Page 26 - Neural Network Modeling and Identification of Dynamical Systems

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

In an environment with high levels of var- under the influence of various kinds of uncer-
ious uncertainties, a change in the situation tainty factors.
may require us to use a higher level of adap-
tation, namely, the adaptation of goals (see Sec- 1.1.3 Classes of Environments
tion 1.2.1.4). However, systems of the class AS
lack the knowledge required to perform this op- Similarly to classes of systems S, we can also
eration, because they do not have a goal-setting introduce classes of the environment E.Inthe
mechanism, i.e., a mechanism that generates following sections we define various environ-
new goals when necessary. Also, AS systems ment classes in order of increasing complexity,
have no tool of influence on the rule AS , i.e., assuming that they interact with a system of the
a mechanism that adjusts the rule of AS behav- general form S.
ior modification.
So, the next step is to add a new property to 1.1.3.1 Regular Environments
the system AS, namely, the goal-setting. 13 Sys- The regular environment SE 15 lies at the low-
tems IS, 14 possessing this kind of property, we est level of the environment hierarchy. It imple-
will call intelligent, and we will represent them ments a regular (i.e., not containing any uncer-
as follows: tainties) effect on the system S. To some extent,
the central gravitational field of some celestial
IS
IS
IS
IS
IS
IS
IS = X ,T, , ,
, , ,
body can be considered as an environment ex-
X IS ⊆ X, T IS ⊆ T, ample of the class SE.
IS
IS = (x,u,ξ,t), AS = AS (γ ,t), 1.1.3.2 Environments With Uncertainties
(1.7)
AS IS IS

⊆
, = (x,u,ξ,γ ,t), The environment with uncertainties UE 16 is the
IS
x ∈ X , u ∈ U IS ,ξ ∈ , γ ∈
, next level of the environment hierarchy. It is
characterized by the fact that the effect it has on
IS ⊆ ,t ∈ T IS ⊆ T.
the system S contains a number of uncertainty
factors, i.e., factors that are unknown a priori.
In comparison with the adaptive system AS,
the rule IS is added to the definition of the The system S cannot manage and measure these
factors. An example of an environment of class
intelligent system IS. This rule describes the UE is a turbulent atmosphere.
method of generating γ ∈
goals. Thus, the in-
telligent system IS has a way of changing the 1.1.3.3 Reacting Environments
IS
set of goals
, as well as another structure, ,
The environments of the classes SE and UE
which specifies such elements as values, mo-
are passive; they act in a certain way on the sys-
tives, etc., that guide the goal-setting process.
tem S, however their own response to the ac-
So, a system of class IS is a dynamical, con-
trolled, purposeful system that has the tools tions of the system S is very limited and not pur-
(mechanisms) of goal-setting. Systems of this poseful. For example, the turbulent atmosphere
class and systems of classes CS and AS interact
15
with the environment both in a regular way and SE is the abbreviation for the Stereotyped Environment,
i.e., a regular environment that acts on the system S in some
routine, standard manner that does not change during the
13 S
Development of a goal-setting mechanism is one of the lifetime T of the system S.
most important topics of modern robotics. However, no sat- 16 UE is the abbreviation for the Uncertain Environment, i.e.,
isfactory solution to this problem has yet been discovered. an environment containing some uncertainties (factors that
The results available in this field are covered in [21]. the system S can neither control nor, in some cases, even
14 IS is the abbreviation for the Intelligent Systems. measure).