identif_td2.py

Created on September 30, 2025
730 Bytes
///Exo 1:

Y(t) = a*u(k-1)
+b*u(k-2)+c*u(k-3)

//Vecteur parametre :
  
Theta^T = (a, b, c)

//Vecteur observation :
  
Phi^T = (u(k-1), u(k-2),
u(k-3))

//Matrice M :
!Attention pas u(0)!

    /u(4-1) u(4-2) u(4-3)\
M = |u(5-1) u(5-2) u(5-3)|
    \u(n-1) u(n-2) u(n-3)/

//Matrice M^T :
  
    /u(4-1) u(5-1) u(n-1)\
M = |u(4-2) u(5-2) u(n-2)|
    \u(4-3) u(5-3) u(n-3)/
    
//Matrice M^T*M :

Sum(k=4;N;...)

S11 =Sum u^2 (k^-1)
S12 =Sum u(k^-1)u(k^-2)
S13 =Sum u(k^-1)u(k^-3)
S21 =Sum u(k^-2)u(k^-1)
S22 =Sum u^2 (k^-2)
S23 =Sum u(k^-2)u(k^-3)
S31 =Sum u(k^-3)u(k^-1)
S32 =Sum u(k^-3)u(k^-2)
S33 =Sum u^2 (k^-3)

//Matrice M^T*Y :

Sum(k=4;N;...)

S11 =Sum u(k-1)y(k)
S21 =Sum u(k-2)y(k)
S31 =Sum u(k-3)y(k)