The Development of Neural Network Based System Identification ...

84 CHAPTER 4 NEURAL NETWORK BASED SYSTEM IDENTIFICATION
parameter vector θ and are defined as:
θ = [W 1 hj W 2 ih b h B i ] (4.3)
Here, the dimension of parameter vector θ is equal to the total number of weight
connections in the network, d. The external inputs to the network are represented as
time regression vector as follows:
ϕ (t) = [X 1 X 2 X 3 · · · X m ] (4.4)
The parameter vector θ is unknown and should be determined through the use of
training algorithms that infer input and output relationship. A set of training data is
normally presented to the training algorithms to obtain a suitable input and output
relationship such that the different between measured output and prediction is below
certain acceptable error threshold given as:
y i (t) − ŷ i (t) ≤ e i (t) (4.5)
4.2.2 Hybrid Multilayer Perceptron
One aspect that we want to address in this work is to investigate whether the hybrid
multi-layered perceptron (HMLP) network is more efficient than the standard Multilayer
Perceptron (MLP) network. In this study, the HMLP architecture consisting of only
one hidden layer is proposed to learn the non-linear relationship of the dynamics model.
The HMLP network is a modified version of the popular Multilayer Perceptron (MLP)
network.
In HMLP network architecture, the network contains extra connections that allow
direct links between input nodes and output nodes of the network. This specific feature
makes the HMLP different from MLP, because in the standard MLP structure, no
connections are allowed to jump across hidden layers. The proposed HMLP network
with one hidden layer is illustrated in Figure 4.5. Note that the HMLP possesses the
same weight connections to hidden layer and output layer as in MLP except with some