parameters) and partial differential ever, in tasks of the complexity level that is typi-
equations (PDEs) (for systems with distributed cal for aerospace technology, this kind of empir-
parameters). As applied to controlled dynam- ical models is very often not capable of achiev-
ical systems, ODEs are most widely used as a ing the required level of accuracy. In addition,
modeling tool. These models, in combination due to the peculiarities of the structural organi-
with appropriate numerical methods, are widely zation of such models, they do not allow solving
used in solving problems of synthesis and anal- the problem of identifying the characteristics of
ysis of controlled motion of aircraft of various the dynamical system (for example, the aerody-
classes. Similar tools are also used to simulate namic characteristics of an aircraft), which is a
the motion of dynamical systems of other types, serious disadvantage of this class of models.
including surface and underwater vehicles and One of the most important reasons for the
ground moving vehicles. low efficiency of traditional-type ANN models
Methods of forming and using models of in problems associated with complex engineer-
the traditional type are by now sufficiently de- ing systems is that a purely empirical (black box)
veloped and successfully used to solve a wide model is being formed, which should cover all
range of tasks. However, in relation to modern the peculiarities of the dynamical system behav-
and advanced engineering systems, a number ior. For this, it is necessary to build an ANN
of problems arise, the solutions of which can- model of a sufficiently high dimension (that is,
not be provided by traditional methods. These with a large number of adjustable parameters
problems are caused by the presence of various in it). At the same time, it is known from ex-
and numerous uncertainties in the properties of perience of ANN modeling that the larger the
the corresponding system and in its operational dimension of the ANN model, the greater the
conditions, which can be parried only if the sys- amount of training data required to configure
tem in question has the property of adaptability, it. As a result, with the amount of experimental
i.e., if there are means of operational adjustment data that can actually be obtained for complex
of the system and its model to the changing cur- engineering systems, it is not possible to train
rent situation. In addition, the requirements for such models, providing a given level of accu-
the accuracy of models imposed on the basis racy.
of the specificity of the applied problem being To overcome this kind of difficulty, which is
solved in some cases exceed the capabilities of characteristic of traditional models, both in the
traditional methods. form of differential equations and in the form