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 U₀ and U₁ by using discontinuous control. A switching control law U₀ is designed to almost globally asymptotically stabilize the state X₀ at both the singular X ₀ (t₀) = 0 case and the non-singular X₀(t₀) ne0 case. Then the state scaling technique is introduced for the discontinuous feedback when dealing with the (x₁,X₂,...,X_n)-subsystem. Based on this, by using backstepping technique the almost global adaptive asymptotical control law U₁ has been presented for (x₁ ,X₂,...,X_n)-subsystem for both different U ₀ under non-singular case and the singular case