![](bg5.png)
Initial Population
(Initialization of the estimates vectors)
Evaluation of each individual fitness
(Performance index for each estimator)
Selection of the parents
(Slection of a subset of
potentially estimator
algorithms)
Generate the offsprings by
applying various genetic
operators, croos over,
mutation, ...
(Obtain the new vector from
the particular estimation
algorithm used)
Replace the population with
the new offsprings
(The new estimates vector are
used for control an supervision
purpouses)
Finish?
End
Next generation
(Next sample, step)
NO
YES
Figure 8: General structure of a genetic algorithm
This is a typical assumption in the adaptive control
problem, the existence of a convex and compact
subset of the parameter space where the real plant
parameter vector is assumed to belong to. Once the
GA is initialised it starts running. First, one of the
above vectors is chosen in order to generate the
control law. The selection is made according to a
performance index which evaluates the quality of
each vector (in the first step the choice may be
arbitrarily). The unique requirements about the
performance index (in a GA context) are that it must
be nonnegative and monotonically increasing with
quality, i.e., the better vector is that which has the
greater performance index. Then, the parameter
estimated vector are modified by applying some
modification rules. The modification rules may
depend on the value of the performance index
associate with each vector. In GA terms, these
modification rules are called, selection, crossover
and mutation. The adaptive counterpart is the
updating rule for the estimation algorithms such as
the least squares one or any of its variants for
example. Once the new chromosomes are obtained,
the algorithm evaluates the quality of each new
vector in order to obtain the best one and the process
is repeated so on. Note that the GA representation
allows a broad class of modification rules for the
estimated vectors which may not be driven by a
classical parameter updating equation. Furthermore,
the number of different models (the number of
chromosomes) may not be constant during the
system operation. This suggests the following
interesting idea for multimodel based controllers. If
the system detects that with a reduced number of
models an acceptable system behaviour is achieved,
then it may suppress some of the models
(chromosomes) in order to prune unnecessary
computations. Thus, the multiple models are
classified into priority sets in such a way that models
with a similar performance belong to the same set
(according to some performance criteria, for
example, all models with performance index inside a
prescribed range belong to the same set). Thus, the
sets associated to models with the worst
performance may be pawn from the GA process
while those sets containing the most accurate models
may be recompensed by increasing the number of
models inside them. Thus, from a general uniformly
spaced different models, the system is able to obtain
an improved number of models achieving an
acceptable system performance.
5 FUZZY LOGIC APPROACH
In this Section, a fuzzy logic approach is given for
multiestimation based control schemes. As it is
known, fuzzy set theory is a generalization of the
classical set theory (Tilli, 1992). It allows a class of
objects with a continuum grade of membership.
Such a set is characterised by a membership
(characteristic) function which assigns to each object
its grade of membership ranging from one to zero.
The classical set theory operations are extended to
the fuzzy case as well. Inference relations over fuzzy
set objects define the so called fuzzy logic. In the
multiestimation scheme presented in Section 2, an
estimated parameter vector is chosen from a set of
parameter estimated vectors to parameterise the
adaptive controller at each sampling time. However,
instead of choosing a single estimated vector, it is
also possible to define a combined estimated vector:
(1) (2)
1, 2, ,
...
e
N
kkk kk Nkk
θαθ αθ αθ
=+ ++ (8)
where
,
ik
α
≤≤,
1
N≤≤
and
k∀≥ . This linear
combination (8), is convex in the sense that
,
1
e
N
ik
i
α
=
=
∑
,
k∀≥ . In the standard cases (considered
above and in (Ibeas et al, 2003)), only one
coefficient
k
α
is different to zero and equal to
unity. However, it is also possible to let each
coefficient
k
α
take a value between one to zero.
Then, we can interpret each one as a membership
ARTIFICIAL INTELLIGENCE REPRESENTATIONS OF MULTI-MODEL BASED CONTROLLERS
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