Page 33 - Neural Network Modeling and Identification of Dynamical Systems

1.2 DYNAMICAL SYSTEMS AND THE PROBLEM OF ADAPTABILITY 21
and irrespective of the uncertainty factors. In 1.2 DYNAMICAL SYSTEMS AND
contrast, the activity (1.21) is only available for THE PROBLEM OF
systems that include the formulation of control ADAPTABILITY
goals in one form or another. These are either
permanent goals (adaptive systems AS)orself- One of the most important classes of dynam-
corrected goals (intelligent systems IS). ical systems is aircraft of various types. As al-
Control of the behavior for the system S is a ready noted, it is necessary to ensure the con-
more general concept than control of its motion. trol of the motion for modern and advanced air-
A list of elements involved in the behavior con- craft under significant and diverse uncertainties
trol is presented in the introduction on page 2. in the values of their parameters and character-
Robotics borrows the concept of the activ- istics, flight regimes, and environmental influ-
ity from the life sciences (biology, psychology, ences. Moreover, during flight, a variety of ab-
ethology). In recent years, research in the field of normal situations may arise, in particular, equip-
robotization of controllable dynamical systems ment failures and structural damage, the conse-
of various kinds has been actively conducted. As quences of which can be compensated in most
a consequence, we need to expand the capabil- cases by reconfiguration of the aircraft control
ities of dynamical system modeling and control system and reallocation of its control surfaces.
tools from traditional motion control tasks to the The presence of significant and diverse un-
tasks of behavior and activity control for such certainties is one of the most severe factors that
systems. These problems are especially relevant complicates the solution of all three problems
for highly autonomous robotic UAVs (so-called (analysis, synthesis, identification) for dynami-
“smart UAVs”) and unmanned cars. cal systems. The problem here is that the cur-
The action executed by the system S does not rent situation for the system can change dra-
necessarily depend only on the current (i.e., con- matically. Besides, the situation change can be
sidered at the time instant t i ∈ T ) values of the unpredictable because of uncertainties. Under
these conditions, the system must be able to ad-
situation λ(t i ) and the goal γ(t i ). In a more gen-
just quickly to such changes in the situation, so
eral case, it depends on the set of situations (t i )
it must be adaptive.
and the set of goals
(t i ) at a given time instant
We need to clarify the meaning of the concept
t i , i.e.,
of system adaptability.Byadaptivewemeansuch
a system that can quickly adjust to a changing
S
(t i ),
(t i ) −−→ λ(t i+1 ), i = 0,1,2,...,N; situation by varying some of its elements. We
S
S
(t i ) ⊂ ,
(t i ) ⊂
. assume that such elements include the control
laws implemented by the dynamical system, as
(1.22)
well as the model of the controlled object. Most
of the changes in these elements can affect both
Here the transition to the situation λ(t i+1 ) de- the parameter values and the structure of the
pends not only on the current situation λ(t i ) and control laws and/or models. In most cases, the
the current goal γ(t i ) at a given time instant t i , changes in these elements relate to the values
but also on the past (prehistory) and future (fore- of their parameters. Sometimes, the structure of
cast) states and goals, which are described by the control laws and/or models is also subject to
corresponding sets: a set of situations (t i ) and change. These topics are discussed in more de-
a set of goals
(t i ) for a given time instant t i . tail in the next section.