Page 44 - Neural Network Modeling and Identification of Dynamical Systems

32 1. THE MODELING PROBLEM FOR CONTROLLED MOTION OF NONLINEAR DYNAMICAL SYSTEMS

and examples of applications of these methods
can be found in Chapters 4 and 6.
1.3.2.1 Design of a Set of Values Describing
the Modeled Object
The first thing that needs to be done during
FIGURE 1.8 Parametrization of the simulated dynamical
system. From [56], used with permission from Moscow Avi- the design of the dynamical system model is to
ation Institute. define a set of variables describing the given sys-
tem. The related considerations were discussed
above, on page 30. We assume that this problem
• this family should be arranged in such a way has already been solved, i.e., we already have
as to simplify as much as possible the process decided which variables should be taken into ac-
of selection for the model (·). count in the simulation.
∗
As a basis for searching solutions that meet
1.3.2.2 Design of a Family of Models That
these requirements, the following sections im- Includes the Desired Model
plement an approach oriented on the effective
To solve the problem of dynamical system
structuring and parametrization of the desired modeling, we first need to design a set (fam-
model (·), implying an appropriate choice of (F)
ily) of model options = j (·), j = 1,2,...,
its structure and the insertion of the required
among which we then choose the best (in some
number of variable parameters (Fig. 1.8).
sense) option (·). As already noted, solving
∗
this part of the dynamical system modeling
1.3.2 The Main Problems That Need to problem requires us to answer the following two
Be Solved During Design of a questions:
Model for a Dynamical System • What is the desired family of options (F) =
{ j (·)}, j = 1,2,...?
During the design process for the dynamical
∗
• How can we select such an option (·) from
system model, some problems need to be solved (F)
the family that satisfies the condition
irrespective of the approach one takes. Namely, (u(t),ξ,ζ) − (u(t),ξ,ζ) ε, t ∈[t 0 ,t f ],
it is required to design:
∀u ∈ U, ξ ∈ , ζ ∈ Z?
• a set of variables that describe the simulated
The main ideas that provide answers to these
object; questions are as follows:
• a class (family) of models that includes the re-
quired model; • key properties of the model family (F) are its
• a representative (informative) set of experi- effective structuring and parametrization;
∗
mental data for the development and testing • key algorithms for choosing (·) from the set
(F) are machine learning algorithms (includ-
of the model;
• tools for selection of a particular model from ing neural network learning algorithms).
a given class (the criterion of adequacy for the 1.3.2.3 Design of a Representative Set of
model and the search algorithm).
Experimental Data for the
Below is a brief description of these prob- Development and Testing of the
lems. In more detail, the methods of their so- Model
lution within the framework of the developed One of the most critical components of the
approach are considered in Chapters 2, 3,and 5, process of dynamical system model design is the