Page 261 - Autonomous Mobile Robots

Adaptive Neural-Fuzzy Control of Mobile Robots 247

are chosen by

˙
ˆ
ˆ
ˆ
ˆ
W Mi =− Mi • ({S Mi }−{S Mci }−{S Mσi })˙νσ i (6.53)
˙
ˆ
ˆ
ˆ
ˆ
W Ci =− Ci • ({S Ci }−{S Cci }−{S Cσi })νσ i (6.54)
˙ ˆ ˆ ˆ ˆ
W Gi =− Gi (S Gi − S Gci − S Gσi )σ i (6.55)
˙
ˆ
C Mi =− Mi •{SW Mci }˙νσ i (6.56)

˙
ˆ
C Ci =− Ci •{SW Cci }νσ i (6.57)

˙ ˆ
C Gi =− Gi SW Gci σ i (6.58)

˙
ˆ Mi =− Mi •{SW Mσi }˙νσ i (6.59)

˙
ˆ Ci =− Ci •{SW Cσi }νσ i (6.60)

˙
ˆ Gi =− Gi SW Gσi σ i (6.61)

n n
˙
ˆ
b m = γ bm ¯ φ m ij |σ i ˙ν j | (6.62)
i=1 j=1
n n
˙
ˆ
b c = γ bc ¯ φ c ij |σ i ν j | (6.63)
i=1 j=1

n
˙
ˆ b g = γ bg ¯ φ g i |σ i | (6.64)
i=1
where matrices Mi , Ci , Gi , Mi , Ci , Gi , Mi , Ci , Gi are symmetric
positive definite, and constants γ bm , γ bc , γ bg > 0, the signals e z and ˙e z asymp-
totically converge to zero, and all the other closed loop signals are semiglobally
uniformly ultimately bounded.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c006” — 2006/3/31 — 16:42 — page 247 — #19