d$.$ Consider a dynamic system $y(k+1)=f(y(k),y(k-1),u(k-1)),$ where the function $f$ is

unknown. Suppose we wish to approximate $f$ by a neural network trained by using a

sequence of N input$-$output data samples measured on the unknown system,

$\{(u(k),y(k))|k=0,1,$dots,$N\}$

Choose a neural network architecture, draw a scheme of network and define its inputs

and outputs.

What are the parameters that must be trained $($optimized$)$ such that the network fits the

data well? Define a cost function for the training and the training method. $(2$ Marks$)$