Page 129 - Neural Network Modeling and Identification of Dynamical Systems

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

The neural network implementation of the de- the residual on the required and realized mo-
pendence k = k(λ) is significantly less critical tion, which determines the nature of the neuro-
to the complexity of this dependence, as well corrector training.
as to the dimensions of the vectors λ and k. To assess the quality of the ANN control, it is
As a consequence, there is no need to minimize necessary to have an appropriate performance
the number of controller tuning parameters. We index. This index (the optimality criterion of
have an opportunity to expand significantly the the neurocontroller) should obviously take into
list of such parameters, including, for example, account not only the presence of variable pa-
not only the dynamic air pressure (as mentioned rameters in the neurocontroller from the regions
above, in some cases it is the only tuning pa- W and V, but also the fact that the dynamical
rameter), but also the Mach number, the angles system with the given neurocontroller is multi-
of attack and sideslip, aircraft mass, and other mode, that is, should be taken into account the
variables influencing the controller coefficients presence of an external set .
on some flight regimes. In the same simple way, In accordance with the approach proposed in
by introducing additional parameters, it is possi- [88], the formation of the optimality criterion of
ble to take into account the change in the motion the neurocontroller on the domain will be car-
model (change in the type of aircraft dynamics) ried out on the basis of the efficiency evaluation
mentioned above. of the neurocontroller “at the point,” i.e., for a
fixed value λ ∈ , or, in other words, for a dy-
∗
Moreover, even a significant expansion of the
namic system in a single-mode version.
list of controller tuning parameters does not lead
to a significant complication of the synthesis To do this, we construct a functional J =
J(x,u,θ,λ) or, taking into account that the vec-
processes for the control law and its use in the
tor u ∈ U is uniquely determined by the vector k
controller.
The variant of the correcting module based on of the controller coefficients, J(x,k,θ,λ).Weas-
sume that the control goal “at the point” is the
the use of the ANN will be called the neurocorrec-
maximum correspondence of the motion real-
tor, and the aggregation of the controller and the
ized by the considered dynamical system to the
neurocorrector we call neurocontroller.
motion determined by a certain reference model
We assume that the neurocontroller is an or-
dered five of the following form: (the model of some “ideal” behavior of the dy-
namical system). This model can take into ac-
count both the desired nature of change in the
= ( ,K,W,V,J), (3.36)
state variables of the dynamical system and the
s
where ⊂ R is the external set of the dynam- various requirements for the nature of its opera-
ical system, which is the domain of change in tion (for example, the requirements for handling
the values of input vectors of the neurocorrec- qualities of the aircraft).
n
tor; K ⊂ R is the range of the values of the Since we are discussing the control “at the
required controller coefficients, that is, the out- point,” the reference model can be local, defin-
ing the required character of the dynamical sys-
put vectors of the neurocorrector; W ={W i }, i =
1,...,p + 1, is the set of matrices of the synap- tem operation for single value λ ∈ . We will call
tic weights of the neurocorrector (here p is the these λ values operation modes. They represent
number of hidden layers in the neurocorrec- characteristic points of the region which are
q
tor); v = (v 1 ,...,v q ) ∈ V ⊂ R is a set of addi- selected in one way or another.
tional variable parameters of the neurocorrector, As the reference we will use a linear model of
for example, tuning parameters in the activation the form
functions; J is the error functional, defined as ˙ x e = A e x e + B e u e , (3.37)