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Mi
M1 =
Υ xy
˜z + e
e=(i,j)∈E
M2 =
e=(i,j)∈E
M3 =
e=(i,j)∈E
M4 =
e=(i,j)∈E
e=(i,j)∈E
Υ ˜z xy
e
e=(j,i)∈E
˜Se z xy
e ,
(z xy
e ) T ( ˜ Se) T Υ ˜z xy
e ,
Υ ˜z xy
e ,
(z xy
e ) T ( ˜ Se) T Υ xy ˜Se ˜z z e
xy
e +
(Σ xy
ze e=(i,j)∈E
)−1 +
(Σ xy
ze e=(j,i)∈E
)−1 .
fi(ˆp a V (t))
ˆp a V (t) = (ˆxa V (t)T , ˆ θ(t) a
V )T
f1 =
Υ xy ˜Se ˜z z e
xy
e ˆ θ a j (t),
f2 =
e=(i,j)∈E
Υ ˜z xy
e ˆxa j (t) +
e=(j,i)∈E
(z xy
e ) T ( ˜ Se) T Υ ˜z xy
e ˆxa j (t) −
mi
m1 = −
e=(i,j)∈E
m2 = −
−
e=(i,j)∈E
e=(i,j)∈E
Υ xy
˜z e ˜zxy e +
e=(j,i)∈E
Υ ˜z xy
e ˆxa j (t) +
e=(i,j)∈E
Υ xy
˜z e ˜zxy e +
(z xy
e ) T ( ˜ Se) T Υ xy
˜z e ˜zxy e +
(Σ z θ e ) −1˜ θ a j −
e=(j,i)∈E
e=(i,j)∈E
e=(j,i)∈E
(Σ z xy
e )−1ˆ θ a j (t) −
e=(i,j)∈E
(Σ z θ e ) −1˜ θ a j +
Υ ˜z xy
e
e=(j,i)∈E
˜Sez xy
e ˜ θ a i −
(z xy
e ) T ( ˜ Se) T Υ xy ˜Sez ˜z e
xy
e ˜ θ a i
e=(i,j)∈E
(Σ z θ e ) −1˜ θ a i +
(Σ z xy
e )−1ˆ θ a j (t).
e=(j,i)∈E
e=(j,i)∈E
Υ ˜z xy
e
(Σ z θ e ) −1˜ θ a i .
˜Sez xy
e ˜ θ a j ,
ˆpi(t) i ∈ V
ˆp a i = [(ˆx a i ) T ˆ θ a i ] T G
i = a ˆp a i (t) = 0
Va ˆp a i
i ∈ Va Υˆp a
Va ˆp a Va Υˆp a Va = (Σˆp a Va)−1
Υˆp a = Va
L −A a Υ˜zxyJ
−J T Υ˜zxy(A a ⊗ I2) T A a Σ −1
zθ (Aa ) T + J T Υ˜zxyJ
,
L Υ˜zxy BΣ −1
w
BΣ −1
a (A ⊗ I2)Υ˜zxy
w =
−J T Y˜zxy
−(A a ⊗ I2)Υ˜zxyJ
A a Υ −1
zθ (Aa ⊗ I2) T + J T Υ˜zxyJ
.