Adaptive Stabilization in Probability of Nonholonomic Systems

This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances. The objective is to design the almost global adaptive asymptotical controllers in probability u
0
and u
1
by using discontinuous control. A switching control law u
0
is designed to almost globally asymptotically stabilize the state x
0
at both the singular x
0
(t
0
) = 0 case and the non-singular x
0
(t
0
) ≠ 0 case. Then the state scaling technique is introduced for the discontinuous feedback when dealing with the (x
1
,x
2
,...,x
n
)-subsystem. Based on this, by using backstepping technique the almost global adaptive asymptotical control law u
1
has been presented for (x
1
x
2
,...,x
n
-subsystem for both different u
0
under non-singular case and the singular case.