Page 35 - Neural Network Modeling and Identification of Dynamical Systems

1.2 DYNAMICAL SYSTEMS AND THE PROBLEM OF ADAPTABILITY 23
boundary between the object and the environ- at medium and long ranges. The adaptation re-
ment. action was to include, in addition to the Su-9
The main idea of this level of adaptation is airplane with the onboard radar TsD-30 and
that the solution of the required target problem the guided air-to-air missiles RS-2-US, the sys-
may be achieved not only by one system S,as tem of automated ground guidance “Vozdukh”
in the previous two cases, but by a team of such (“Air”).
μ
systems {S μ },μ = 1,...,N , that interact with
each other. Therefore, instead of a single rule 1.2.1.4 Adaptation of Control Goals
S
S
= (x,u,ξ,t) we consider a set of interact- If theadaptationofthesystem S does not al-
S
S
ing rules ={ μ } , corresponding to different low us to solve the assigned problem, i.e., to
μ
systems S μ ,μ = 1,...,N . ensure the achievement of the system goals, it
S
is quite possible that these goals γ ∈
are un-
Example 4. Let us assume that the problem to be reachable for S. In this case, it remains possible
solved involves an interception of aerial targets, to change control goals so that they become at-
including group targets. If the airspace area and tainable. This operation is performed using the
the number of targets in the group are relatively rule = (λ,γ ,t), based on the motivational
S
S
small, then in some cases the problem can be set of elements IS ⊆ . Adaptation of goals is,
solved by a single fighter-interceptor, possessing in essence, the adjustment of the needs of the
missile armament and a multichannel system for subject of control.
detecting and tracking targets. If these condi-
tions are not met, the capabilities of one aircraft Example 6. We can explain the essence of adap-
are not enough. tation of control goals as follows. Suppose that a
In order to solve this problem we need to use self-propelled vehicle delivered to some celestial
a group of systems aimed at a cooperative solu- body must examine a particular object. It may be
tion of a common problem. An example of such found that the solution of the assigned task re-
approach is the MiG-31 [36,37] interception com- quires too much expenditure of resources, which
plex, in which a group of four interacting air- jeopardizes the fulfillment of other tasks of the
craft of this type manages the airspace in front expedition. In this case, proceeding from general
of them with a length of 800–900 km. In the vari- settings (for example, to get the maximum pos-
ant MiG-31B, the interception complex has an sible knowledge about the celestial body under
additional opportunity to automatically trans- study), the system S can replace one goal with
mit the data about the targets detected by the another and find for study an object “similar”
fighter to ground-based air defense systems in to one that it failed to investigate, or refuse alto-
order to support the targeting of antiaircraft mis- gether from this point of the program, switching
siles. In this case an expansion of the intercep- to others.
tion complex has been performed by adjusting
the boundary between this complex and the en- 1.2.2 General Characteristics of the
vironment. Adaptive Control Problem
Example 5. A similar example of the adapta- As is well known [38,39], the traditional con-
tion of the object is the development of the first trol theory requires knowledge of the mathemat-
Soviet interception complex Su-9 [36]. This com- ical model of the object. We need to know pa-
plex, adopted in 1960, was a response to the rameters and characteristics of the object, as well
fact that a “sole” interceptor, even with missile as parameters and characteristics of the environ-
weapons, cannot effectively intercept air targets ment in which the object operates.