# Nonlinear system identification

Here the non-linear system identification using MEE cost function is examined and compared with that using the MSE cost function. The main difference between the non-linear systems using MEE and MSE cost functions is the back propagation of the error through the output layer to the hidden layers of the neural network, details of which are given later. It is observed that the MEE cost function performs better than the MSE cost function in tracing the desired response and hence, identifying the system parameters more accurately.

## Topology of the System

In the non-linear system identification the output obtained from the unknown system when presented with a predefined input signal is considered as the desired response and try to identify the structure of this unknown system using another system with predefined parameters with the same input signal. The schematic of the model for non-linear system identification is as shown in figure .1. As can be seen in the figure the input signal is given to the "unknown system" and the system to be adapted. The output from the adapting system and the desired response from the unknown system are compared to obtain the error which then passes into the cost function to obtain the rule for adaptation.

## Error Back Propagation

As back propagation sing MSE cost function is well known, it is not explained here and can be referred at [1].

## References

[1] Mohamad H. Hassoun,"Fundamentals of Artificial Neural Netowrks",1995.