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signal. In this work, a weighted sum of two components are utilized: control signal
error and its first derivation. Equation 7 shows the proposed formula to generate
stress in this phase.
=
+
st ress
imit
w
1
e
u
w
2
e
u
(7)
5.2
Optimization Phase
In optimization phases, we use particle swarm optimization to improve stress gen-
eration after imitation phase, in this step the stress signal is obtained by equation 8,
and the goal is to find proper weights (
w
1
to
w
6
).
st ress
opt
=
w
1
e
a
+
w
2
e
a
+
w
3
e
p
+
w
4
e
p
+
w
5
s
cf
+
w
6
s
cf
(8)
in above equation
e
a
and
e
a
are angle error and its first derivation,
e
p
and
e
p
are
position error and its first derivation and
s
cf
and
s
cf
are control force signal and its
first derivation.
In previous sections we mentioned that there are 2 phase for optimization. In
first phase of optimization we run 10 BELBICs which have been learned by a basic
controller in parallel as our particles and one basic controller as the best candidate
for proper controller. After each iteration of optimization (including one sinusoidal
period with disturbance), controller will be evaluated by their error reduction and
if there is a better solution than basic controller, we will consider it as the best
candidate; else the next iteration will be done. After some iteration if we find a new
candidate as the best solution we will switch to second phase of optimization. In this
phase only 10 BELBICs run in parallel as desired particles and the stress generated
by the best particle will be improved gradually.
5.2.1
Particle Swarm Optimization
Particle Swarm Optimization (PSO) is a technique used to explore the search space
of a given problem to find the settings or parameters required to maximize a par-
ticular objective. This technique, first described by James Kennedy and Russell C.
Eberhart in 1995 [13], originates from two separate concepts: the idea of swarm in-
telligence based on the observation of swarming habits by certain kinds of animals
(such as birds and fishes) and the field of evolutionary computation. The PSO algo-
rithm consists of just three steps, which are repeated until some stopping condition
is met [2]: First, evaluation of the fitness of each particle, second, updating individ-
ual and global best fitnesses and positions and third, update velocity and position of
each particle. [3]
The first two steps are fairly trivial. Fitness evaluation is conducted by supplying
the candidate solution to the objective function. Individual and global best fitnesses
and positions are updated by comparing the newly evaluated fitnesses against the
previous individual and global best fitnesses, and replacing the best fitnesses and
positions as necessary. The velocity and position update step is responsible for the
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