Page 25 - Neural Network Modeling and Identification of Dynamical Systems

1.1 THE DYNAMICAL SYSTEM AS AN OBJECT OF STUDY 13
ilar to those introduced above for the system general they can be represented as follows:
(1.3). The difference between these systems again
lies in the form of the rule CS .Thisrulefor AS = X AS ,T AS , AS , AS ,
AS ,
the system CS depends not only on the current AS AS
X ⊆ X, T ⊆ T,
state x(t i ) of the system, uncontrollable distur-
AS = AS (x,u,ξ,t), AS = AS (γ ,t), (1.6)
bances ξ,andtime t, but also on the so-called
control variables u = (u 1 ,...,u m ) ∈ U,which
AS ⊆
, x ∈ X AS ,u ∈ U AS ,
take (instantaneous) values from some region ξ ∈ , γ ∈
,t ∈ T AS ⊆ T.
U CS .
So, the system of the class CS is a dynami- In the definition of the adaptive system AS,com-
cal, controlled, purposeful system, regularly re- pared to a controllable system of the class CS,
sponding to the effects of the environment E.In two new elements have appeared. The first of
a more general case, a system of the class CS these is the AS rule (“adaptation rule”) that de-
can be influenced by various kinds of uncertain scribes how to modify the rule AS ,which deter-
factors ξ ∈ . The system of this class is char- mines the current behavior of the system under
acterized by the fact that, unlike the systems of consideration. The second new element is the set
the next two hierarchical levels (adaptive and of goals
AS , according to which the work of the
intelligent), the control objective is external to rule AS proceeds.
the system and is taken into account only at the So, the system of the class AS is a dynamical,
stage of synthesis of the control law for this sys- controlled, purposeful system with adjustable
tem. control law AS that regularly interacts with the
environment and is also influenced by various
1.1.2.4 Adaptive Systems kinds of uncertainty factors. The set of goals
AS
The most important difference between sys- that organize behavior in systems of class AS re-
mains unchanged during the system operation.
tems of class CS and systems of classes VS and
DS is that systems CS can actively respond to
1.1.2.5 Intelligent Systems
influences of the environment E. These possibil-
In comparison with the systems of the class
ities, however, are limited by the fact that the
rule CS (the control law of the system CS)in CS, adaptive systems AS are able to modify their
behavior directly in the process of the system
(1.5) is assumed to be preserved. There is no
functioning due to the influence that the rule
way to modify this rule during the operation of AS AS
has on the control law whichinturn
the system (1.5). But if the region of uncertainty determines the current behavior of the system
is “large enough,” it can turn out that it will AS.
be impossible to form a control law such that it
However, the characteristic feature of AS sys-
provides the required level of control quality for AS
tems is that the rule for modifying the be-
any values of ξ ∈ . As a consequence, there is havior pattern is defined during the system de-
a need to change the form of the control law of sign stage and remains fixed afterwards. The
the system (the rule) during the process of the choice for the rule AS was made according to
system operation. The systems AS, 12 which have the specific goals
AS , the achievement of which
this kind of property, are called adaptive and in was the purpose of the system AS development.
Hence the behavior of the AS system will be ad-
equate so long as the goals
AS remain relevant
12 AS is the abbreviation for the Adaptive System. in a changing situation.