Adaptive robust control of nonholonomic systems with stochastic disturbances. (English) Zbl 1117.93027
Summary: 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 \(u_1\) for the systems by using discontinuous control. A switching control law \(u_0\) is designed to almost globally asymptotically stabilize the state \(x_0\) in both the singular \(x_0(t_0)=0\) case and the non-singular \(x_0(t_0)\neq0\) case. Then the state scaling technique is introduced for the discontinuous feedback into the \((x_1,x_2,\dots,x_n)\)-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law \(u_1\) has been presented for \((x_1,x_2,\dots,x_n)\)-subsystem for both different \(u_0\) in non-singular \(x_0(t_0)\neq0\) case and the singular case \(x_0(t_0)=0\). The control algorithm validity is proved by simulation.
MSC:
| 93B35 | Sensitivity (robustness) |
| 93C42 | Fuzzy control/observation systems |
| 93E03 | Stochastic systems in control theory (general) |
| 93E15 | Stochastic stability in control theory |
Keywords:
nonholonomic systems; stochastic disturbances; almost global adaptive asymptotical control; switching control; discontinuous state feedbackReferences:
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