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CHAPTER
3
Neural Network Black Box Approach to
the Modeling and Control of Dynamical
Systems
3.1 TYPICAL PROBLEMS Situation = External-Situation (Environment) +
ASSOCIATED WITH Internal-Situation (Object).
DEVELOPMENT AND The main problem is that, due to the pres-
MAINTENANCE OF ence of uncertainties, the current situation for
DYNAMICAL SYSTEMS the dynamic system under consideration may
change significantly and unpredictably. This cir-
As noted earlier, the object of our research is cumstance we have to take into account both in
a controlled dynamical system, operating under modeling the system and in controlling its be-
conditions of various uncertainties. havior.
Among the main types of uncertainties that In Chapter 1, the dynamical system S was de-
need to be considered when solving problems fined as an ordered triple of the following form:
related to controlled dynamical systems are the
following: S = U,P,Y , (3.1)
• uncertainties generated by uncontrolled dis- where U is the input to the simulated/con-
turbances acting on the object; trolled object, P is the simulated/controlled ob-
• incomplete and inaccurate knowledge of the ject (plant), and Y is a response of the object to
properties and characteristics of the simu- the input signal. In this definition:
lated object and the conditions in which it
• the input actions U are the initial conditions,
operates;
• uncertainties caused by a change in the prop- controls, and uncontrolled external influences
erties of the object due to failures of its equip- on the object P;
ment and structural damage. • the simulated/controlled object P is an air-
craft or another type of controllable dynam-
As shown in Chapter 1, the behavior of the ical system;
system is largely determined by the current • the outputs Y of the dynamical system S are
and/or predicted situation, including external the observed reactions of the object P to the
and internal components, i.e., input actions.
Neural Network Modeling and Identification of Dynamical Systems
https://doi.org/10.1016/B978-0-12-815254-6.00013-7 93 Copyright © 2019 Elsevier Inc. All rights reserved.
