Page 135 - Neural Network Modeling and Identification of Dynamical Systems

124 3. NEURAL NETWORK BLACK BOX APPROACH TO THE MODELING AND CONTROL OF DYNAMICAL SYSTEMS

In the problem of general optimization (3.56) which will have to be paid for such a decision.
for the ENC we remove the condition of fix- For modern and, especially, advanced aircraft
ing the number N of neural controllers i ,i = with high performances, the required depen-
1,...,N. It is possible, in such a case, to vary dence is multidimensional and has a very com-
(select) also the number of neurocontrollers in plicated character, which, also, can be consider-
the ENC minimizing the value of the optimal- ably complicated if the aircraft requires the im-
ity criterion (3.50), (3.52)or(3.51), (3.53). Obvi- plementation of various types of behavior corre-
ously, the problem of optimizing ENC parame- sponding to different classes of problems solved
ters (3.55) and, consequently, the optimal distri- by the aircraft. As a result, the synthesized neu-
bution problem (3.54) are included in the general ral network cannot satisfy the designers of the
optimization problem (3.56) as subtasks. control system due to, for example, a too high
The solution of the optimal distribution prob- network dimension, which makes it difficult to
lem (3.54) allows the best divide (in the sense of implement this network using aircraft onboard
the criterion (3.50), (3.52)or(3.51), (3.53)) the ex- tools, or even makes such an implementation
ternal set of the considered MDS into the spe- impossible, and also significantly complicates
cialization domain D i ⊂ , i = 1,...,N,speci- the solution of the problem of training the ANN.
fying where it is best to use each of the neuro- Besides, the larger the dimension of the ANN,
controllers i ,i ∈{1,...,N}. By varying the pa- the longer the time of its response to a given
rameters of the neurocontrollers in the ENC and input signal when the network is implemented
solving the optimal distribution problem each using serial or limited-parallel hardware, which
time, it is possible to reduce the value of the cri- are the dominant variants now.
terion (3.50), (3.52)or(3.51), (3.53), which evalu- It is to this kind of situation that the approach
ates the efficiency of the ENC on the external under consideration is oriented, according to
set as a whole. The removal of the restriction which the problem of decomposing one ANN
on the number of neurocontrollers in the ENC (and, correspondingly, one neurocontroller) into
provides, in general, a further improvement in a set of mutually coordinated neurocontrollers,
the ENC effectiveness value. In the general case, implemented as an ensemble of ANNs, is solved.
for the same MDS with a fixed external set ,the We have shown how to perform this decompo-
following relation holds: sition optimally within the framework of three
classes (levels) of task optimization of ENCs.
F (1) ( ) F (2) ( ) F (3) ( ), We have described here the formation of the
optimal ENC concerning the conservative ap-
where F (1) ( ), F (2) ( ),and F (3) ( ) are the val- proach to the use of ANNs in control problems.
ues of the optimality criteria (3.50), (3.52)or However, this approach is equally suitable after
(3.51), (3.53) obtained by solving the optimal a small adaptation for the radical approach to
distribution problem (3.54), the parameter op- neurocontrol for multimode dynamic systems,
timization problem (3.55), or the general opti- and, consequently, also for a compromise ap-
mization problem (3.56)for agivenMDS. proach to solve this problem.
Generally speaking, the required dependence Moreover, if we slightly reformulate the con-
of the controller coefficients on the parameters sidered approach, it can also be interpreted as
of the regime description can be approximated an approach to the decomposition of ANNs,
with the help of a neural network at once to the oriented to solving problems under uncertainty
entire region of the modes of the MDS operation conditions, that is, as an approach to replacing
(that is, on its whole external set). However, here one “large” network with a mutually agreed ag-
it is necessary to take into account the “price” gregate (ensemble) of “smaller” networks, and